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1 


l^-.i-  ^■M^  vf^i      j 


ELLEN 


,  ,     )  OR 


BY  JOSEPH   BATTELL 


"  Gooi/  sense,  7vhich  only  is  the  Gift  of  Heaven, 
And,  though  no  science,  fairly  worth  the  seven." 


SECOND  EDITION,  REVISED  AND  ENLARGED 
IN  TWO  VOLUMES. 


VOLUME   II. 


AMERICAN   PUBLISHING   COMPANY' 

MIDDLEBURY,   VERMONT 

ARTHUR   F.   BIRD 

22  BEDFORD   STREET,   STRAND 

LONDON 

1908 


,^*   tfWOX  M«>^ 


Copyright,  1901,  by  Joseph  BattelL 
Copyright,  1908,  by  Joseph  Battell. 


Entered  at  Stationers*  Hall. 


TO  THE 

PEOPLE    OF   AMERICA 

THIS  BOOK  IS  DEDICATED 

BY  THE 

AUTHOR 


N 

CO 

00 


PREFACE, 


IN  presenting  to  the  public  Volume  II.  of  "Ellen,  or  Whisper- 
ings of  an  Old  Pine,"  the  author  would  say  that  while  there 
have  been  quite  a  number  of  favorable  notices  of  Volume  I. 
and  suggestions  that  its  reasoning  is  correct,  no  attempt  has 
been  made  anywhere  to  answer  its  criticisms  of  modern 
science,  although  the  Rutland  Herald,  one  of  the  largest  and 
ablest  of  Vermont  daily  papers,  says  editorially  that  "  *Ellen ' 
is  a  series  of  Platonic  dialogues  designed  to  make  an  all-around 
attack  upon  science  as  it  is  taught  in  the  schools.  Before  its 
quick-firing  batteries  evolution,  the  undulatory  theories  of 
matter,  certain  propositions  in  algebra  and  geometry,  the  nature 
of  the  soul,  and  other  philosophic  and  scientific  tenets,  long 
considered  secure,  are  razed  to  the  ground.'*  And  adds: 
**  As  two  more  volumes  are  promised,  we  will  not  here  record 
our  impression  of  the  Battellian  theory  of  creation;  but  we 
will  say  that  in  just  this  way  the  thoughts  of  man  have  been 
turned  from  the  ruts  of  error  into  truth." 

And  yet  there  was  no  intention,  much  less  desire,  in  writing 
"Ellen,"  to  attack  anything  or  anybody. 

After  finding  that  modern  science,  in  certain  things,  certainly, 


VIU  PREFACE 

was  badly  in  error,  an  earnest  attempt  was  made,  on  common 
sense  lines,  to  arrive  at  the  truth  of  the  difficult  subjects  con- 
sidered. 

It  at  once  became  evident  that  the  Universality  of  Natural 
Law,  upon  which  all  science  rests,  was  the  key  with  which  to 
unlock  the  secrets  of  nature.  For  whilst  we  can  have  only 
opinions,  which,  as  Socrates  said,  ''are  bad,  all,"  of  how  things 
are  accomplished  which  are  beyond  our  perceptions,  we  know 
how  we  do  them,  or  how  they  are  done  by  any  order  of  mind 
whose  methods  come  within  our  observation. 

But  we  find  that  all  things  made  by  man, — who  has  a  large 
amount  of  constructive  ability, — are  made  from  matter,  to 
conform  to  a  model  in  mind.  That  is,  every  material  thing  is 
a  copy,  the  thing  it  is  copied  from  being  a  spiritual  or  mental 
production ;  and  therefore  the  whole  conqsption  of  evolution 
by  material  forces  is  a  palpable  humbug. 

Again,  we  find  that  man  in  creating  things  works  by  special 
creation.  That  is,  if  he  wants  a  piano  he  does  not  make  a 
violin,  or  any  other  material  thing,  which  will  evolute  into  a 
piano,  but  directly,  through  the  operations  of  mind,  he  makes 
a  piano;  and  this  method  is  universal  with  him,  and  with  any 
other  order  of  mind  with  which  we  have  acquaintance.  And 
thus  again  material  evolution  is  proven  to  be  a  humbug. 

The  evolution  takes  place,  in  the  line  of  improvement  and 
variety,  but  it  is  accomplished  by  mind  not  matter.  Thus 
an  ordinary  railroad  car  evolutes,  in  the  mind,  to  a  palace 
car,  and  afterwards  by  the  direction  of  mind  the  material  for 
this  palace  car  is  gathered  and  the  car  built ;  but  the  ordinary 
railroad  car  from  which  it  was  designed  is  still  running,  not  a 


PREFACE  IX 

single  particle  of  its  material  entering  into  the  improved  car. 
Similarly  in  nature  are  made  the  different  varieties  and  species 
of  things. 

** Ellen'*  also  demonstrates  that  the  body  is  a  machine;  not 
only  the  material  part  of  the  body  which  we  see,  and  which 
remains  a  limited  time  after  death ;  but  as  well  that  which  we 
call  the  life  of  the  body,  the  respiration,  circulation  of  the  blood, 
digestion  and  assimilation. 

Then  must  the  intelligence  that  runs  it  be  entirely  inde- 
pendent of  it.  Of  this  there  can  be  no  possible  question.  For 
the  laws  of  nature  are  universal ;  and  when  the  intelligence  which 
operates  any  material  thing  is  found  in  one  case  to  be  entirely  dis- 
tinct from  that  thing,  we  know  that  it  is  so  in  all  cases,  whether 
or  not  our  physical  vision  is  able  to  detect  it.  But  that  they 
are  thus  separate  we  know  to  be  true  in  regard  to  an  engine, 
and  all  machinery  made  by  man,  and  therefore  is  it  true  through- 
out the  universe. 

The  entirely  material  character  of  the  body  may  be  seen,  in 
the  nature  of  its  forces,  and  the  various  devices  used  in  the  dif- 
ferent parts  of  the  machinery,  such  as  joints,  valves,  hinges,  etc., 
which  are  precisely  similar  to  those  used  for  similar  purposes 
by  man ;  also,  in  the  fact  that  we  can  see  the  operations 
which  take  place,  as  completely  as  we  can  those  of  a  clock  or 
factory.  In  either  case  intelligence  must  be  at  hand  to  guide 
the  running,  but  in  either  case  a  certain  part  is  entirely  mechani- 
cal. It  is  further  demonstrated  by  the  fact  that  it  is  impossi- 
ble for  the  will  directly  to  stop  the  beating  of  the  heart,  or 
permanently  the  act  of  breathing. 

For  a  body,  as  for  an  engine,   supplies  of  fuel  are  needed. 


X  PREFACE 

But  all  the  designs  of  intelligence  are  for  the  use  of  intelli- 
gence. There  is  no  other  cause  or  occasion.  And,  too,  every 
design  of  intelligence  must  be  looked  after  and  operated  by 
intelligence. 

And  therefore  it  is  just  as  necessary  that  this  machine  of  the 
body  should  have  an  engineer, — that  is,  intelligence  to  look 
after  and  manage  it, — as  that  an  engine  should.  In  this  case 
there  is  no  difference  in  the  order  of  intelligence  which  oper- 
ates, only  in  one  case  it  is  called  an  engineer  and  in  the  other 
a  soul.  They  are  one  and  the  same  thing.  That  is,  the  soul, 
clothed  with  the  apparel  of  the  body,  which  is  necessary  to  its 
action  in  material  conditions,  becomes  the  engineer. 

This  same  soul  has  to  supply  both  the  machinery  of  the 
body  with  fuel,  and  the  engine  that  it  runs.  It  is  dependent 
upon  the  engine  for  its  ability  to  travel  quickly  or  to  draw 
freight;  and  it  is  dependent  upon  the  body  to  live  among 
and  operate  material  things.  The  two  conditions  are  similar, 
and  the  one  not  in  any  way  more  remarkable  than  the 
other.  Both  take  place  in  accordance  with  the  laws  governing 
the  construction  of  the  universe.  Nor  is  it  possible  to  conceive 
how  a  universe,  or  any  part  of  it,  could  exist  without  design,  or 
laws  to  govern  it,  nor  how  any  better  could  be  made  than  those 
which  operate.  But  they  are  all  of  a  practical  character  and 
of  universal  application. 

It  follows  that  a  soul  must  enter  a  body  in  connection  with, 
or  soon  after  its  organization,  and  this  in  as  distinct  a  manner 
as  an  engineer  enters  an  engine. 

Bodies  are  produced  through  the  processes  of  generation, 
and  are  made  for  the  use  of  the  soul  whilst  living  or  in  material 


PREFACE  XI 

conditions,  as  much  so  as  an  engine  or  any  vehicle  is  for  the 
use  of  man. 

The  soul  dwells  in  a  body,  and  uses  the  facilities  of  the  body 
for  its  convenience.  And  so,  too,  in  connection  with  the  body» 
it  enters  a  house,  a  boat,  a  car,  a  carriage,  a  balloon,  or  indeed 
any  material  thing,  which  it  is  able  to  use  for  its  convenience 
or  pleasure. 

It  would  appear  that  it  uses  bodies  in  material  conditions  as^ 
in  connection  with  the  body,  it  uses  boats  to  travel  upon  the 
water,  and  in  each  case  for  the  same  reason,  because  it  cannot 
live  in  material  conditions,  or  travel  upon  the  water  to  advan- 
tage, or  for  any  long  time,  without  such  aid. 

These  contrivances  of  the  body  are,  then,  but  some  of  the 
innumerable  material  things  which  souls  use  in  the  various  phases 
of  their  existence.  For  souls  are  as  numerous  throughout  the 
universe  as  trees  in  a  forest,  and  as  active  as  fishes  in  a  sea. 
They  unquestionably  constitute  a  very  important  part  of  the  uni- 
verse, acting  under  the  authority  of  a  Supreme  Ruler,  and  in  ac- 
cordance with  laws  made  by  Him.  Like  all  things,  they  are  indi- 
vidual, and  the  nature  of  their  existence  is  occupation  or 
action. 

That  is  what  existence  means.  It  must  mean  something,  and 
it  does  mean  this. 

The  innate  power  of  the  soul  is  also  demonstrated  in  '*  Ellen," 
which  shows  beyond  any  possible  question  that  Locke's 
contention  that  there  is  no  such  thing  as  innate  ideas,  if  in- 
terpreted to  mean  that  there  is  no  such  thing  as  a  soul,  was 
not  correct,  as  it  would  be  as  utterly  impossible  for  concepts 
to  arrange  themselves  into  thought,  as  for  numbers  or  letters 


xn  PREFACE 

upon  a  blackboard  to  do  so,  or  for  a  bottle  of  ink  to  write  a 
novel.  There  must  be  something  back  of  the  concepts  to  do 
this.  This  something  is  the  soul.  And  though  it  would  appear 
to  have  no  ideas  of  material  things,  until  they  are  brought 
within  its  comprehension,  its  power  to  learn  is  innate ;  and  also 
its  power  to  construct  and  use.  Then  must  its  knowledge  be 
innate,  for  it  is  impossible  to  conceive  how  a  soul  can  construct 
or  use  anything  without  innate  knowledge.  But  innate  knowl- 
edge means  knowledge  that  has  existed  perhaps  from  eternity, 
and  perhaps  that  will  exist  to  eternity.  That  is,  the  soul  is  an 
immortal  substance. 

The  soul,  then,  is  an  entity  having  the  power  of  thought  and 
feeling.  All  of  the  conditions  which  lead  up  to  this  demonstra- 
tion are  carefully  explained  in  the  first  volume  of  **  Ellen."  The 
present  volume  is  almost  entirely  occupied  in  the  discussion 
of  the  last  eight  books  of  geometry, — that  of  the  first  book 
appearing  in  Volume  I., — plane  trigonometry  and  the  undu 
latory  theories,  especially  that  of  sound.  This  last  was  con- 
sidered, in  part,  in  Volume  I.  of  the  first  edition  of "  Ellen,*' but 
has  been  carefully  revised,  and  the  action  of  sound  in  telephone 
and  graphophone,  a  very  important  feature,  added.  The  argu- 
ment as  it  now  stands  sweeps  out  forever  these  theories,  and 
we  believe  will  be  accepted  by  all  intelligent  readers.  That  such 
a  theory  ever  took  root  is  most  extraordinary,  as  there  isn't  a 
single  one  of  its  essential  features  that  comes  within  the  scope 
of  possibility. 

The  statement  upon  which  it  starts,  that  sound  is  composed 
of  vibrations,  is  wiihout  any  possible  basis,  as  can  be  proven  by 
five  minutes*  experiment  with  a  tuning  fork.     Sound  exists  first 


PREFACE  xni 

in  the  fork,  or  any  vibrating  body,  before  it  enters  the  air.  It  is 
produced  by  shock — a  blow — and,  as  is  proven  beyond  any 
possible  doubt  in  this  volume  of  "Ellen,"  consists  of  infinitesi- 
mal particles  of  electrical  matter,  which,  like  the  light-footed 
Aurora  that  in  a  moment  may  span  the  whole  arch  of  heaven, 
returning  in  another  to  its  northern  palaces,  have  the  power  of 
movement;  and  although  with  sound  this  movement  is  not 
especially  rapid  it  is  adapted  like  all  of  nature's  works,  to  the  pur- 
poses for  which  it  is  made,  and  rapid  enough,  and  far  extending 
enough,  to  accomplish  these  both  thoroughly  and  agreeably. 

Because  of  its  infinitesimal  character  sound  is  able  to  pervade 
every  part  of  the  atmosphere,  and  thus  to  enter  all  ears ;  and 
also  because  of  this,  different  sounds  can  pass  each  other,  con- 
tinually and  without  serious  difficulty,  as  people  can,  or  flies. 
There  is  no  other  way  for  things  to  pass,  no  other  possible 
way.  Motions  under  certain  conditions  will  go  from  one  body 
to  another,  when  these  bodies  touch,  and,  being  forces,  carry 
the  bodies  in  which  they  remain.  And  motions  only  pass, 
when  two  bodies  meet,  because  there's  room  for  them  to. 
The  example  of  a  supposedly  different  method — that  of  water 
waves,— is  a  delusion,  as  is  fully  explained  in  this  volume,  and 
as  should  have  been  perfectly  known  and  explained  by  all 
text-books  or  teachers  of  sound.  The  waves  do  what  the  boat 
does  that  rides  upon  them,  go  up  and  then  back,  whilst  with 
each  excursion  a  new  circle  of  waves  is  made  through  the  joint 
action  of  momentum  and  gravity. 

The  statement  that  the  slow  movement  of  a  tuning  fork — not 
over  about  seven  feet  a  second^-or  any  other  similarly  vibrating 
body,  causes  particles  of  air,  or  anything  else,  by  hitting  them, 


XIV  PREFACE 

to  move  1040  feet,  more  or  less,  a  second, — upon  which  the 
undulatory  theory  of  sound  rests, — is  a  monstrous  lie,  as  any 
person  with  any  knowledge  of  the  laws  of  mechanics  knows. 

The  sound,  after  being  formed  in  the  vibrating  body  by  the 
shock,  is  easily  and  certainly  traced  in  its  onward  mission. 
Vibration  moulds  it,  and  throws  it  into  the  air,  whence  it  is 
most  easily  distributed  in  all  directions,  although  it  can  be  car- 
ried in  greater  quantities  and  far  more  quickly  by  a  rod  of  wood 
or  metal,  letting  the  lower  part  of  the  fork  touch  one  end  of 
the  rod,  the  other  end  being  held  in  the  teeth  or  placed  against 
the  bones  of  the  chest  or  head. 

Indeed,  it  was  the  perception  of  the  inconsistency  and  absurd- 
ity of  these  undulator>'  theories  more  than  any  other  one  thing, 
which  first  influenced  us  to  criticize  modern  science.  It  was 
too  plain  a  case  to  be  ignored.  The  absurd  statements  in  the 
text-books  in  regard  to  the  nature  of  matter  and  motion  were 
equally  prominent,  and  soon  it  was  evident  that  the  scientists 
had  made  a  bad  mess  of  it  generally,  one  error  leading  of  neces- 
sity to  others,  until  the  whole  structure  of  modern  science  is 
perforated  with  them. 

Part  II.  of  this  volume,  which  treats  of  the  undulatory  theories, 
was  written  in  part  before  the  discovery  of  radium,  by  which  now, 
as  also  by  X  and  Cathode  rays,  Newton's  corpuscular  theory  of 
light  is  demonstrated  experimentally  to  be  correct,  and  all  undu- 
latory theories  erroneous. 

For  any  suggestion  that  nature  has  two  methods  of  produc- 
ing light  cannot  for  a  moment  be  entertained ;  nor  could  it 
possibly  be  suggested  by  any  one  who,  as  Newton  expresses  it, 
has  in  philosophical  matters  a  competent  faculty  of  thinking. 


PREFACE  XV 

In  the  Appendix  of  this  volume  and  Preface  of  Volume  I., 
second  and  third  editions,  will  be  found  references  to  several 
articles  from  very  prominent  physicists,  admitting  a  change  of 
opinion  in  regard  to  these  theories ;  and  indeed  we  know  of  no 
eminent  physicist,  and  doubt  whether  there  is  any,  eminent  or 
not  eminent,  certainly  no  intelligent  one,  who  would  now  under- 
take openly  to  sustain  them. 

And  yet  the  anomalous  condition  exists,  so  far  as  we  know 
both  in  this  country  and  Europe,  that  they  are  still  taught  in 
every  college  and  scientific  school.  Whether  in  teaching  them 
the  scholars  are  told  additionally  that  they  are  utterly  erroneous 
we  do  not  know,  but  doubtless  most  of  them  have  found  out 
that  they  are  so. 

The  new  lines  of  demonstration  chosen,  in  geometry,  which 
appear  for  the  first  time  in  this  volume,  practically  revolutionize 
the  seience,  making  it  much  simpler  and  plainer. 

The  object  of  a  book  like  '* Ellen"  is  the  finding  of  Truth, 
the  nature  of  this  endeavor  being  double,  to  correct  what  is 
erroneous,  and  to  discover  new  truth.  Certainly  in  the  first  the 
book  has  been  very  successful.  Starting  out  single  handed 
and  looking  upon  the  subject  simply  from  a  common  sense  stand- 
point, it  demonstrated  the  absurdity  and  impossibility  of  a 
large  part  of  the  physics  as  taught  in  all  text-books.  It  also 
demonstrated  the  impossibility  and  absurdity  of  the  Darwinian 
theory,  or  any  theory  of  material  evolution.  It  also  detected 
many  errors  in  other  branches  of  philosophy  and  science, 
and  exposed  some  very  blundering  and  entirely  erroneous 
statements  in  mathematics,  all  of  which  errors  have  been  hitherto 
accepted  in  all  modern  text-books,  and  some  for  hundreds  of 


XVI  PREFACE 

years.  No  answer  has  been  made  to  any  of  these  criticisms, 
as  indeed  none  is  possible,  but  the  more  distinguished  scientists 
of  the  world  have  already  accepted  the  more  important  posi- 
tions taken  in  **  Ellen,"  which  took  the  lead,  and  whose  ideas  were 
widely  advertised  in  the  newspapers  and  in  the  circulation  of  the 
books  when  the  first  edition  was  published,  in  1901.  And  this 
means  that  a  large  part  of  the  science  of  the  world,  as  taught 
in  the  text-books  and  sustained  in  encyclopaedias,  is  being 
slowly  but  surely  revolutionized. 

In  this  department  alone  the  necessity  of  such  a  book  as 
"Ellen"  has  been  fully  vindicated.  In  the  second  field,  that 
of  independent  discovery,  ** Ellen"  has  been,  perhaps,  equally 
successful,  and  the  numerous  discoveries  made  in  the  nature 
of  existence,  and  the  order  of  the  universe,  promise  to  lead  to 
others  even  more  important. 

It  is  not  true  that  such  a  book  is  or  can  be  dry  or  uninterest- 
ing. Many  of  the  truths  which  it  seeks  are  the  most  import- 
ant and  intensely  interesting  of  all ;  for  they  have  to  do  not  only 
with  the  affairs  of  this  life,  but  with  its  destiny,  the  life  which 
we  believe  to  be  succeeding  this,  as  surely  as  day  succeeds 
the  night,  or  night,  day. 

For  some  years  a  wave  of  materialism  has  swept  over  the 
world,  permeating  all  society  with  its  baneful  influence.  And 
this,  although  nothing  can  be  more  certain  than  that  the  soul 
is  a  substance,  entirely  distinct  from  the  body,  and  must  con-« 
tinue  to  exist  with  all  its  original  powers,  when,  the  life  of  the 
body  being  spent,  it  is  no  longer  habitable  for  a  soul. 

And  from  the  opposite,  death,  is  the  beginning  of  a  new  life — 
the  dawn  of  another  day.     For  the  day  comes  from  the  night 


PREFACE  xvn 

and  the  night  from  the  day.  They  follow  each  other  in  succes- 
sion, nor  is  it  possible  that  they  would  do  otherwise,  the  great 
system  of  order,  in  which  or  by  which  the  universe  is  con- 
structed, forbidding  it. 

And  so  life  comes  from  death  and  death  from  life ;  accord- 
ing to  the  great  law  of  opposites,  universal  in  nature. 

And  that  which  follows  is  controlled  by  another  of  nature's 
universal  laws,  that  of  cause  and  effect.  As  Paul  expressed  it, 
**  Be  not  deceived,  God  is  not  mocked.  For  whatsoever  a  man 
soweth,  that  shall  he  also  reap." 

All  of  this  is  plain  common  sense;  the  fundamental  truths 
of  existence ;  the  fundamental  truths  of  religion ;  the  funda- 
mental truths  of  the  Bible. 

The  next  thing  that  the  mind  seeks  is  under  what  laws  does 
existence  continue.  Is  the  spiritual  always  connected  with  the 
material — mind  with  matter,  or  any  other  substance,  acting  as 
a  body?  The  only  suggestion  from  analogy  is  that  the  soul 
when  it  leaves  the  body  enters  another  body.  Paul  speaks 
of  a  spiritual  body.  Can  the  laws  under  which  continued  exist- 
ence takes  place  be  discovered  by  the  mind  of  man?  We 
believe  that  they  may;  that  the  spiritual  part  of  man,  the 
mind's  eye,  will  fathom  this  mystery,  so  that  the  whole  nature 
of  that  existence,  of  which  we  are  a  part,  may  become  under- 
stood. But  this  will  depend  upon  the  highest  possible  motive — 
what  is  best. 

There  is  indeed  in  "Ellen"  but  one  more  step  to  be  reached, 
the  first  one  being  the  peception  that  the  soul  is  distinct  from  the 
body,  and  continues  its  existence.  Christ's  remark,  "Seek 
and  ye  shall  find,"  always  true,  points  the  way.     And  we  know 


XViil  PREFACE 

not  why  these  laws  will  not  become  manifest,  as  others  have  in 
**  Ellen*'  that  seemed  equally  hidden;  as  the  law  of  memory, 
the  law  of  dreams,  the  nature  of  the  connection  of  the  soul 
with  the  body,  the  material  character  of  truth,  justice  and  all 
abstract  qualities,  the  operation  of  light  in  vision,  the  nature  of 
sound,  the  nature  of  matter,  the  nature  of  motion,  and  other 
most  important  truths,  discovered  first  in  *' Ellen,"  or  redis- 
covered, and  presented  so  as  to  be  accepted,  the  arguments 
sustaining  them  being  too  strong  to  be  overthrown. 

This  book  is  dedicated  to  the  American  people  because  the 
great  body  of  the  people  is  the  ultimate  authority  for  the 
decision  of  all  questions  which  are  world-wide  in  their  scope. 

Their  attention  may  not  ordinarily  be  called  to  questions 
looked  upon  as  purely  scientific,  but  when  it  is  they  are  not 
hampered  by**  knowing  so  many  things  that  are  not  so,"  as 
Artemus  Ward  said  of  the  scientists,  but  will  judge  all  ques- 
tions upon  their  merits,  and  do  it  correctly. 

For  further  criticisms  and  reviews  of  ** Ellen"  see  Appendix. 

JOSEPH  BATTELL. 
Bread  Loaf  Inn,  Ripton,  Vt., 
October  i,  1907. 


ILLUSTRATIONS. 


PART  1 


FRON-nSPIECE 

Bread  Loaf  Mountain,  Ellen's  Mountain  in  Distance, 
Bridge  Bi-h-n^'een  North  and  Solth  Hero,  Vt., 
WiNn«:R  from  Fj-len's  Mountain,  No.  i.. 
On  the  Green  Mountains  near  Hancock  Pass, 
Altitude  2200  feet. 

The  Oak, 

Highway  near  Starksboro,  Vt.,     . 

Adirondacks  and  Lake  Champlaix,  No.  i., 

Grand  Isle  CoL7n*\',  Vermont, 

Green  Mouniains  from  Middlebury,  Vt., 

Bread  Loaf  Park  No.  i.,       . 

Bread  Ix)af  Cottages,    .... 

View  in  Warren,  No.  i.. 

Near  Bread  Loaf,  No.  i.,     . 

Ellen's  Mountain  near  the  Summit,  No.  i 

Vermoni'  Scene,      .        .        .        .        , 

"I  wandered  by  the  Brook-side,"  , 

The  Linden,  Warren  Woods, 

Near  Bread  Loaf  Inn, 

WiNiTR  on  Ellen's  Mountain,  No.  2., 


I 
24 

36 
47 
53 
61 

72 
78 
84 
94 
105 
118 

132 

139 
148 

i5« 
166 

173 


XX 


ILLUSTRATIONS 


PART    II. 

Ellen, 2 

Summer, 12 

Winter  Scene  in  Vermont,     .        .                 ....  25 

Mountain  Stream, 37 

Northwest  from  Ellen's  Mountain, 51 

Southwest  from  Ellen's  Mountain, 61 

Southeast  from  Ellen's  Mountain, 74 

Northeast  from  Ellen's  Mountain, 86 

Near  Bread  Loaf,  No.  2, 96 

Among  the  Brakes, 109 

Ellen's  Mountain  from  the  East, 121 

Adirondacks  and  Lake  Champlain,  No.  2,     .        .        .         .  133 

By  the  Old  S'ix>ne  Wall,  Warren, 144 

Bread  Ix)af  Park,  No.  2, 157 

View  in  Warren,  No.   2, 168 

West  from  Ellen's  Mountain, 182 

Autumn, 193 

Vermoni   Hills, 206 

Ice-Bound, 217 

A  Pastoral  Scene, 230 

Mountain,  Dale  and  River, 239 

Mount  Ethan  Allen  from  the  East, 253 

Morning, 266 

"  Night's  candles  are  burnt  out,  and  jocund  day 
Stands  tiptoe  on  the  misty  mountain  tops." 

May  Among  the  Mountains,  . 

Evening, 

Winter  from  Ellen's  Mountain,  No.  3 

The  Mountains  in  Winter,     . 

A  Winter  Scene  from  ihe  Mountains, 


277 

289 

303 

3U 
326 


ILLUSTRATIONS  xxi 

Upon  the  Rocks,  Ellen's  Mountain  No.  2,          ...  335 

Mountain  Valley, 349 

Ellen's  Mountain,  near  the  Summit,  No.  2.,        .        .        .362 

A  Vermont  Meadow, 373 

"  Far  from  the  madding  throng's  ignoble  strife." 

Contemplation, 383 

Maple  Grove,  Warren, 397 

A  Mountain  River, 411 

Winter, 423 

Edith, 435 

Lake  Champlain,  Grand  Isle  County, 451 

Near  Runaway  Falls,    ....                 ...  461 

Bread  Loaf  Mountain,  Ellen's  Mountain  in  Distance,        .  473 

WiNOOSKi  River, 481 

Elm  Tree, 495 

Rochester,  Vt., 514 

Green  Mountains,  Addison  Couniy,  Vt.,  No.  i.,           .         .  531 

View  From  the  Sileni'  Cliff, 544 

Four-in-hand, 559 

Eastern  Vermont, 565 

The  Hickory, 574 

White  River,  Rochester,  Vt., 587 

Green  Mountains,  Addison  County,  Vr.,  No.  2.,           .         .  600 

Brf^d  Ia^af  Park,  No.  3, 612 

On  the  Green  Mountains,  Fern  Lake,         .         .         .         .627 

Middleijury,  Vt., 642 

Gathering  Applf^^, 655 

Lake  Champi.ain, 667 

The  Three  Sisters, 676 

"She  Walks  in  Beauty  like  the  Nkiht,"      ....  690 

FiNispiECE, 707 


CONTENTS. 

PART  I. 


CHAPTER  I. 


Introduction.  Review  of  geometry  continued.  Euclid's  method  of  giving  defini- 
tions. Book  II.  The  Circle  and  the  Measurement  of  Angles.  Definitions. 
Discussion  of  circles.  Limits  and  variables.  Not  correct  to  speak  of  that  as 
limited  which  has  no  limit  nor  lo  call  that  a  limit  which  can  never  be  reached. 
(>ther  inaccuracies  of  modern  geometries  criticised i 

CHAPTER  n. 

Review  of  geometry  continued.  Book  III.  Similar  polygons.  Euclid  referred 
to.  Criticism  of  the  manner  in  which  ratio  or  proportion  is  treated  in  modern 
geometries,  and  the  same  compared  with  its  demonstration  in  Euclid.  Dcmon- 
stratioas  of  this  subject  in  Volume  I.  of  Ellen  referred  to.  Definitions.  Dis- 
cussion of  triangles,  and  analysis  of  the  relative  length  of  their  sides.  Quanti- 
ties varying  between  limits  include  all  intermediate  values.  Projection.  Euclid's 
demonstration  of  the  square  of  the  sum  and  difference  of  two  quantities 24 

CHAPTER  III. 

Review  of  geometry  continued.  Book  IV.  Areas  of  Polygons.  Equal  and 
equivalent  figures.  Definitions.  Areas  of  triangles,  parallelograms  and  trape- 
zoids    47 

CHAPTER  IV. 

Review  of  geometry  continued.  Book  V.  Regular  Polygons  and  Circles. 
Definitions.  A  circle  composed  of  a  series  of  contiguous  circumferences  de- 
creasing uniformly  in  length.  The  infinitely  small  as  remarkable  and  real  as 
the  infinitely  large.    The  ratio  of  a  circumference  to  its  diameter 53 


XXIV  CONTENTS 

CHAPTER  V. 

Review  of  geometry  continued.  Book  VI.  Planes,  Diedral  and  Polyedral  Angles. 
Definitions 6i 

CHAPTER  VI. 

Review  of  geometry  continued.  Book  VII.  Polyedrons.  Definitions.  Volume 
equals  product  of  average  dimensions 72 

CHAPTER  VII. 

Review  of  geometry  continued.  Book  VIII.  Cylinder,  Cone  and  Sphere. 
Definitions.  Lune,  spherical  angles,  triangles  and  polygons.  Discussion 
of  spherical  angles  pointing  out  that  they  are  equal  to  plane  angles,  not  because 
their  lines  have  the  same  direction  but  because  their  difference  of  direction  is 
the  same 84 

CHAPTER  VIII. 

Review  of  geometry  concluded.  Book  IX.  Measurement  of  Cylinder,  Cone  and 
Sphere.  A  cylinder  may  be  supposed  to  consist  of  a  series  of  contiguous  sur- 
faces similar  to  the  convex  surface,  and  extending  from  that  to  the  axis  of  the 
cylinder,  each  one  uniformly  shorter  than  the  one  preceding.  English  used  in 
statement  of  propositions  criticised.  Discussion  of  the  cone.  Euclid's  demon- 
stration  that  a  cone  is  a  third  part  of  a  cylinder  having  the  same  base  and  alti- 
tude. Every  body  however  small  has  three  dimensions.  Points,  lines  and 
superficies  a  basis  of  measurement.  The  surface  of  a  sphere  equals  four  great 
circles,  because  the  amount  of  material  necessary  to  cover  any  surface  will  be 
the  same  whether  used  upon  a  plane  surface,  or  many  plane  surfaces,  whose 
aggregate  equals  this  plane  surface.  Theory  of  limits  considered.  The  surface 
of  a  circle  equal  to  its  mean  or  average  circumference  by  its  radius,  and  there- 
fore the  surface  of  a  sphere  would  be  equal  to  four  times  this  or  the  circum- 
ference by  the  diameter.  Volume  of  a  sphere  may  be  expressed  in  terms  of  its 
surface  used  as  a  standard  of  measure,  and  is  e(]ual  to  this  surface  multiplied 
by  one  third  the  radius.  Average  surface  of  a  sphere  and  average  base  of  a 
pyramid,  where  situated.     "  On  every  height  there  is  repose." 105 

CHAPTER  IX. 

Description  of  the  late  Autumn^  Plane  Trigonometry.  Trigonometric  functions. 
Their  mutual  interdependence.    Variable  quantities ^    ...  132 


CONTENTS  XXV 

CHAPTER  X. 

Relationship  between  functions.  Their  values  not  altogether  accurate.  Size  rela- 
tive. Value  of  cosines  of  angles  in  the  first  quadrant  with  three  orders  of 
differences.  Cavalieri's  estimate  of  lines,  surfaces  and  solids.  Newton's  con- 
ception of  the  same .* 139 

CHAPTER  XI. 

Solution  of  right-angled  triangles.  Solution  of  oblique-angled  triangles.  Law  of 
tangents.  Relationship  between  two  sides  of  a  triangle  and  their  projections  on 
the  third  side 148 

CHAPTER  XII. 

Trigonometrical  Formulae.  The  methods  of  teaching  largely  responsible  for  the 
failure  of  scholars  to  learn  mathematics  easily.  Remarks  about  teaching.  The 
highest  of  all  motives,  doing  a  thing  because  it's  best.  Expression  for  sine  and 
cosine  of  a  double  arc;  for  sine  and  cosine  of  half  a  given  arc;  for  the  products 
of  sines  and  cosines.  Other  formulae,  and  expressions  for  the  tangents  of 
arcs • 158 

CHAPTER  XIII. 

Learning  mathematical  truths  by  manipulation  of  symbols  not  a  desirable  method. 
All-important  that  the  principles  arc  learned  upon  which  mathematics  rest. 
'ITiis  illustrated  by  demonstration  of  several  formuliv  by  figures  or  values.  Other 
principles  of  mathematics  expounded.  Explanation  of  logarithms.  End  of 
Plane  Trigonometry 173 


CONTENTS. 


PART  II. 


CHAPTER  I. 


June  upon  the  mountains.  The  discussion  of  Undulatory*  Theories.  Statement 
of  Ganot  in  his  '*  Physics'*  that  the  intimate  nature  of  gravitation,  heat,  light, 
magnetism  and  electricity  is  completely  unknown.  Sound  and  Light  governed 
by  similar  laws.  Sound  given  two  distinctly  different  definitions  in  the  old 
theory,  which  illustrates  the  looseness  of  the  theory 3 

CHAPTER  II. 

The  Copemican  system  superseding  the  Ptolemaic.  The  five  senses,  touch,  taste, 
smell,  hearing  and  sight.  Discussion  of  odors  by  Ferdinand  Papillon.  Qose 
connection  between  all  natural  phenomena.  The  experimental  method  erects 
barriers,  which  greatly  hinder  the  completing  of  knowledge.  Olfaction, 
mechanism  of,  quite  simple.  Smell  both  voluntary  and  involuntary.  Sense  of 
smell  sometimes  wanting.  Qose  connection  between  smell  and  taste;  four 
primitive  tastes — sweet,  sour,  salt  and  bitter.  Emanations  from  odorous  bodies 
perceptible  to  sight.  Experiments  made  by  Prevost  1799.  Very  important 
experiments  by  Legeois.  Molecules  emitted  from  odorous  substances  and 
diffused  through  the  atmosphere.  Effect  of  water  upon  fragrance.  Air  the 
vehicle  of  dispersing  odors.  Remarkable  diffusibility  of  certain  odorous  sub- 
stances. Odors  affect  the  olfactory  nerves  as  sounds  the  auditorj-  nerves. 
Odors  made  artificially  identical  with  those  in  nature 13 

CHAPTER  III. 

Odor  considered  as  a  mode  of  motion  by  Thomas  Hobbs  (1588 — 1679)  and 
other  writers.     All  such  writing  unmitigated  nonsense,  but  no  more  so  than 


CONTENTS  XXVii 

similar  remarks  about  sound.    All  undulatory  theories  assume  something  to  be 
got  from  nothing 24 

CHAPTER  IV. 

Sound  produced  by  collision  or  shock.  Music  of  the  spheres  not  necessarily  a 
myth.  Definition  of  vibration.  Motion  caused  by  pressure.  Discussion  of 
Motion.  Motion  and  matter  inseparable.  All  motion  a  part  of  matter  and 
any  matter  in  which  the  principal  of  motion  is  unbalanced  must  move.  Motion 
progressive;  entering  into  a  material  thing  at  rest,  until  of  sufficient  quantity  to 
carry  it  or  cause  it  to  move.  No  end  to  nature's  circulatory  methods.  Long 
quotation  from  Dr.  Guyot.  Inertia  of  matter  an  error.  Force,  moving 
matter.    Action  of  one  body  on  another,  result  of  contact 35 

CHAPTER  V. 

Elasticity.  Quotations  from  Lord  Kelvin,  "  Chambers'  Encyclopaedia  "  and  Ganot. 
Modulus  of  elasticity.  Limit  of  elasticity.  Elasticity  of  traction.  Elasticity  of 
torsion.  Elasticity  of  flexure.  Effect  of  hardening  and  annealing.  Moment 
of  the  force  of  torsion.  Formulae  for  the  ^peed  of  sound.  Quotations  from 
Ganot  and  David  Thompson 50 

CHAPTER  VI. 

Elasticity,  used  indiscriminately  by  scientists  to  denote  a  property,  force  and 
ratio.  Elastic  force,  matter  in  motion.  Sound  made  in  the  same  manner  as  all 
other  material  things,  and  perishes  in  the  same  manner.  Sound  like  other 
things  moves  with  different  speed  over  or  through  different  bodies.  Character 
uf  the  nerves;  made  to  convey  sounds  and  other  causes  of  sensation  to  the  soul. 
The  causes  of  all  sensations  material.  Extracts  from  Buchner's  "  Force  and 
Matter"  on  the  Universality  of  Nature's  Laws.  Composition  of  the  sun  and 
other  heavenly  bodies.  Matter  supposed  to  be  essentially  identical  in  the 
whole  universe.     Identity  of  the  laws  of  mind  throughout  the  universe 67 

CHAPTER  VII. 

The  undulatory  theory  of  sound  impossible.  All  sensations  have  a  material  cause 
even  to  the  most  minute  particular;  thus  the  sensation  of  a  tree  or  a  leaf  is  in 
exact  accordance  with  the  material  thing  by  which  it  is  produced ;  if  a  twig  is 
broken  or  an  indenture  occurs  in  a  leaf,  this  will  be  produced  in  the  sensation, 
and  thus,  too,  it  must  be  with  sound;  hence  any  supposed  cause  of  sound 


XXVlll  CONTENTS 

must  be  capable  to  produce  its  sensation;  that  is,  all  the  marvelous  differences 
of  sound,  which  are  as  many  and  as  manifest  as  any  that  exist  in  any  of  the 
phenomena  of  nature,  must  be  first  formed  materially.  Function  of  the  nerves 
again  referred  to.  Communication  by  symbols  possible,  but  only  in  accordance 
with  pre-conceived  arrangement.  The  scientific  suggestion  of  creating  sensa- 
tions by  the  slight  movement  of  particles  of  matter  in  certain  bodies,  not  in 
conformity  with  nature's  laws 87 

CHAPTER  VIII. 

Speed  of  sound.  Hypotheses  taught  as  known  principles  not  justifiable.  Proposi- 
tions in  the  "  Principia  "  by  Mr.  Newton  relative  to  sound,  in  which  he  under- 
takes to  explain  the  propagation  and  velocity  of  sound,  saying  that  the  pro- 
gressive motion  of  the  pulses  arises  from  the  perpetual  relaxation  of  the  denser 
parts  toward  the  antecedent  rare  intervals.  This  explanation  which  is  the  only 
intelligent  one  ever  made  or  even  attempted,  practically  disproves  the  whole 
theory  of  sound,  as  the  conditions  necessary  to  its  propagation  could  not  gener- 
ally, if  ever,  take  place.  Boyle's  or  Mariotte's  Law;  not  always  correct. 
Boyle's  Law,  known  to  be  true  only  as  far  as  demonstrated  by  experiment. 
Sound  impossible  under  wave  theory 97 

CHAPTER  IX. 

Air  waves  contemplated  in  the  undulatory  theory  of  sound  impossible  by  the  laws 
governing  motion.  Newton's  explanation  of  the  undulatory  theory  of  sound 
again  referred  to;  this  has  been  dropped  out  of  text-books,  because  seen  to 
be  inapplicable,  and  no  other  offered  because  there  is  none  possible.  Quota- 
tion from  the  "New  York  Sun"  concerning  the  use  of  a  megaphone  for 
warning  in  fogs,  which  says,  after  describing  the  experiments,  that  they  com- 
pletely upset  the  pre-conceived  ideas  of  the  peculiarity  of  sound  because  they 
show  it  is  possible  to  confine  a  sound,  even  so  powerful  as  that  from  a  syren, 
and  to  project  it  into  space  in  a  given  direction  with  the  same  certainty  and 
accuracy  that  we  can  project  the  rays  of  a  searchlight.  Propositions  XLIIL, 
XLV.,  XLVL,  XLVIL,  XLVIIL,  on  sound,  from  Newton's  "Principia." 
Mr.  Newton's  theoretical  velocity  of  sound  incorrect.  Quotation  from  "Cham- 
bers' Encyclopaedia  "  regarding  this 112 

CHAPTER  X. 

Newton's  propositions  concerning  sound   founded  upon  hypotheses  which  have 


CONTENTS  XXIX 

nowhere  been  proved.  Disagreement  of  undulatory  theories  with  facts  further 
discussed.  Such  theories  impossible  under  the  kinetic  theory  of  gases.  Quota- 
tions from  Ganot  and  others  concerning  the  kinetic  theory  of  gases.  Newton's 
conception  of  the  wave  theory  of  sound  shown  to  be  impossible  by  Herschel, 
Lagrange  and  other  eminent  physicists.  Those  who  have  accepted  Newton's 
theory  of  sound  consider  his  theory  of  light  to  be  utterly  without  foundation. 
Danger  of  building  upon  hypotheses 145 

CHAPTER  XI. 

All  science  should  rest  upon  knowledge,  not  hypothesis.  Mathematics  in  scien- 
tific discovery  worse  than  useless  without  good  sense  to  use  them.  Review  of 
Mr.  Tyndall's  book  "On  Sound."  A  system  of  waves  could  not  be  gathered  by 
a  megaphone;  this  alone  a  fatal  objection  to  the  airwave  theory  of  sound. 
Mr.  Tyndall's  statements  corrected.  Elxperiments  in  a  vacuum,  in  hydrogen 
and  on  mountains.  Inte  sity  of  sound  depends  on  the  density  of  the  air  in 
which  it  is  generated,  and  not  on  that  in  which  it  is  heard.  Ejcperiment  by 
Mr.  Tyndall  incorrectly  explained.     Sympathetic  vibration 169 

CHAPTER  XH. 

Sound  of  an  electrical  character.  Quotation  from  M.  Oersted.  Other  quotations 
from  eminent  authorities  showing  marked  similarity  between  the  laws  governing 
sound  and  electricity.  Ganot,  Deschanel  and  other  authorities  in  regard  to  the 
timbre  or  quality  of  sound,  admitting  that  the  differences  of  timbre^  or  generally 
of  sensations,  must  be  produced  by,  and  exactly  correspond  to,  the  differences 
of  that  which  causes  the  sensation.  Sound  composed  of  particles  of  matter 
which  can  be  scattered  or  collected.  Their  collection  illustrated  by  a  mega- 
phone or  ear  trumpet,  and  abo  by  the  sail  of  a  ship 183 

CHAFFER  Xni. 

Sound  an  entity.  A  vibrating  body  cannot  make  any  body  move  faster  than  it 
moves  itself.  Further  review  of  Mr.  Tyndall's  book.  Velocity  of  sound. 
Serious  errors  by  scientists.     Mr.  Faraday  upon  radiant  matter 207 

CHAPTER  XIV. 

Transmission  of  sound.  One  medium  exists  in  another.  Neither  sound  or  elec- 
tricity passes  through  a  vacuum.  Intensity  of  sound  diminished  in  rarefied 
air.    Superstitions  of  science 216 


XXX  CONTENTS 

CHAPTER  XV. 

Theories  of  Laplace  and  Poisson  on  propagation  of  sound,  with  criticisms  of  same 
by  Prof  Potter,  Rev.  Samuel  Eamshaw  and  Rev.  James  Challis. 238 

CHAPTER  XVI. 

Article  published  in  the  "  Quarterly  Journal "  by  Henry  Meikle  exposing  the  errors 
and  fatal  defects  of  the  undulatory  theory  of  sound.  Mr.  Meikle,  eminent  as  a 
mathematician,  but  still  more  so  as  a  man.  He  shows  the  undulatory  theory  of 
sound  mathematically  and  physically  impossible.  Similar  criticisms  previously 
made  by  Professor  Leslie 252 

CHAPTER  XVIL 

Further  review  of  Mr  Tyndall's  book,  in  which  he  admits  that  for  every  sonorous 
impression  there  must  be  a  correlative  without — "  that  all  differences  in  sound 
must  be  purely  a  mechanical  condition  of  the  intervening  air.'*  This  impossible 
under  the  undulatory  theory;  and  as  sound  is  in  every  part  of  the  air  as  well  as 
all  the  air,  could  only  be  done  by  infinitesimals.  Length  of  air  waves.  Quota- 
tion from  Professor  Challis  concerning  the  correlative  without 270 

CHAPTER  XVin. 

Experiments  of  sound  in  iron  and  in  air,  with  relative  speed.  If  sounds  are  of 
same  pitch,  rate  of  vibration  is  the  same.  Hydrogen  gas  not  desirable  for 
the  manufacture  of  sound.  Sound  variously  transmitted  by  different  bodies. 
Vibration  decides  the  pitch,  but  does  not  make  sound ;  thus  double  vibration 
changes  the  pitch,  but  does  not  make  more  sound.  Quotation  from  Baron 
Munchausen.  Movement  of  sound.  Sympathetic  vibration  due  to  channels 
in  which  sound  flows.  Sound  not  controlled  by  gravitation.  Statement  in  Mr. 
TyndalPs  book  concerning  resonance  not  correct.  Experiments  in  resonance. 
Interference  of  sound  a  delusion 282 

CHAITER  XIX. 

Experiments  to  test  velocity  of  sound,  from  Ganot  and  other  sources.  Music  of  a 
band  shows  that  musical  sounds  have  same  velocity;  and  as  tested  by  many 
other  experiments,  carefully  tried,  with  same  temperature,  sound  generally  has 
the  same  velocity,  but  is  sometimes  impeded  by  a  strong  wind.  Its  velocity  abo 
uniform 302 


CONTENTS  XXXI 

CHAFl'ER  XX. 

Article  on  waves  from  **  Giambers  Encyclopaedia."  Popular  acceptance  of  undula- 
tory  theories  largely  due  to  comparison  wilh  water  waves.  Quotation  from 
''Circle  of  Sciences";  also  from  Tyndall.  Full  explanation  of  water  waves 
showing  that  Ihey  are  made  by  momentum  and  gravity ;  the  comparison  of  sound 
with  them  a  delusion  or  illusion,  as  the  force  which  make  water  waves  could 
not  possibly  act  in  air,  or  the  body  uf  any  fluid 318 

CHAPTER  XXI. 

Mechanical  effects  of  Electricity.  Quotation  from  Ganot.  Mind  able  to  compre- 
hend all  material  things.  Further  discussion  of  motioiL  Experiments  with 
elastic  balls  showing  motion  to  be  transferable.  Motion  a  result  of  pressure 
and  pressure  a  result  of  contact.  Opposite  motions  destroy  each  other, 
being  changed  into  something  else.  Destruction  of  one  thing  precedes  forma- 
tion of  another.  The  nature  of  water  waves  not  explained  in  text-books 
Photography  of  sound  waves  claimed,  but  shown  to  be  a  photograph  of  the  dis- 
turbance in  particles  of  air  caused  by  an  electric  spark.  Qaim  that  the  speed 
of  all  pulses  in  a  tube  is  the  same,  whatever  the  force  making  them,  and  that 
they  will  be  transmitted  with  uniform  velocity  (upon  which  the  undulatory 
theory  of  sound  was  founded),  proved  to  be  an  error 354 

CHAPTER  XXII. 

Air  in  a  tube  acts  very  differently  from  unconfined  air,  and  hence  the  sdr  wave 
theory  of  sound,  founded  upon  the  action  of  air  in  a  tube,  is  again  shown  to  be 
impossible.  Quotation  from  Jacob  Abbott.  Force  consists  of  matter. 
Thought  and  the  emotions  made  from  matter.  All  things  made  by  mind. 
All  science  folly  which  does  not  recognize  the  distinction  between  mind  and 
matter.  All  science  baseless  which  does  not  recognize  the  universality  of 
nature's  laws.  The  statements  of  Ganot  and  other  scientists  in  regard  to  ac- 
tion of  a  pulse  in  a  tube  shown  to  be  entirely  erroneous.  Mathematical  demon- 
stration that  rarefactions  must  go  faster  than  condensations  if  the  undulatory 
theory  is  true.  Other  very  palpable  errors  in  Ganot*s  statements  of  this  theory. 
Quotation  from  Prof.  Challis  of  Oxford  University,  England,  showing  that 
both  plane  waves  and  spherical  waves  are  physically  impossible.  Analysis  of 
mathematics.  Criticism  of  the  inaccuracy  of  the  Calculus.  Quotations  from 
Prof.   G.  La  Conte,  University  of  South  Carolina,  and  James  Clark  Maxwell, 


XXXll  CONTENTS 

the  very  eminent  Mathematician,  pointing  out  these  inaccuracies,  and  showing 
that  no  deduction  from  mathematical  analysb  is  of  value  which  does  not  admit 
of  a  natural  physical  interpretation  capable  of  being  tested  by  experiment 348 

CHAPTER  XXIIl. 

Very  accurate  experiments  of  action  of  a  pulse  in  a  tube,  by  M.  Regnault  of  Paris, 
show,  first,  that  gases  are  not  perfectly  elastic;  second,  that  the  walls  of  tubes 
exert  a  notable  influence;  third,  a  strong  force  creates  a  movement  of  the  par- 
ticles of  air  which  increases  their  velocity ;  fourth,  the  compression  of  the  sdr 
made  by  means  of  a  cannon  is  very  great,  but  diminishes  rapidly;  "whence  the 
results  of  my  experiments  often  disagree  with  theory.''  Sound  entirely  distinct 
from  a  pulse  of  air 372 

CHAPTER  XXIV. 

Mobility,  the  characteristic  property  of  fluids.  Quotations  from  Herschel  and 
Laplace.  Remarks  about  light.  Abundance  of  room  in  the  universe  for  all  its 
various  things 382 

CHAFl  ER  XXV. 

Action  of  sound  in  telephone  and  graphophone.     Quotation  from  Ganot 391 

CHAPTER  XXVI. 

Quotation  from  article  on  **  Acoustics  "  in  "  Encyclopaedia  Britannica;"  explanation 
of  cause  of  air  waves  in  same  is  criticised,  and  shown  to  be  erroneous.  Inten- 
sity of  sound  depends  upon  density  of  air  where  sound  is  produced;^  but  varies 
inversely  as  the  square  of  the  distance  from  the  source  of  sound.  Sound 
produced  in  water.  Sound  always  made  by  initial  sounding  body  or  bodies, 
except  in  unison  vibration.  Sympathetic  vibration  only  possible  in  bodies 
having  the  same  normal  vibration 401 

CHAITER  XXVll. 

Action  of  sound  in  the  telephone.  Scientific  explanation  that  the  sound  at  the 
receiver  is  caused  by  the  repetition  of  vibrations,  through  the  action  of  the  elec- 
tric current,  shown  to  be  erroneous.  Action  of  electric  current  limited. 
Graphophone  record  not  caused  by  the  action  of  sound  upon  the  diafram  of  the 
recorder,  but  directly  by  sound  itself  making  its  own  impression.  Waves  not 
possible  in  body  of  a  fluid.     If  diafram  of  a  receiver  repeats  sound,  diafram  at 


CONTENTS  XXXIll 

transmitter  must  also.     Progress  of  sound  successive.     Cross-talk  on  telephone 
lines,  how  caused.     Sound  carried  by  the  electric  current 410 

CHAPTER  XXVIII. 

Electromagnectic  and  electrostatic  induction.  Telegraph  signals  heard  on  an 
adjacent  telephone  line.  Graphophone  record,  how  made.  Sound  reproduces 
itself,  in  thb  respect  similar  to  animals  and  plants.  A  make-and-hreak  neces- 
sary for  the  production  of  sound  by  an  electrio  current.  Sound  includes  a 
power  of  movement.  Sensations  produced  by  the  operations  of  matter. 
Reproduction  of  graphophone  record.     Matter  the  correlative   of  mind 422 

CHAPTER  XXIX. 

Order,  Nature's  Brst  law.  Diaframs  not  made  to  repeat  sounds.  Quotation  from 
Faraday  on  accepting  hypotheses.  Diaframs  gather  and  reflect  sound  as  a  stove 
heat.  The  principle  of  the  graphophone  used  for  the  records  of  memory. 
Electricity  a  phase  of  matter.  Discovery  of  the  telephone  suggested  by  that 
of  the  telegraph.  First  electric  telephone  attempted  by  Reis,  a  German,  who 
failed  because  employing  an  interrupted  current 434 

CHAPTER  XXX. 

All  sounds  made  by  elastic  bodies,  but  nu  elastic  body  can  make  any  sound  it  was 
not  made  to  make.  Sound  intinitesimal  particles  of  matter  thrown  off  by  the 
sounding  body.  Each  sensation  caused  by  a  combination  of  matter.  Variable 
resistance  transmitter.  Continuous  current  of  electricity  essential  to  a  telephone. 
The  telegraphone.  Sound  of  bells  focused  by  a  sail  and  heard  at  a  distance  of 
icx)  miles.  Increased  effects  come  from  increased  amounts.  Prof  Silliman  on 
distance  that  sound  can  be  heard 450 

CHAFFER  XXXI. 

Length  of  so  called  sound  waves.  Odor,  infinitesimal  particles  of  matter,  thrown 
off  by  the  odoriferous  body.  Sounding  boards.  Vibration  diminishes  as  the 
sound  diminishes.     Quotation  from  Sylvanus  P.  Thompson 460 

CHAFrER  XXXII. 

Quotation  from  "  The  Modern  Applications  of  Electricity "  on  different  kinds  of 
telephones.  Telephones  without  vibrating  plate,  membrane,  or  magnet.  Tele- 
phone without  receiver.     Quotation  from  Huxley  regarding  hypotheses 472 


XXXIV  CONTENTS 

CHAPTER  XXXIII. 

Graphophone  record,  how  reproduced.  Impossible  for  any  sound-producing  in- 
strument to  produce  all  sound.  Always  the  same  instrument  makes  the  same 
sound.    Quotation  from  Newton 480 

CHAPTER  XXXIV. 

String  or  wire  telephone.  Action  of  sound  in  such  demonstrates  that  sound  enteis 
the  wire  of  the  electric  telephone  and  is  carried  by  the  current.  Sound  always 
material,  but  Intelligence  necessary  to  construct  the  instruments  which  make  it. 
Sound  not  dependent  upon  an  auditor.  Quotation  from  Gray's  Eligy.  Early 
description  of  telephone  from  "  Good  Words." 494 

CHAPTER  XXXV. 

Membrane  of  the  ear,  function  of.  Reproduction  of  species  an  essential  part  of 
creation.  Sounds  of  a  graphophone  made  by  the  record.  Faraday,  persever- 
ance and  honesty  of;  quotations  from  life  of,  by  Sylvanus  P.  Thompson 515 

CHAPTER  XXXVI. 

(Quotations  from  biography  of  Philip  Reis.  Description  of  mechanical  telephone 
from  "  Nature."  Very  interesting  experiments  on  the  transmission  of  sounds  by 
wires,  from  "  The  Philosophical  Magazine,"  London,  1878.  Quotation  from 
"Practical  Telephony"  by  James  Bell,  1898.  Quotation  from  "Problem  of 
Human  Life"  by  Rev.  Mr.  Hall 530 

CHAPTER  XXXVII. 

Experiments  with  microphone  transmitter.  Transmission  of  sound  by  loose  elec- 
trical contact.  Distribution  of  sound.  Experiments  by  Prof  J.  Henry  of  Wash- 
ington, D.  C,  with  vibrations  of  tuning  forks.  Sound  the  cause  of  vibration. 
Law  of  resonance 545 

CHAPTER  XXXVIII. 

Remarkable  action  of  sounding  boards;  caused  by  the  flow  of  sounds  into  them. 
Experiment  by  Mr.  Charles  Whcatstone.  Sounds  do  not  mix  chemically  with 
one  another 558 

CHAPTER  XXXIX. 
All  things  made  by  machinery;  distributed  in  various  ways.     Some  things  made 


CONTENTS  XXXV 

by  stationary,  others  by  moving  mills.  Echoes.  Motion  a  property  of  matter. 
Kinetic  theory  of  gases.  Sound  the  correlative  of  hearing.  Mind  affected  by 
matter < 364 

CHAPTER  XL. 

Quotation  from  "  LittelPs  Living  Age  "  on  the  telephone,  with  criticisms  of  same. 
A  current  always  necessary  for  the  transmission  of  sound  in  a  telephone.  Inten- 
sity dependent  upon  amplitude  of  vibration,  and  pitch  upon  rate  of  vibration. 
Fundamental  and  overtones.    Timbre  or  clang 575 

CHAPTER  XLI. 

Other  things  equal,  same  cause,  same  effect.    Artificial  odors  manufactured  iden- 
tical with  natural   ones.     Reproduction  of  sound  by  a  graphophone   record. 
Laws  of  motion  imiversal.    Articulate    speech    complex.      Laws  governing 
telegraphy  and  the  telephone  plain  and  simple 601 

CHAPTER  XLIL 

Quotation  from  "The  Telephone,  the  Microphone  and  the  Phonograph  "  by  Count 
Du  Moncel.  Demonstrations  that  the  scientific  explanations  of  the  telephone 
do  not  explaiiL  All  known  conditions  explained  by  the  theory  that  sound  is  an 
entity  carried  by  the  electric  current.  Sound  transmitted  through  a  string  tele- 
phone by  connecting  it  with  different  parts  of  an  electric  telephone.  Electric 
telephone  without  diafram,  coil  or  magnet 613 

CHAPTER  XUH. 

Graphophone  records,  how  reproduced.  Quotation  from  Cowper.  Sensations 
caused  by  action  of  matter  upon  mind.  Graphophone  records,  how  made. 
Graphophone  records  made  by  sound,  the  sound  separately  making  its 
impression  in  the  paraffin  and  wax.  Principle  of  the  graphophone  for  the 
purposes  of  memory.  Sounds  reproduced  by  the  indentures.  Sounds  of  the 
world  made  by  elastic  bodies.  The  same  body  always  emits  the  same  sound. 
Sensations  caused  by  effect  of  matter  upon  spirit.  Quotation  from  Wood- 
worth.  Acknowledgement  of  Mr.  Edison's  persistency  and  ability.  Bodies 
only  produce  such  sounds  as  they  were  made  to  produce;  that  Is,  have  the 
appropriate  machinery  for  producing.  Sound-producing  instruments  always 
material,  and  sound  itself  material.    Sound  makes  vibration,  not  vibration  sound. 


XXXVl 


CONTENTS 


Very  interesting  experiment  of  VtoL  Henry  of  Washington,  D,  C,  with  tuning 
forks.  Suund  will  flow  from  the  bottom  of  a  tuning  Jork  through  a  small  stick 
to  the  teeth*  thence  into  the  head.  Vibration  stops  proportionately  as  sound 
f^ows  away.  Sympathetic  vibratLon  demonstrates  that  sound  makes  vibration, 
and  hence  must  be  an  entity.  Quotation  from  Shakespeare.  Sensation  of 
hearing  may  convey  accurate  knowledge.     UnduUlory  theories  ended .645 

CHAPTER  XUV. 

Sound  electrical,  antt  consisting  of  intinitely  small  particles  is  able  to  enter  nearly 
all  bodies,  and  to  travel  through  them  M'ith  facility.  Enoneous  theories,  sup- 
ported by  orgsuiiiation,  sometimes  last  a  long  time. ..,.,.... 666 

CHAPTER  XLV. 

Sensation,  a  system  of  Universal  Telegraphy.  Mind  and  matter  connected  by 
the  machinery  of  the  body.  Sensations  caused  by  the  introduction  of  matter  as 
light,  sound  and  odor  into  the  body  and  thus  into  contact,  or  the  immediate 
presence  of  the  soul.  Soul  always  sensitive  to  contact  of  matter,  as  illustrated 
by  eating  and  drinking.  All  creations  of  the  soul  in  material  conditions  con- 
structed of  matter— as  thought  and  Ihe  emotions*  Helen  Keller  both  deaf  and 
blind,  how  instructed.  Natural  instruction  assisted  by  artificial,  thus  the  child 
taught  articulate  speech  or  names  of  things,  through  which  knowledge  is  con- 
veyed to  the  soul  by  different  signals,  the  same  as  in  telegraphy;  and  thus  lito, 
pictures,  formed  by  light  mixing  chemically  with  the  visual  purple  of  the  eye, 
convey  knowledge.  Soul,  essence  of,  to  construct,  collect  and  enjoy.  Mcmor)'. 
a  record,  and  all  knowledge  bruught  ioto  the  soul  by  the  Sensations  is  recorded 
in  the  gray  matter  of  the  brain.  Material  the  soul  cannot  create.  Without 
mind  creation  impossible.  Mind  and  matter  intimately  related.  Quotation 
from  Cuwper,     Quotation  from  Byron.  . , .  , .,,...,,.  677 

CHAFFER  XLVI. 

History  of  the  different  theories  of  sound.  Sound  thought  to  be  an  entity  by 
Sir  G,  S.  McKenzie,  vice-president  of  the  Ro>^l  Society  of  Edinburgh  ini  835. 
Subject  ably  discussed  by  Rev.  A.  W.  Hall  in  **Thc  Problem  of  Human  Life." 
Quotation  from  J.  Goodman  on  the  "Identity  of  Light,  Heat,  IJectricity  and 
Gravitation."  Quotation  from  "  Modem  Re&lism  Examined,"by  Mr.  Herbert 
Quotation  from  M r.  Justice  Grove..  , , . . ......  691 


CONTENTS  XXXVll 

CHAPTER  XLVII. 

Recapitulation.  Undulatory  theory  of  sound  shown  to  be  impossible  mathemati- 
cally and  physically;  conversely  the  corpuscular  theories  sustained  by  conmion 
sense,  all  experiments,  and  the  universality  of  natural  law.  Quotation  from  Mr. 
Huxley  in  "  Lectures  on  the  Origin  of  Species."  Quotation  from  **  Life  and 
Letters  of  Faraday."  Quotation  from  Wm.  Crookes,  inventor  of  the  Crookes 
radiometers,  on  **  Radiant  Matter."    The  End 699 


THFNFW  YrFJr     I 
f'UBLICilrKfKY 


i  *  L  ^  a  N    f  .  :.   k 


Liii 


OR 

WHiSPERIIIGS  OF  All  OLD  PIIIE. 


I. 


T^HE  winds  of  the  autumn  blew  fresh,  and  its  deep  colors 
•*  stretched  far  and  wide  over  our  mountains,  when  Ellen 
came  again. 

She  held  her  hat  in  her  hand  as  she  emerged  from  the  forest, 
and  the  sunshine  seemed  to  be  comparing  itself  with  her  soft 
hair,  to  see  if  there  was  any  difference  in  their  color.  Stepping 
lightly  across  the  rocks,  and  addressing  me,  she  said : 

"Ellen  has  come  back  to  continue  her  review  of  the  Yale 
College  geometry.  The  second  book  treats  of  circles,  and  she 
is  awfully  in  hopes  that  it  will  appear  better  than  the  first  did ; 
and  she  thinks  it  will,  for  it  would  be  almost  impossible  that 
any  one  in  writing  one  treatise  should  again  wander  away  so 
far  from  the  canons  of  common  sense  as  this  author  has  in  his 
definitions  of  points,  lines,  and  superficies. 

"Ellen  will  make  another  figure  with  which  to  explain  the 
principles    upon    which   circles  are   constructed.      And    again 


2  ELLEN   OR 

will  we  have  illustrated  the  universality  of  natural  law.  For 
it  would  be  utterly  impossible  for  us  to  have  a  circle  except  as 
it  is  constructed  upon  these  principles.  And  therefore  when 
we  understand  the  principles  we  will  understand  all  about  cir- 
cles; can  take  them  apart'and  put  them  together  again  without 
difficulty. 

"They  will  illustrate  also  the  difference  in  the  character  of 
straight  and  curved  lines,  something  that  the  old  Pine  will  want 
to  make  himself  entirely  familiar  with  iif  he  wants  to  be  a  great 
mathematician. 

**  Ellen  will,  too,  use  largely  her  own  definitions,  arranging 
them  in  what  she  believes  the  best  method  for  the  instruction 
of  the  scholar ;  and  indeed  she  will  cut  loose  altogether  from 
the  methods  of  this  book,  excepting  to  quote  the  propositions 
in  order,  so  as  to  illustrate  the  science  as  taught  by  the  most 
recent  geometries. 

"  In  giving  definitions  she  will  follow  the  system  adopted  by 
Euclid,  of  giving  those  used  in  a  book  at  the  beginning  of  the 
book.  For  this  system  is  unquestionably  as  a  general  principle 
the  best.  Modern  geometries  frequently  intersperse  them  with 
the  propositions. 

BOOK  II. 

The  Circle  and  the  Measurement  of  Angles, 

DEFINITIONS. 

"  I.  A  circle  is  a  plane  figure  terminating  with  a  curved  line 
called  the  circumference,  every  point  of  which  is  equally  distant 
from  a  point  within  called  the  centre. 


WHISPERINGS   OF  AN   OLD   PINE  3 

"2.  A  radius  is  any  straight  line  from  the  centre  terminating 
with  the  circumference. 

"The  old  Pine  will  see  that  Ellen  has  revised  her  own  defini- 
tions of  a  circle  and  circumference. 

**3.  A  diameter  measures  the  circle  at  its  widest  part.  It  is 
therefore  equal  to  two  radii,  and  passes  through  the  centre. 
All  radii  and  diameters  of  the  same  or  equal  circles  are  mutually 
equal. 

"4.  An  arc  is  any  part  of  a  circumference. 

"5.  A  chord  is  a  straight  line  connecting  the  extremities  of 
an  arc ;  when  passing  through  the  centre  it  is  a  diameter. 

**  Any  chord  subtends  two  arcs  whose  sum  equals  the  cir- 
cumference of  a  circle.  When  only  one  arc  is  mentioned  the 
shorter  is  intended. 

"  6.  A  segment  is  the  part  of  a  circle  between  an  arc  and  its 
chord. 

**  7.  A  sector  is  the  part  of  a  circle  between  two  radii  and 
the  intercepted  arc. 

**8.  An  inscribed  angle  is  one  whose  vertex  is  in  the  cir- 
cumference and  whose  sides  are  chords. 

"9.  An  inscribed  polygon  is  one  all  of  whose  vertices  are  in 
the  circumference,  and  whose  sides  are  chords;  in  this  case  the 
circle  is  circumscribed  about  the  polygon. 

**  10.  The  secant  is  a  straight  line  drawn  from  any  point  with- 
out the  circle,  and  which  crosses  the  circle.  After  crossing,  it 
may  or  may  not  be  further  extended.  Ellen  calls  the  secant 
that  ends  with  the  circle  a  limited  secant. 

"II.  A  tangent  is  a  straight  line  which  touches  the  circum- 
ference of  a  circle  at  one  point  only,  however  far  it  may  be 


4  ELLEN   OR 

produced.  A  tangent  may  or  may  not  end  at  the  point  where 
it  touches  the  circle.  Ellen  calls  the  tangent  which  does  so  end 
a  limited  tangent. 

"  12.  Two  circles  are  tangent  to  each  other,  when  they  touch 
each  other  at  only  one  point.  They  may  touch  internally  or 
externally. 

"  13.  A  polygon  is  circumscribed  about  a  circle,  when  each 
of  its  sides  is  tangent  to  the  circle ;  in  this  case  the  circle  is 
inscribed  in  the  polygon. 

"  14.  Concentric  circles  have  the  same  centre. 

"15.  A  degree  of  angle  is  one-ninetieth  of  a  right  angle. 

"16.  A  degree  of  arc  is  the  arc  intercepted  by  a  degree  of 
angle  at  the  centre. 

"17.  The  arc  intercepted  by  a  right  angle  at  the  centre  is 
called  a  quadrant. 

"Hence  a  quadrant  contains  90  degrees  of  arc,  since  a  right 
angle  contams  90  degrees  of  angle. 

**Also,  since  four  right  angles  at  the  centre  contain  360 
degrees  of  angle,  and  four  such  right  angles  intercept  a  com- 
plete circumference,  a  circumference  contains  360  degrees 
of  arc. 

**  Hence  a  quadrant  is  one-quarter  of  a  circumference. 

"Ellen  will  take  a*  little  bit  of  a  dot,  C,  and  call  it  a  centre. 
Draw  the  stationary  line  AC,  and  upon  it  place  a  line  of  equal 
length,  BC,  and  with  BC  as  a  radius,  fastened  upon  a  pivot  at 
C,  generate  the  circle  BFHL.  The  line  BC  in  revolving  will 
occupy  the  place  of  every  possible  radius  to  this  circle,  as  CD, 
CE,  CF.  CH,  CL. 


WHISPERINGS   OF  AN   OLD   PINE 


5 


.  "Reaching  H  it  forms  with  AC  the  straight  line  AH,  twice 
the  length  of  AC,  and  this  is  a  diameter.  That  is,  a  diameter 
consists  of  twice  a  radius,  and  the  old  Pine  will  see  there  may  be 
half  as  many  of  them  as  there  are  radii,  and  always  a  radius  may 
be  extended  so  as  to  become  a  diameter,  as  DI,  EK,  FL. 
For  every  straight  line  which  passes  through  the  centre  and 
whose  extremities  are  in  the  circumference  consists  of  two  radii, 

F 


Figure  I. 

and  no  other  chord  can.  And  therefore  the  circle  might  be 
formed  by  revolving  a  diameter,  as  BH  about  C,  as  well  as  by 
revolving  the  radius  BC.  This  might  indeed  be  a  more  com- 
plete illustration  of  the  nature  of  a  circle.  And  this  diameter, 
after  having  completed  its  circle,  might  revolve  indefinitely  in 
the  same  place  as  a  wheel  upon  its  axis.     It  follows : 

"First.— That  when  the  angles  BCF  andFCH  are  equal 
and  the  radius  FC  is  perpendicular  to  AC,  as  was  explained 
in  Book  I.,  Figure  I.,  the  radius  BC,  or  diameter  BH,  will 
have  revolved  one-half  the  distance  from  B  to  H,  or  one- 
quarter  of  its  whole  revolution. 


6  ELLEN   OR 

"  Hence  BF  is  called  a  quadrant  and  BFH  a  semi-circum- 
ference. And  therefore  the  diameter  BH  divides  the  circum- 
ference into  two  semi-circumferences.  But  any  diameter,  as 
DI  or  EK  or  HL,  will  do  the  same  thing. 

"Ellen  showed,  too,  in  Book  I.,  Figure  I,  how,  as  the  radius 
BC  revolves,  it  makes  all  kinds  of  plane  angles  with  the 
line  A  H,  but  she  wants  the  old  Pine  now  to  remember 
that  every  diameter  represents  two  radii,  thrown  into  one 
straight  line. 

**  Second. — ^That  every  one  of  those  diameters,  and  there 
is  an  awfully  big  number  of  them,  is  a  chord ;  for  it  connects 
the  extremities  of  an  arc,  and  indeed  of  two  arcs  as  BFH  and 
BLH,  or  DGI  and  DKI,  which  are  the  complements  of 
each  other;  that  is,  their  sum  is  a  circumference.  These  arcs, 
being  semi-circumferences,  are  equal. 

**  Draw  DK,  DL,  DM.  As  these  lines  also  connect  the 
extremities  of  arcs — the  arcs  DFK  and  DLK;  DFL  and 
DML;  DFM  and  DBM — they,  too,  are  chords.  But  the 
old  Pine  will  see  that  they  are  shorter  than  the  diameter  DI, 
because  they  don't  reach  as  far.  Always  lines  are  shorter  than 
others,  if  they  don't  reach  as  far.  And  they  do  not  reach  as 
far  because,  as  we  have  seen,  a  diameter  is  composed  of 
two  radii,  and  these  are  not.  It  is  also  evident  that  they  do  not 
reach  as  far  because  they  connect  the  extremities  of  arcs  less 
or  greater  than  a  semi-circumference,  whilst  the  diameter  D I 
connects  those  of  a  semi-circumference. 

**  And  thus   a  chord  may  connect  the  extremities  of  two 
arcs,  and  the  sum  of  these  arcs  will  always  be  a  circumference 
Their  extremities,  too,  may  lie  on  either  side  of  the  diameter. 


WHISPERINGS   OF  AN   OLD    PINE  ^ 

the  limits  of  the  arcs  being  mutually  zero  and  a  circumference 
or  a  circumference  and  zero. 

"Third. — That  for  every  diameter  there  may  be  a  series  of 
chords  drawn  parallel,  the  first  contiguous  to  the  diameter  and 
each  following  contiguous  to  the  preceding,  until  the  whole 
half  circle  is  bridged  or  covered  by  these  parallel  chords ;  in 
which  case  each  chord,  because  of  the  uniform  curvature  of  the 
circle,  is  uniformly  diminished  in  length,  the  limits  beinrr 
a  diameter  and  zero;  the  arcs,  too,  whose  ends  it  connects 
being  mutually  diminished,  or  increased,  their  limits  being  zero 
and  a  circumference.  And  therefore  in  the  same  or  equal  circles 
equal  chords  subtend  mutually  equal  arcs,  and  conversely 
mutually  equal  arcs  are  subtended  by  equal  chords.  And 
therefore,  again,  in  the  same  or  equal  circles  chords  are  of 
equal  lengths  if  at  equal  distances  from  the  centre,  and  con- 
versely if  of  equal  lengths  are  at  equal  distances  from  the  centre. 

**  Fourth. — ^That  as  a  diameter  may  connect  any  two  points  in  a 
circumference  at  the  distance  of  two  radii  from  each  other,  and 
any  diameter  may  revolve  around  the  whole  circle,  all  possible 
diameters  with  all  parallel  chords  include  all  possible  chords. 

**  Fifth. — ^That  a  perpendicular  to  a  diameter,  bisecting  it  at 
the  centre,  will  bisect  every  chord  parallel  to  it,  and  this  because 
of  the  uniform  shortening  of  these  chords  on  each  side  of  the 
perpendicular  caused  by  the  uniform  curvature  of  the  circum- 
ference. 

**  For  a  circumference  curves  equally  in  every  part,  and 
curves  in  such  a  way  that  after  a  certain  time  it  arrives  at  the 
point  from  which  it  started,  when  you  may  consider  that  it 
stops,  or  that  it  repeats  its  course  and  thus  may  continue  to 


8  ELLEN   OR 

repeat  it  indefinitely.     And  therefore  is  it  that  it  has  no  end. 

"In  a  certain  sense,  as  Ellen  thinks,  it  might  be  said  to 
always  have  the  same  direction,  although  this  direction  is  en- 
tirely different  from  that  of  a  straight  line. 

'•  Every  part  of  this  circumference  is  equally  distant  from  a 
point  within  called  the  centre,  being  in  the  nature  of  a  resultant 
of  two  forces,  one  from  and  the  other  towards  the  centre. 

"Draw a  line  NO  through  F,  parallel  to  BH;  it  will  be  tan- 
gent to  the  circle  at  F,  and  perpendicular  to  the  radius  C  F. 

**  Sixth. — ^The  angles  formed  at  F  on  one  side  of  N  O  will 
consist  of  two  right  angles.  And  therefore  the  full  measure 
of  angles  situated  at  a  point  on  the  circumference,  formed  by 
chords  or  a  chord  and  a  tangent,  will  be  two  right  angles ;  or 
one-half  as  many  as  of  angles  formed  at  the  centre  of  the  circle. 
For  each  right  angle  formed  at  the  centre  is  measured  by  a 
quarter  of  the  circumference,  or  a  quadrant  of  the  circle,  and 
four  such  right  angles  may  be  formed  at  the  centre,  two  on 
each  side  of  a  diameter.  It's  awfully  funny !  Doesn't  the  old 
Pine  think  that  Ellen  has  got  a  dreadfully  pretty  figure?" 

"  She  has,  certainly,"  I  replied. 

*'It's  almost  as  fine  as  the  first  one.  Ellen  will  now  continue 
her  review  of  the  propositions  as  given  in  the  Yale  College 
geometry. 

PROPOsrriON  I. 

*  Circles  which  have  equal  radii  are  equal,  and  if  their  centres  be 
made  to  coincide  they  will  coincide  throughout;  conversely,  equal 
circles  have  equal  radii.' 


WHISPERINGS   OF  AN   OLD   PINE  9 

Proposition  II. 
•The  diameter  of  a  circle  is  greater  [longer]  than  any  other  chord/ 

**  One  hundred  and  nine  words  are  used  to  demonstrate  these 
propositions,  both  of  which  Ellen  includes  in  definitions. 

PROPOSmON  III. 

'  In  the  same  circle  or  equal  circles,  equal  angles  at  the  centre  inter- 
cept equal  arcs ;  conversely,  equal  arcs  are  intercepted  by  equal  angles 
al  ine  centre.* 


"Because  the  divergence  of  the  sides  of  an  angle  is  uniform. 

"Eleven  words  instead  of  79,  or  189,  including  previous 
demonstrations  referred  to ,  the  application  of  which  is  often 
more  difficult  to  the  scholar  than  the  demonstration  of  the 
proposition  under  consideration ;  and  the  real  reason. 

Proposition  IV. 

'  In  the  same  circle  or  equal  circles,  equal  chords  subtend  [mutually] 
equal  arcs ;  conversely  [mutually]  equal  arcs  are  subtended  by  equal 
chords.' 

"  Because  of  the  uniform  curvature  of  a  circle." 
"  But  why/'  I  asked,  "does  Ellen  add  the  word  *  mutually'  in 
the  Proposition?  " 


lO  ELLEN    OR 

*'  Because,  as  Ellen  has  said,  every  chord  subtends  two  arcs, 
which  together  make  a  circumference." 

•'Eight  words  instead  of  102,  or  500,  with  previous  dem- 
onstrations referred  to.     And  again  the  real  reason. 

PROPOsmoN  V. 

*In  the  same  circle  or  equal  circles,  if  two  arcs  are  unequal  and  each 
is  less  than  a  semicircumference,  the  greater  arc  is  subtended  by  the 
greater  chord  ;  conversely,  the  greater  chord  subtends  the  greater. arc' 


"  Chords  connect  the  extremities  of  arcs  and  therefore  so 
long  as  the  extremities  of  a  variable  arc  diverge,  its  chord  is 
lengthened ;  and  conversely  if  they  converge  the  chord  is  short- 
ened. But  a  diameter  is  the  longest  chord  and  therefore  marks 
the  limit  of  this  divergence. 

"Seventy-two  words  instead  of  150,  plus  210,  of  propositions 
quoted,  plus  254  more,  with  references  included  in  these  las^. 
The  old  Pine  knows  all  about  these  principles?" 

"Why,  certainly,"  I  said.  "The  old  Pine  understands  that  a 
circle  is  such  that  the  distance  between  any  two  points  on  the 
circumference  connected  by  a  line  passing  through  the  centre 
is  equal  to  that  of  any  other  two  points  on  t'ae  circumference  so 
connected.  That  hai^  of  this  line  is  a  radius,  the  whole  of  it,  or 
two  radii,  a  diameter,  and  that  a  diameter  divides  a  circle   into 


WHISPERINGS   OF  AN   OLD   PINE 


n 


two  semicircles,    and  the  circumference  into  two  semicircum- 
ferences.** 

"Then,*'  she  said,  "he  can  see  how  self-evident  it  is  that  the 
diameter  is  the  longest  chord,  and  how  unnecessary  is  any 
demonstration.  And  Ellen  is  awfully  glad  that  the  old  Pine 
was  sensible  enough  to  get  the  foundation  of  his  geometry  well 
fixed.  For  it  makes  entirely  unnecessary  the  larger  part  of 
geometrical  demonstrations. 

PROPOsmoN  VI. 

*The  perpendicular  bisector  of  a  chord  passes  through  the  centre 
of  the  circle.* 


"  Because  of  the  uniform   curvature   of  the  circumference. 
See  Figure  I.  (Fourth). 

PROPOsmoN  VII. 

*If  two  circumferences  intersect,  the  straight  line  joining  their  cen- 
tres bisects  their  common  chord  at  right  angles.' 


**  Included  in  Proposition  VI. 


12  ELLEN   OR 

PROPOSmoN  VIIL 
'In  the  same  circle,  or  equal  circles,  equal  chords  are  equally  dis* 
tant  from  the  centre;    conversely,  chords  equally  distant  from  the 
centre  are  equal.' 

"  Because  of  the  uniform  curvature  of  a  circle.  See  Figure 
page  9. 

'*As  Ellen  has  said,  all  diameters  with  chords  parallel  to 
them  represent  all  chords.  But  all  diameters  pass  through  the 
centre  and  are  equal,  and  all  contiguous  parallel  chords  dimin- 
ish equally  and  uniformly.     See  Figure  I.  (Fourth). 

PROPOsmoN  IX. 
'  In  the  same  circle  or  equal  circles,  the  less  of  two  chords  is  at  the 
greater  distance  from  the  centre ;  conversely,  the  chord  at  the  greater 
distance  from  the  centre  is  the  less.' 

**  Because  subtending  converging  arcs. 

"For  of  necessity  with  converging  arcs  the  distance  between 
extremities  is  diminished.     See  Figure  I.  (Third). 

"These  four  propositions  Ellen  has  demonstrated  in  66 
words,  against  231  directly  in  the  book,  and  860  in  articles  re- 
ferred to. 

PROPOsrriON  X. 

'A  straight  line  perpendicular  to  a  radius  at  its  extremity  is  tangent 
to  the  circle ;  conversely,  the  tangent  at  the  extremity  of  a  radius  is 
perpendicular  to  that  radius.' 

"Because  of  the  uniform  curvature  of  the  circumference. 
"Eight  words  to  97  in  the  book,  plus  400  more  in  proposi- 
tions referred  to. 


THI  FE^  TORK 
PUBLIC  LIBRARY 


WHISPERINGS   OF  AN   OLD    PINE  1 3 

"This  proposition  is  all  right  with  the  definitions  given  by 
Ellen,  but  very  loosely  drawn  in  connection  with  those  in  the 
book,  or  in  any  modern  geometry,  consistent  only  with  the 
idiotic  assumption  that  a  material  thing  can  exist  without  occu- 
pying space.  For  by  the  definition  of  the  book  a  radius 
is  the  distance  from  the  centre  of  a  circle  to  the  circumference, 
the  circumference  being  a  line.  Hence  no  tangent  could 
touch  the  radius.  Correctly  stated  with  such  definition  the 
proposition  would  read : 

**  A  straight  line  tangent  to  a  circle  is  perpendicular  to  the 
radius  extended  to  the  point  of  tangency;   conversely,  a  line. 


perpendicular  to  a  tangent  at  the  point  of  tangency,  will,  if 
extended,  pass  through  the  centre  of  the  circle. 

**  Here  follow  definitions  of  ratio  and  commensurable  quanti- 
ties. Ellen  thus  far  has  copied  the  textbooks  in  her  definitions 
of  ratio,  although  saying  that  she  considered  Euclid's  definition, 
*  A  mutual  relation  of  two  magnitudes,  of  the  same  kind,  to  one 
another  in  respect  of  quantity,'  much  the  best. 

**  But  she  would  greatly  prefer  the  word  proportion  to  ratio. 
Thus :  *  Proportion  is  the  mutual  relation  of  two  magnitudes  of 
the  same  kind  to  one  another  in  respect  of  quantity.* 

**A  bushel  will  contain  32  quarts,  and  32  is  the  relation 
or  proportion  of  a  bushel  to  a  quart,  or  ^^^  that  of  a  quart  to 
a  bushel. 


14  ELLEN   OR 

**  Ellen  certainly  considers  Proportion  by  far  the  best  word  to 
denote  the  subject  referred  to." 

**Then  what  would  Ellen  call  an  equality  of  proportions?"  I 
asked. 

"  She  would  call  them  proportionals,'*  she  answered. 

** Again,  the  Yale  College  book  illustrates  in  metres;  Ellen 
would  illustrate  in  feet.  That  is,  she  would  use  her  own  lan- 
guage. 

**The  definitions  of  commensurable  quantities  show  that  while 
a  yard  and  a  rod  are  not  commensurable  in  a  foot  they  are  in  an 
inch  standard.  And  this  Ellen  thinks  is  always  true.  Two 
things  may  not  be  commensurable  in  each  other,  as  the  circum- 
ference and  diameter  of  a  circle ;  but  doubtless  there  are  quan- 
tities which  will  be  contained  equally  in  each. 

**  Limits  are  next  referred  to  and  the  following  definitions 
given : 

*  A  constant  quantity  is  one  that  maintains  the  same  value  throughout 
the  same  discussion. 

*A  variable  is  a  quantity  which  has  different  successive  values  during 
the  same  discussion. 

'The  limit  of  a  variable  is  a  constant  from  which  the  variable  can  be 
made  to  differ  by  less  than  any  assigned  quantity,  but  to  which  it  can 
never  be  made  equal. 


?     f 


-B 


Thus,  suppose  a  point  P  to  move  over  a  line  from  A  to  B  in  such  a 
way  that  in  the  first  second  it  passes  over  half  the  distance,  in  the  next 
second  half  the  remaining  distance,  in  the  third  half  the  new  remainder, 
and  so  on. 


WHISPERINGS   OF  AN   OLD   PINE  1 5 

'The  variable  is  the  distance  from  A  to  the  moving  point.  Its  suc- 
cessive values  are  AP',  AP",  AP'",  etc.  If  the  length  of  AB  is  two 
inches,  the  value  of  the  variable  is  first  i  inch,  then  ij,  ij,  ij,  etc. 

*  (i)  P  will  never  reach  B,  for  there  is  always  half  of  some  distance 
remaining. 

*  (2)  P  will  approach  nearer  to  B  than  any  quantity  we  may  assign. 
'Suppose  we  assign  Yi^(ny  ^^  ^"  ^^^^*     ^Y  continually  bisecting  the 

remainder  we  can  reduce  it  to  less  than  xu^nr  ^^  ^°  ^'^^^^  Hence  the 
distance  from  P  to  A  is  a  variable  whose  limit  is  AB,  and  the  distance 
from  P  to  B  is  a  variable  whose  limit  is  zero.* 

"Ellen  would  say,  it  is  a  variable  disappearing  in  infinity. 
For  she  does  not  think  it  correct  to  speak  of  that  as  limited, 
which  has  no  limit,  nor  to  call  that  a  limit  which  can  never  be 
reached. 

Proposition  XL 

*  In  the  same  circle  or  equal  circles  two  angles  at  the  centre  have  the 
same  proportion  as  their  intercepted  arcs.* 


** Because  the  lines  (radii),  which  form  the  angles  and  limit 
the  arcs,  are  equal  and  their  divergence  uniform. 

**  Eighteen  words  to  248  in  direct  demonstration  and  300 
more  in  articles  referred  to  in  the  book. 

PROi>osrriON  XII. 
'  An  inscribed  angle  is  measured  by  one-half  its  intercepted  arc' 


1 6  ELLEN   OR 

**  This  isn't  true ;  it  is  measured  by  its  intercepted  arc.     If  the 
idea  intended  here  is  that  an  inscribed  angle  is  half  as  large  as 


an  angle  at  the  centre  having  the  same  intercepted  arc  it  should 
be  so  expressed.  And  this  because  of  the  uniform  divergence 
of  the  sides  of  an  angle  and  uniform  curvature  of  a  circumfer- 
ence. 

Ellen  will  illustrate.  The  proposition  is  reasonably  self- 
evident,  but  Ellen  wants  to  make  the  old  Pine  very  familiar 
with  the  essentially  plain  laws  which  hold  throughout  the 
construction  of  the  universe. 

"  Ellen  will  start  with  two  diameters  and  two  radii,  with 
which  to  make  inscribed  angles,  and  angles  at  the  centre.  Of 
course  the  diameters  are  twice  the  length  of  the  radii.  And 
Ellen  will  bunch  these  four  together,  the  two  diameters  under- 
neath and  the  two  radii  above,  all  lying  in  the  same  direction. 
Thus  far  Ellen  has  no  angles,  but  now  she  will  start  the 
machinery  by  moving  one  diameter  and  one  radius  contin- 
uously to  the  right,  passing  through  all  intermediate  distances 
between  the  point  of  departure  and  where  the  diameter 
becomes  perpendicular  to  the  other  diameter,  forming  with  it 
two  right  angles,  but  only  one  subtended  by  the  circumfer- 
ence; and  where  the  radius  is  in  line  with  the  other  radius, 
thus  making  two  right  angles,  both  subtended  by  the  circum- 
ference. 


WHISPERINGS   OF  AN   OLD   PINE  IJ 

"  In  this  illustration  one  side  of  the  inscribed  angle  is  double 
that  of  the  equal  angle  at  the  centre,  and,  of  course,  because  of 
the  uniform  divergence  of  the  sides  of  all  plane  angles,  will  have 
done  its  part  in  making  its  subtending  arc  double.  The  other 
side  as  cut  by  the  circumference  is  not  double,  but  the  curva- 
ture of  the  circumference  supplies  the  deficiency,  and  we  have 
the  inscribed  angle  subtended  by  double  the  arc  of  its  equal 
angle  at  the  centre."* 

•*  But  how  does  Ellen  know,"  I  asked,  **  that  the  curvature 
of  the  circumference  supplies  the  deficiency  ?  " 

**  Ellen  will  prove  it,"  she  said.  **  For  she  will  fasten  the 
end  of  a  radius  to  a  diameter  in  such  a  way  as  not  to  interfere 
with  the  movement  of  either,  and  then  revolve  them  together. 
Immediately  there  are  two  sweet  little  angles,  but  Ellen  notices 
that  the  one  at  the  centre  is  much  the  larger;  she  notices, 
too,  that  when  one  radius  is  perpendicular  to  the  other, 
showing  that  their  angle  is  a  right  angle,  the  diameters  which 
form  the  inscribed  angles  are  not  more  than  half  that. 

'*  Ellen  continues  to  revolve  these  sides,  until  the  radius  lies 
in  line  with  the  other  radius,  making  with  it  two  right  angles, 
both  subtended  by  the  circumference ;  and  at  the  same  time 
she  finds  the  diameters  perpendicular  to  each  other,  forming 
two  right  angles,  one  of  which  is  subtended  by  the  circumfer- 
ence, the  other  outside  of  it. 

"That  is,  the  inscribed  angle  is  subtended  by  double  the  arc 
of  its  equal  angle  at  the  centre. 


*  Since  this  was  written  our  attention  has  been  called  to  the  fact  that  Euclid  deBnes 
this  proposition  substantially  as  corrected  in  Ellen.  Thus,  Proposition  XX,  Book  II, 
of  Euclid  reads :  "  The  angle  at  the  center  of  a  circle  is  double  of  the  angle  at  the 
circumference  upon  the  same  base,  that  is,  upon  the  same  part  of  the  circumference." 


1 8  ELLEN   OR 

**  And  as  the  angle  we  are  considering  passes  through  all  inter- 
mediate values  from  a  right  angle  to  zero,  using  at  every  change 
its  proportionate  part  of  the  circumference,  we  have  a  demon- 
stration that  always  an  inscribed  angle  is  subtended  by  double 
the  arc  of  its  equal  angle  at  the  centre.'* 

"As  Ellen  has  said,  she  has  extended  her  illustration  beyond 
the  necessities  of  demonstration,  as  on  its  face  it  is  perfectly 
evident  that  an  inscribed  angle  is  subtended  by  double  the  arc 
of  its  equal  angle  at  the  centre,  because  the  lines  at  the  centre 
cross,  making  four  right  angles,  two  upon  each  side  of  a 
straight  line,  whilst  it  is  impossible  to  make  more  than  two 
right  angles  upon  one  side  of  a  straight  line,  and  only  one  side 
can  be  used  in  making  inscribed  angles. 


Proposition  XI IL 

'An  angle  formed  by  a  tangent  and  a  chord  is  measured  by  one-half 
its  intercepted  arc  [is  one-half  as  large  as  the  angle  at  the  centre  having 
the  same  intercepted  arc].* 

"As  Ellen  doesn't  know  what  part  of  an  angle  thus  formed 
is  subtended,  or  measured,  by  the  arc  intercepted  by  its  chord, 
the  proposition  becomes  to  her   unintelligible. 

Proposition  XIV. 
*The  angle  between  two  chords  which  intersect  within  the  circumfer- 


WHISPERINGS   OF  AN   OLD   PINE  *  1 9 

ence  is  measured  by  one-half  the  sum  of  its  intercepted  arc  and  the  arc 
intercepted  by  its  vertical  angle.' 

"  Here  is  another  attempt  to  say  that  one  half  of  the  sum  of 
the  arcs  subtending  any  two  vertical  angles  formed  by  the  in- 
tersection of  two  chords  within  a  circumference,  is  equal  to  the 
arc  subtending  an  equal  angle  at  the  centre. 

"  And  this  because  all  mutually  vertical  angles  are  equal, 
and  the  divergence  of  their  sides  uniform.  And  therefore,  if 
at  the  centre,  they  will  be  subtended  by  equal  arcs,  their  sides 
Seing  radii ;  and  if  not  at  the  centre  one  will  be  subtended  by 
an  arc  as  much  longer,  as  that  subtending  the  other  is  shorter, 
than  the  arc  subtending  each  at  the  centre, — because  of  the 
uniform  divergence  of  their  sides. 


"Thus  the  vertical  angles  ACF  and  GCB,  formed  by 
chords  AB  and  FG  crossing  at  the  centre,  are  subtended  by 
the  equal  arcs  FA  and  BG,  because  of  the  equality  of  their 
sides,  which  are  radii,  and  their  uniform  divergence. 

*•  Ellen  will  illustrate  further: 


20  ELLEN   OR 

"Draw  DE  parallel  to  AB,  intersecting  FG  at  H.  The 
angles  DHF  and  GHE  are  equal  to  ACF  and  GCB, 
their  sides  extending  in  the  same  direction,  or  opposite 
directions;  but  the  arc  FD,  subtending  H,  is  shorter  by 
DA  than  the  arc  FA,  subtending  C.  Conversely,  the  arc  EG, 
subtending  H,  is  longer  than  the  arc  B  G,  subtending  C,  by  EB, 


an  amount  equal  to  DA,  they  being  arcs  of  the  same  circle 
included  between  parallel  chords.  But  we  have  seen  that  all 
chords  are  diameters  or  parallel  to  diameters,  and  therefore 
one-half  of  the  sum  of  the  arcs  of  all  vertical  angles  formed 
by  chords  crossing  each  other  will  be  equal  to  the  arc  subtend- 
ing an  equal  angle  at  the  centre. 

Proposftion  XV. 

*The  angle  between  two  secants  intersecting  without  the  circumfer- 
ence, the  angles  between  a  tangent  and  a  secant,  and  the  angle  between 
two  tangents,  are  each  measured  by  one-half  the  difference  of  the  in- 
tercepted arcs.' 


WHISPERINGS   OF  AN  OLD   PINE 


21 


•*  There  is  an  attempt  made  here  to  say  that  half  the  differ- 
•ence  in  the  arcs  intercepted  by  the  sides  of  these  angles  equals 
the  arc  intercepted  by  an  equal  angle  at  the  centre  of  the  circle. 

"And  this  because  of  the  uniform  divergence  of  the  sides  of 
an  angle  and  the  nature  of  a  circle. 


"  Ellen  will  draw  another  pretty  nice  figure ;  from  the  cen- 
ter C  the  circle  ABDEFGHIKN  and  from  the  point  L  above 
the  circle  the  tangents  LB  and  LK  and  the  secant  LF  passing 
through  the  centre  C.  Ellen  will  draw  also  the  secant  M I  par- 
allel to  the  tangent  LK  and  the  chord  AH,  and  the  radius  CG 
also  parallel  to  the  tangent  L  K.  Then  Ellen  will  draw  the  chord 
AD  and  the  radius  CE  parallel  to  the  tangent  LB.  Ellen  has 
now  a  beautiful  figure  illustrating  the  angle  BLK  betwe  en  two 
tangents,  the  angle  FLK  made  by  a  tangent  and  a  secant,  and 


22  ELLEN   OR 

the  angle  FMI  by  two  secants.  Also  the  inscribed  angles 
D AH,  FAD  and  FAH,  and  the  angles  at  the  centre  FCG. 
FCEandECG. 

"  It  will  be  seen  from  this  figure  that  the  angles  B  L  K 
formed  by  the  two  tangents,  and  D  A  H  by  the  two  chords,  are 
equal,  being  made  by  parallel  lines,  also  the  angle  FLK,  made 
by  secant  and  tangent,  is  equal  to  the  inscribed  angle  FAH, 
being  made  by  the  same  and  parallel  lines.  This  inscribed 
angle  FAH  is  also  equal  to  the  angle  FMI,  made  by  two 
secants,  because  by  the  same  and  parallel  lines. 

"  From  a  glance  the  old  Pine  can  see  that  half  the  difference 
in  the  arcs  intercepted  by  the  angles  FLK,  made  by  secant 
and  tangent,  and  FMI,  made  by  two  secants,  equals  the  arc  F G 
intercepted  by  an  equal  angle  at  the  centre. 

**For  the  difference  of  the  arcs  AK  and  FK  intercepted  by 
the  lines  LF  and  LK  is  the  arc  FH,  the  arcs  AK  and  HK 
lying  between  parallel  lines  being  equal,  and  the  difference 
of  the  arcs  AN  and  FI,  intercepted  by  the  lines  M  I  and  MF 
of  the  angle  at  M,  is  FH. 

**But  the  arc  FH  is  the  arc  intercepted  by  the  inscribed 
angle  FAH,  and  it  has  been  proven  that  the  arc  intercepted 
by  an  inscribed  angle  is  equal  to  double  the  arc  intercepted  by 
an  equal  angle  at  the  centre  (as  FCG).  It  is  also  directly 
evident  that  FG,  the  arc  intercepted  by  FCG  the  angle  at  the 
centre,  equal  to  the  angles  FMI'and  FAH  being  made  by  the 
same  and  parallel  lines,  is  half  the  difference  of  the  arcs  inter- 
cepted by  the  angle  at  M,  and  the  angle  FLK,  and  also  that 
E  G  is  half  the  difference  of  the  arc  D  H  intercepted  by  the 
lines  LB  and  LK  of  the  angle  BLK,  formed  by  two  tangents.'* 


WHISPERINGS   OF  AN   OLD   PINE  23 

"And  what  does  Ellen  mean  by  the  uniform  divergence  of 
the  sides  of  an  angle  ?  " 

**  Because  the  sides  of  a  plane  angle  are  straight,"  she  replied, 
**  and  have  two  directions,  their  divergence  must  be  uniform  for 
whatever  distance  they  extend,  and  theoretically  they  extend  to 
infinity.  It  follows  that  if  their  ends  are  connected  at  any 
point  by  a  straight  line  the  length  of  that  line  will  be  just 
double  that  connecting  the  sides  at  one-half  the  distance  from 
the  apex ;  or  four  times  as  much  as  that  connecting  them  at 
one-quarter  that  distance ;  and  this-  ratio  must  hold  at  all  dis- 
tances. 

"This  is  a  very  important  self-evident  principle  in  mathe- 
matics, and  may  be  used  to  great  advantage  in  the  demonstra- 
tion of  many  propositions. 


24  ELLEN  OR 

ii. 

BOOK   III. 

^^TPHE  first  eight  pages  of  Book  III.  treat  of  Proportion,  in 
*  as  unintelligible  a  manner  as  it  would  be  possible  to  do 
it,  no  attempt  being  made  to  familiarize  the  scholar  with  the 
principles  which  underlie  this  subject. 

**In  this  respect  it  differs  radically  from  the  method  of 
Euclid,  who  undertook  to  make  all  things  as  rational  and  sen- 
sible as  possible,  using  for  such  purpose  the  most  practical 
illustrations.  For  Euclid  was  by  far  too  able  a  man  to  neglect 
this  all-important  feature  of  instruction,  a  feature  that  like 
Truth  is  of  paramount  importance, — more  important  than  all 
things  else. 

"  It  is  true  that  the  book  through  these  methods  has  been 
greatly  condensed,  a  desirable  thing  when  done  intelligently, 
but  inadmissible  if  not.  As  a  matter  of  fact,  it  is  accomplished 
by  the  abandonment  of  all  principles,  and  a  resort  to  what 
might  be  called  a  Icgerdermain  of  numbers  or  letters. 

"Ellen  and  the  old  Pine  greatly  condensed  this  book  of 
Euclid  without  abandoning  at  all  the  principles  upon  which  it 
is  founded.  And  having  done  this  Ellen  will  omit  this  part 
and  begin  Book  III.  with  definitions  of  Similar  Figures. 

"I.  Similar  Polygons  are  those  which  are  mutually  equi- 
angular, and  have  their  corresponding  sides,  taken  in  the  same 
order,  proportional. 


■ 

TBI  HEW  YORK     1 

PUfiUC  UBRART 

9,                         ^ 

^^ 

1 

WHISPERINGS   OF  AN   OLD   PINE  25 

'*  The  Yale  College  definition  is :  '  Similar  polygons  are  poly- 
gons which  have  the  angles  of  one  equal  to  the  angles  of  the 
other,  each  to  each,  and  the  corresponding,  or  homologous, 
sides  proportional/     Which  is  both  prolix  and  inaccurate. 

"  2.  The  corresponding  parts  of  similar  polygons  arc  called 
homologous. 

**  3.  Similar  arcs,  sectors,  or  segments,  in  different  circles,  are 
those  which  correspond  to  equal  angles  at  the  centre. 

"  4.  A  diagonal  of  a  polygon  is  a  straight  line,  other  than  a 
side,  joining  two  vertices. 

**  5.  The  perimeter  of  a  polygon  is  the  sum  of  its  sides. 

*•  6.  The  altitude  of  a  triangle  is  the  perpendicular  distance 
from  any  vertex  to  the  opposite  side,  or  the  opposite  side  pro- 
duced, considered  as  a  base. 

"7.  The  altitude  of  a  parallelogram  is  the  perpendicular  dis- 
tance between  two  opposite  sides,  called  the  upper  and  lower 
base. 

"  8.  The  altitude  of  a  trapezoid  is  the  perpendicular  distance 
between  its  parallel  sides,  called  the  upper  and  lower  base. 

"9.  The  area  of  a  surface  is  the  space  which  it  occupies 
expressed  in  some  unit  of  measure,  as  a  square  inch,  foot,  rod, 
or  acre. 

*'  10.  Two  straight  lines  are  divided  proportionally  when  one 
line  is  to  either  of  its  segments  as  the  other  to  its  corresponding 
segment. 

"II.  A  line  is  divided  internally  when  the  point  of  division  is 
between  the  extremities  of  the  line. 

"  A  line  is  divided  externally  when  the  point  of  division  is  on 
the  line  produced. 


26  ELLEN   OR 

"  In  each  case  the  segments  are  the  distances  from  the  point 
of  division  to  the  extremities  of  the  line.  The  line  is  the  sum 
of  the  internal  segments,  and  the  difference  of  the  external  seg- 
ments. 

"  A  line  is  divided  harmonically  when  it  is  divided  internally 
and  externally  in  the  same  ratio. 

•*  12.  A  straight  line  is  divided  in  extreme  and  mean  ratio 
when  one  of  its  segments  is  a  mean  proportional  between  the 
whole  line  and  its  other  segment. 

PROPosmoN  L 

*  A  straight  line  parallel  to  one  side  of  a  triangle  divides  the  other 
two  sides  proportionally. 

Proposftion  IL 

*  If  a  straight  line  divides  two  sides  of  a  triangle  proportionally,  it  is 
parallel  to  the  third  side.* 


"These  two  propositions  might  as  well  be  expressed  in  one. 
Thus: 

Proposition  I. 

"  A  straight  line  parallel  to  one  side  of  a  triangle,  cutting  the 
other  two  sides,  divides  them  proportionally;  conversely,  if  a 
straight  line  divides  two  sides  of  a  triangle  proportionally,  it  is 
parallel  to  the  third  side. 


WHISPERINGS   OF  AN   OLD   PINE  2^ 

**  Because  of  the  uniform  divergence  of  the  sides  of  an  angle. 

"Eleven  words,  to  322  directly  and  over  1300  indirectly  in 
the  book. 

"Corollary. — The  parts  of  the  divided  sides  are  pro- 
portional to  each  other,  and  the  sides  are  proportional  to  their 
parts." 

"  And  is  the  converse  of  a  mathematical  proposition  always 
true?"  I  asked. 

*'  Ellen  thinks  it  is,"  she  replied;  "if  in  each  case  language 
is  accurately  used  and  interpreted.  It's  a  poor  rule  that  won't 
work  both  ways. 

PROPOSmON  III. 
*  Two  triangles  which  are  mutually  equiangular  are  similar.' 


"  Because  their  sides  are  proportional,  and  this  because  of 
their  uniform  divergence. 

'CoROLiARY  I. — If  two  trianglcs  have  two  angles  of  the  one  equal  to 
two  angles  of  the  other,  the  triangles  are  similar.' 

"  Because  they  arc  equiangular,  for  two  angles  of  a  triangle 
decide  the  direction  of  all  its  sides  as  they  include  the  sides  of 
the  third  angle. 


28  ELLEN   OR 

'Corollary  IL — If  two  straight  lines  are  cut  by  a  series  of  parallels^ 
the  corresponding  segments  of  the  two  lines  are  proportional. 

Proposition  IV. 
'Two  triangles  are  similar  when  their  homologous  sides  are  propor- 
tional.* 

"Because  mutually  equiangular. 

"Two  sides  of  any  triangle  may  be  mutually  proportional  to 
two  sides  of  any  other  triangle,  but,  because  of  the  uniform 
divergence  of  the  sides  of  any  angle,  the  third  sides  can  only 
be  proportional  when  all  angles  are  equal. 

Proposftion  V. 
'Two  triangles  are  similar  when  an  angle  of  the  one  is  equal  to  an 
angle  of  the  other,  and  the  sides  including  these  angles  are  proportional.' 

"  Because  they  must  be  equiangular,  and  this  because  of  the 
uniform  divergence  of  the  sides  of  an  angle. 

Proposition  VI. 
'Two  triangles  which  have  their  sides  parallel  each  to  each,  or  per- 
pendicular each  to  each,  are  similar.' 


"Because  there  is  the  same  difference  of  direction  in  their 
sides,   and   hence  they  are   equiangular.     For  sides  mutiiaiiJy 


WHISPERINGS   OF  AN   OLD   PINE 


29 


parallel  have  the  same  difference  of  direction  between  them; 
and  perpendicular  sides  will  become  parallel,  or  else  coincide 
in  direction,  if  the  sides  of  one  triangle  are  rotated  a  right  angle. 

PROPOsmoN  VII. 
'  In  two  similar  triangles,  corresponding  altitudes  are  proix)rtional  to 
the  corresponding  sides.* 


•*  Because  corresponding  sides  diverge  uniformly  from  lines 
representing  corresponding  altitudes. 

Proposition  VIII. 
*  I  f  three  or  more  straight  lines  drawn  through  a  common  point  inter- 
sect two  i)arallels,  the  corresponding  segments  of  the  parallels  are  pro- 
j>ortional.' 

*•  Because    of   the    uniform    divergence    of    the    sides  of    an 
an^lc. 


A     B      C      Ji 

PROPOsrrioN  IX. 
Two  ix)lygons  similar  to  a  third  are  similar  to  each  other.' 


30  ELLEN   OR 

"This  is  under  the  principle  that  things  equal  to  the  same 
thing  are  equal  to  each  other,  and  is  entirely  self-evident. 

Thus,  if  2  :  4:14  :  8 
and  3  :  6::4  :  8 
then        2  :  4::3  :  6 

**One  thousand  and  seventy-one  words  directly,  and  6483 
indirectly,  in  propositions  referred  to,  are  used  in  the  book  to 
demonstrate  these  nine  propositions,  to  208  words  in  **  Ellen," 
who  always  demonstrates  directly — 7554  to  208  or  36  to  i. 

"Ellen  wants  the,  old  Pine  to  remember  that  the  sides  of  a 
polygon  of  four  or  more  sides  may  be  proportional  without  its 
angles  being  equal,  and  conversely  its  angles  may  be  equal 
without  its  sides  being  proportional,  but  this  is  not  so  with  a 
triangle,  and  for  the  reason  Ellen  has  given,  because  the  sides 
of  any  two  angles  of  a  triangle  include  the  sides  of  the  third. 

"There  follow  several  propositions  upon  polygons  radially 
situated,  ray  ratio,  etc.,  with  which  the  book  seems  to  be  as 
much  interested  as  a  boy  with  a  new  top,  and  which,  so  far  as 
Ellen  can  see,  are  as  unimportant  as  tricks  with  cards.  Then 
comes 

PROPOsmoN  XIV. 

*  In  a  right  [angle]  triangle,  if  a  perpendicular  is  drawn  from  the 
vertex  of  the  right  angle  to  the  hypotenuse : 

*  I.  The  triangles  on  each  side  of  the  perpendicular  are  similar  to  the 
whole  triangle  and  to  each  other. 

*  II.  The  perpendicular  is  a  mean  proportional  between  the  seg- 
ments of  the  hypotenuse. 


WHISPERINGS   OF  AN   OLD   PINE 


31 


'III.  Each  side  about  the  right  angle  is  a  mean  proportional  between 
the  hypotenuse  and  the  adjacent  segment.' 

"  Because,  first,  the  angles  of  the  three  triangles  are  mutually 
equal ;  and  they  are  equal  because  each  triangle  has  a  right 
angle,  and  the  two  smaller  triangles  have  each  one  angle  of  the 
large,  which  are  complements  of  each  other.  Thus,  in  the  tri- 
angle ABC,  right  angled  at  A,  if  B=6o°,  C  must  equal  30° 


for  the  sum  of  the  angles  is  180^.  And  so  in  triangles  ABD, 
and  ADC,  right  angled  at  D,  if  B  is  60^,  and  C  30^,  for  same 
reason  the  angle  BAD  must  be  30°,  and  DAC,  60°. 

*' Second,  because  of  the  uniform  divergence  of  the  sides  of 
an  angle,  the  sides  opposite  equal  angles,  in  similar  triangles, 
are  proportional.     That  is,  BD  :  AD::  AD  :  DC. 

**  Third,  also  because  of  the  uniform  divergence  of  the  sides 
of  an  angle — BC  and  AB  being  opposite  equal  angles  (right 
angles)  of  the  two  triangles  ABC  and  ABD;  and  AB  and 
BD  opposite  equal  angles  (ACB  and  BAD)  of  the  same  tri- 
angles— BC  :  BA::BA  :  BD.  For  the  same  reasons  BC  : 
AC::  AC  :  DC  in  the  triangles  ABC  and  ADC 

Proposition  XV. 
*The  square  of  the  hypotenuse  of  a  right  triangle  is  equal  to  the  mm 
of  the  squares  of  the  other  two  sides.* 


32     . 


ELLEN   OR 


'•This,  as  introduced  here,  is  properly  a  corollary  to  Propo- 
sition XIV. 

"Thus,  in  that  proposition, 

(AC)2=BCXDC 
and  (AB)2=BCXBD 
Therefore  (AC)2  +  (AB)2=BC  (BD+DC)  =  (BC)2 

*'  It  can  also  be  illustrated  and  proven  by  experiment,  thus :  " 


i 1 — L_ 


**  And  why  should  this  be?"  I  asked. 

**The  old  Pine  might  as  well  ask  why  it  should  not  be,"  she 
answered.  '^The  sides  of  all  triangles  must  have  a  certain  fixed 
relation  to  their  angles,  and  hence,  also,  the  squares  of  these 
sides.  Evidently  this  proportion  exists  because  the  sum  of  the 
other  two  angles  is  equal  to  a  right  angle. 


'  Corollary  I. — The  square  of  either  side  about  the  right  angle  is 
equal  to  the  difference  of  the  squares  of  the  other  two  sides. 

•Corollary  II. — The  diagonal  of  a  square  is  equal  to  the  side  multi- 
j)Hed  by  the  square  root  of  two. 


33 


WHISPERINGS    OF   AN   OLD    PINE 
Proposition  XVI. 

*  If  through  a  fixed  point  within  a  circle  two  chords  are  drawn,  the 
product  of  the  two  segments  of  one  is  equal  to  the  i)rodact  of  the  two 
segments  of  the  other.' 


"Because  of  the  uniform  curvature  of  the  circumference. 

**  Ellen  will  illustrate.     Let  the  point  be  the  centre.     Then 


all  chords  will  be  diameters,  and  all  segments  radii.  Hence, 
the  segments  being  equal,  their  products  must  be  equal. 

"If  now  we  move  one  diameter,  as  BD,  constantly  to  the 
left  (B'D',  B"D",  etc.),  it  will  finally  disappear  as  a  chord  at 
A,  and  the  product  of  its  two  segments  will  vary  uniformly 
from  BCxCD  too. 

"  The  products  of  the  other  segments,  A  C  X  C  K,  A  C'  X  C  E, 
AC"X  C"E,  etc.,  also  vary  uniformly  and  between  the  same  ex- 
tremes, the  product  of  the  radii  and  zero.  But  this  being  true, 
it  is  also  true  that  the  corresponding  products  of  these  seg- 
ments will  constantly  equal  each  other.  The  same  will  be  true  if 
the  chords  are  not  perpendicular  to  each  other.     But,  as  Ellen 


34  ELLEN   OR 

has  shown,  with  every  diameter  and  its  parallel  chords,  all 
chords  are  included;  and  therefore  where  chords  cross  each 
other  within  a  circle,  the  products  of  their  segments  are  equal." 

**And  does  Ellen  think,"  I  asked,  "that  always  when  two 
quantities  varj'  thus  between  limits,  they  include  every  possible 
intermediate  value?" 

**Most  certainly  they  do,"  she  replied,  "just  as  the  swinging 
pendulum  includes  every  possible  position  between  the  limits  of 
its  arc. 

"In  the  problem  considered  there  are  three  factors — the 
diameter,  crossing  chord,  and  circumference  of  the  circle. 
Starting  at  zero,  the  diameter  is  divided  into  two  segments  by 
the  cutting  chord,  and  as  that  chord  moves,  one  of  these  seg- 
ments is  uniformly  lengthened,  and  the  other  shortened,  until 
they  become  equal.  Because  of  the  principle  that  the  product 
of  two  factors,  whose  sum  is  constant,  is  largest  when  the  factors 
are  equal,  and  hence  such  product  increases  or  decreases  with 
absolute  uniformity  as  the  factors  approach,  or  recede  from, 
equality,  the  product  of  these  segments  of  the  diameter  will 
continuously  increase  until,  as  radii,  the  segments  are  equal. 
From  this  point  until  they  disappear  the  conditions  are  ex- 
actly reversed. 

"  So,  too,  the  segments  of  the  other  chord,  because  of  the 
absolutely  even  curvature  of  the  circumference,  beginning  at 
zero,  gradually  and  uniformly  increase  until  they  reach  their 
greatest  length  at  the  centre,  when  the  conditions  arc  reversed 
until  they  disappear.  And  these  segments  are  all  the  time 
equal  to  each  other,  their  product  increasing,  like  that  of  the 
other  segments,  until  they  reach  their  greatest  length,  and  then 


WHISPERINGS   OF  AN   OLD    PINE 


35 


decreasing  with  the  same  uniformity  until  they  disappear. 
Under  such  conditions,  the  products  of  the  segments,  starting 
equal,  must  remain  equal,  according  to  the  universality  of  nat- 
ural law. 

Proposition  XVII. 
*  If  from  a  point  without  a  circle  a  tangent  and  a  secant  are  drawn, 
the  tangent  is  a  mean  proportional  between  the  whole  secant  and  its 
external  segment.' 


**  In  the  proposition  both  tangent  and  secant  are  limited,  the 
tangent  at  the  point  where  it  touches  the  circumference,  and 
the  secant  where  it  touches  it  the  second  time. 

**The  proposition  is  that  such  a  secant  is  to  such  a  tangent 
as  the  tangent  is  to  the  outside  segment  of  the  secant.  All  the 
conditions  are  controlled  and  indeed  made  possible  by  a  circle. 
Without  it  there  could  be  neither  secant  or  tangent." 

**And  shouldn't  Ellen  say,"  I  asked,  "neither  secant  nor 
tangent?" 

**  Ellen  doesn't  prefer  it,"  she  replied,  '*forto  her  it  is  some- 
what stilted.  We  say,  it  is  a  man  or  a  boy.  Then  we  may  say 
it  is  neither — a  man  or  a  boy. 

"  In  the  proposition  the  tangent  is  constant,  the  secant  vari- 
able.    Wc   will  first  draw  a  line  coinciding  with   the  tangent. 


36  ELLEX   OR 

then  move  it  to  the  left  lengthening  it  and  afterwards  shorten- 
ing it  so  that  it  will  constantly  end  in  the  circumference,  until 
it  again  becomes  a  tangent. 

"  Because  of  the  absolutely  uniform  curvature  of  the  circle  this 
secant  line  will  be  lengthened  within  the  circle,  and  shortened 
without  proportionally,  until  it  passes  through  the  centre  of  the 
circle  after  which  it  is  lengthened  without  and  shortened  within 
proportionally  until  it  again  becomes  a  tangent.  And  therefore 
the  tangent  is  a  mean  proportional  between  the  secant  and  its 
outside  segment. 

"For  the  same  reason,  if  two  or  more  straight  lines  are 
drawn  from  a  point  outside  the  circle  through  the  circumfer- 
ence of  a  circle,  and  extended  until  they  again  touch  the 
circumference,  they  are  reciprocally  proportional  to  their  ex- 
ternal segments.     See  Figure,  page  19. 


'DEFiNmoN. — The  projection  of  a  straight  line  AB  upon  another 
straight  line  M  N,  is  the  portion  of  M  N  included  between  the  perpen- 
diculars let  fall  from  the  extremities  of  A  B  upon  M  N. 

Proposition  XVIII. 
*In  any  triangle  the  square  of  the  side  opposite  an  acute  angle  is 
equal  to  the  sum  of  the  squares  of  the  other  two  sides,  minus  twice  the 
product  of  one  of  these  sides  and  the  projection  of  the  other  side 
upon  it. 


1 

■ 

V' 

TRJ  FIW  TOm     ! 
i  PUBLIC  UBRABT' 

1       '                                ^ 

r^H 

1 

J 

WHISPERINGS   OF  AN   OLD    PINE 


37 


Proposition  XIX. 
*In  an  obtuse-angled  triangle  the  square  of  the  side  opix)site  the 
obtuse  angle  is  equal  to  the  sum  of  the  squares  of  the  other  two  sides, 
plus  twice  the  product  of  one  of  these  sides  and  the  projection  of  the 
other  side  upon  it.* 

"These  are  both  readily  enough  proved  from  Proposition  XV. 
On  general  principles  it  is  very  evident,  first,  that  the  square 
of  either  side  is  equal  to  the  square  of  the  other  two  plus  or  minus 
some  quantity ;  and  second,  since  the  square  of  the  side  oppo- 
site the  right  angle  is  equal  to  the  sum  of  the  squares  of  the 
other  two  sides,  the  square  of  the  side  opposite  an  acute  angle  is 
equal  to  the  sum  of  the  squares  of  the  other  sides  minus  some 
quantity,  and  the  square  of  the  side  opposite  an  obtuse  angle 
is  equal  to  the  sum  of  the  squares  of  the  other  sides  plus  some 
quantity. 


<y--.F 


**Draw  the  triangle  ABC  right  angled  at  C.  With  AC  as  a 
radius  and  C  as  a  centre,  describe  the  arc  AA'E,  and  from  any 
point  upon  this  arc,  as  A',  draw  a  perpendicular,  as  A'D,  to 
BC.  Then  will  (A'R)^  opposite  the  acute  angle  at  C  be  equal 
to  (A'C)2  +  (BC)2-2BCXDC. 

"For  in  the  right  angle  triangle  BA'D,  (A'B)*  =  (A'D)« 


38  ELLEN   OR 

+  (BD)2.  But  (A'D)2=(A'C)2-(DC)2,  as  A'DC  is  a 
right  angle  triangle.  Hence  (A'B;^,  or  the  square  of  the  side 
opposite  the  acute  angle,=:(A'C)2— (DC)2  +  (BD)2.  But 
BD  equals  the  difference  between  BC  and  CD.     Hence 

(A'B)2  =  (A'C)2-(DC)2  +  (BC-DC)2 

=  (A'C)2-(DC)2  +  (BC)2-2BCXDC+(DC)^ 
=  (A'C)2  +  (BC)2-2BCXDC. 

"And  this  means  that  it  is  equal  to  the  squares  of  the  sides 
of  the  original  triangle,  minus  a  rectangle  equal  to  twice  the 
product  of  the  base  by  the  amount  that  the  extremity  of  the 
perpendicular  has  been  rotated  to  the  left  in  forming  the  acute 
angle. 

**  Should  we  revolve  CA  so  as  to  make  the  angle  at  C 
obtuse,  then  the  square  of  the  side  opposite  it  will  be  equal 
to  the  sum  of  the  squares  of  the  other  two  sides  plus  twice  the 
product  of  the  base  by  CF.  For  the  line  BF  represents  the 
sum  of  the  quantities  BC  and  CF,  and  the  square  of  the  sum 
equals  the  square  of  the  first  plus  the  square  of  the  second  plus 
twice  the  product  of  the  first  by  the  second. 

**  This  is  a  demonstration  of  the  proposition,  and  ingenious 
enough,  but  not  a  direct  and  complete  explanation  of  the 
principles  upon  which  it  depends.  It  is  indeed  an  improved 
version  of  the  usual  proof  offered  by  modern  geometries. 

**  Ellen  will  combine  these  two  propositions  and  demonstrate 
them  on  entirely  independent  lines.     Thus : 

"In  any  triangle  the  square  of  a  side  opposite  any  angle 
equals  the  squares  of  the  other  sides  plus  if  obtuse,  or  minus  iC 
acute,  twice  the  product  of  one  of  those  sides  by  the  distance 


WHISPERINGS   OF  AN   OLD    PINE  39 

from  the  projection  of  the  other  side  upon  it.  See  Def- 
inition page  36. 

**  And  this  for  the  only  possible  reason,  because  this  product 
represents  the  difference,  to  be  subtracted  or  added,  as  the  case 
may  be,  between  the  square  of  the  side  opposite  a  right  angle 
and  the  square  of  a  side  opposite  any  other  angle  less  than 
iSo'^. 

**  Draw  the  lines  AD  and  BE  perpendicular  to  each  other. 
Let  FC  coincide  with  AC.  With  C  as  a  centre  and  FC  as  a 
radius  generate  the  circle  A  BDE.  Then  will  AC B  be  a  right 
angle.     See  figure,  page  36. 

"Connect  A  B,BD.  (AB)2  =  (BC)2+(AC)2  ;  and  (BD)^ 
=  (BC)2  +  (CD)2. 

*' Revolving  FC  as  on  a  pivot  at  C,  Ellen  will  now  experi- 
ment with  all  angles  at  C  from  zero  to  180°. 

'*In  the  first  place  this  is  certain,  that  as  an  angle,  even  the 
smallest  possible,  begins  to  show  at  C  there  may  be  a  side 
opposite  to  it.  This  side  Ellen  might  draw  anywhere,  but  she 
will  draw  at  AG,  AH  and  AN. 

'*Let  it  be  supposed,  then,  that  such  a  side  constantly  sub- 
tends an  in<:reasing  angle  at  C,  thus  forming  a  triangle,  the 
other  two  sides  remaining  constant,  this  third  side  must  increase 
continuously  with  the  angle  and  will  represent  every  possible 
straight  distance  connecting  the  other  two  sides,  between  the 
limits  supposed  of  zero  and  180  degrees. 

*'Draw  the  chords  GP,  HQ,  NR  parallel  to  B  E  cutting 
AD  in  the  points  I,  K  and  O.  Complete  the  squares  AG 
UV,  AH  J  J',  ABDE,  ANST  and  WXYZ.  Connect  CG, 
CH,  CN. 


40 


ELLEN   OR 


"Ellen  will  call  the  figure  she  has  drawn  the  figure  of  the 
rectangles,  or  alphabetical  figure.  For  she  has  used  up  in  it 
all    the  alphabet,  and  one    letter  twice;  and  she  thinks  there 


was  never  such  a  variety  of  rectangles  brought  together  before 
in  one  figure. 

"If  the  old  Pine  examines  very  carefully  he  will  see  that 
always,  as  the  angle  at  C  increases  the  revolving  side  will  be- 
come the  diagonal  of  a  rectangle   with  lines  as  G  I,  G  M  ;   H  K, 


wfiisrERTxns  ov  an  old  \nsE 


4t 


HI.,  NO,  NL,  drawn  perpendicular  from  the  end  of  the 
revolving  side  to  ihe  diameters  A  1)  attcl  B  E, 

"  It  has  been  proven  that  the  square  of  the  hypoieniise  is 
equal  to  the  square  of  the  other  two  sides  of  a  right  aiti^le  tri- 
Mglc.      rheref ore  ( A  B ) «  =  ( A  C )  ^  -f-  (  H  C )  ^ . 

**  It  is  most  evident,  as  Ellen  has  pointed  out,  that,  in  any  tri- 
angle, the  -square  of  the  side  opposite  an  acute  anfjlc  must  be 
equal  to  the  square  of  the  other  sides  minus  some  quantit\%  and 
that  opposite  an  obtuse  equal  to  the  square  of  these  sides  plus 
Home  quantit)'.  It  is  equally  certain  that  these  quantities  may 
be  represented  by  rectangles ;  (or  all  such  quantities  may  be 
represented  hy-  rectangles. 

"It  is  also  certain  that  they  are  ciosely  related  to  the  con- 
stant sides  of  the  triangle.  For  it  is  the  square  of  these  sides 
ihal  equals  the  square  of  the  hypotenuse;  and  hence,  as  the 
hypotenuse  is  decreased,  these  sides  must  be  decreased  propor- 
tionally in  order  that  their  squares  should  continue  tn  represent 
the  square  of  the  third  side;  and  such  proportional  decrease, 
or  the  rectangles  produced  by  it,  must  represent  the  difference 
betuxen  the  square  of  the  hypotenuse  and  that  of  the  side 
opposite  any  other  angle.  This  difference  might  be  represented 
by  these  sides  in  several  different  ways,  but  it  can  be  done  in 
no  simpler  way  than  to  let  one  of  thetii  remain  constant  and 
the  oihcr  to  be  uniforml)'  and  constantly  diminished  or  increased 
between  its  full  length  and  zero,  or  zero  and  its  full  length.  In 
this  manner  the  product  of  the  two  would  be  unifornih'  and 
constantly  proportional  to  the  ever- varying  side  opposite  a 
eofistantly  and  uniformly  increasing  or  decreasing  angle. 

*'lfi  the  figure  KUen  finds  that  the  line  which  lies  between 


ft  I  itilaill"  Mfek  r 


42  ELLEN   OR 

the  foot  oi  the  perpendicular  let  fall  from  the  end  of  the 
moving  side  to  the  base,  as  HK,  GI,  etc.,  and  the  vertex  of 
the  varying  angle,  represents  a  uniform  and  constant  increase 
(or  decrease)  in  the  perpendicular,  between  its  limits  of  zero 
and  full  length  (radius),  or  radius  and  zero;  and  therefore  if 
the  base,  remaining  constant,  is  continuously  multiplied  by 
this  constantly  increasing  or  decreasing  line,  the  rectangle 
formed  will  uniformly  be  proportional  to  the  increasing  or  de- 
creasing difference  between  the  square  of  the  third  side  and 
the  square  of  the  other  two. 

"It  only  remains  to  find  out  what  this  proportion  is,  which 
can  be  readily  done  at  the  point  where  the  perpendiciil;  r 
divides  the  base  equally  at  K.  For  the  sides  of  the  triang  e 
AHC  are  equal,  HC  and  AC  being  radii  of  the  same  circle, 
and  AH  and  HC  opposite  equal  angles. 

''Let  the  radius  be  four  feet. 

"(AH) 2^  which  is  the  square  of  the  side  opposite  the  acute 
angle  at  C,  equals  (AC)^.  But  (AC)^  equals  the  rectangle 
AWBC,  and  this  is  equal  to  i(AB)2,  (AB)2  being  the 
square  of  the  hypotenuse  of  the  right  angle  triangle  ACB. 
And  therefore  (AW)^,  equal  to  (AC)^,  equals  i6  (square 
feet),  and  ACX  KC  equals  8. 

"And  therefore  twice  ACxKC  will  represent  the  difference 
between  the  square  of  the  hypotenuse  and  the  square  of  the 
side  opposite  any  other  angle  between  zero  and  i8o^. 

"  And  therefore,  and  for  no  other,  no  other  possible  reason, 
the  square  of  a  side  opposite  any  angle  equals  the  square  of 
the  other  two  sides,  minus  if  acute,  and  plus  if  obtuse,  twice 
one  side  by  the  distance  from  the  angle  considered  to  the  foot 


WHISPERINGS   OF  AN   OLP   PINE 


43 


of  the  perpendicular  let  fall  from  the  opposite  angle  upon  the 
base  or  base  produced  (projection  of  one  side  upon  the  other) 

"  And  this  will  be  equally  true,  whatever  may  be  the  respec- 
tive length  of  the  base  and  perpendicular. 

•*  In  all  such  discussions  it  is  always  to  be  remembered,  and 
therefore  enforced  in  the  instruction,  that  the  quantities  consid- 
ered represent  rectangles;  are  things,  and  not  symbols  This 
Euclid  never  omitted  to  do;  all  of  his  demonstrations  being  of 
this  character.  And  in  this  consists  the  great  value  of  the 
science  of  geometry  as  a  study.  For  it  is  the  perception  and 
comprehension  of  all  these  conditions  which  strengthens  and 
steadies  the  intellect,  and  this  geometr>'  does,  perhaps  more 

? 


A  C         B 

than  any  other  study.  But  the  manipulation  of  the  quantities 
as  symbols,  however  ingenious  it  may  be,  or  convenient  in 
computation,  cannot  in  the  same  manner  instruct  and  develop 
the  mind. 

•*  luiclid  has  illustrated  beautifully  the  fact  that  tiic  square  of 
the  sum  of  two  quantities  is  equal  to  the  square  of  the  first,  plus 
the  square  of  the  second,  plus  twice  the  product  of  the  first  by 
the  second.  And  also  that  the  square  of  the  difference  of  two 
quantities  is  equal  to  the  square  of  the  first,  plus  the  square  of 
the  second,  minus  twice  the  product  of  the  first  by  the  second. 


44  ELLEN    OR 

*'Thus,  let  the  straight  line  AB  be  divided  into  two  parts 
in  C  ;  the  square  of  A B  is  equal  to  the  squares  of  AC,  C B,  and 
twice  the  rectangle  of  AC  and  CB,  that  is  (AB)2  =  (AC)2-|- 
(CB)2+2ACxCB. 

**Upon  AB  describe  the  square  ABED,  and  through  C 
draw  CF  parallel  to  AD  or  BE:  take  FG  equal  to  BC  and 
through  Gdraw  HK  parallel  to  AB  or  DE.  Then  will  GE  be 
equal  to  the  square  on  BC,  and  AE  and  AG  to  the  squares  on 
AB  and  AC  respectively;  also  DG  and  BG  each  equals  the 
rectangle  of  AC  by  BC. 

•'Therefore  (AB)2  =  (AC)*^+2AC  XBC  +  (BC)2. 

**  In  a  similar  manner  it  may  be  demonstrated  that  the  square 
of  the  difference  of  two  quantities  equals  the  square  of  the  first» 
plus  the  square  of  the  second,  minus  twice  the  product  of  the 
first  by  the  second.  If  the  quantities  are  AB  and  BC,  AC  is 
their  difference  and  (AC)2  =  (AB)2— 2  ABxBC  +  (BC)2. 

'*  If  the  old  Pine  remembers  his  trigonometry  he  will  see  that 
these  lines,  as  GM,  HL,  etc.,  which  represent  every  possible 
line  that  can  be  drawn  parallel  to  the  radius  A  C  in  the  quadrant 
ABC  of  a  circle,  are  the  sines,  in  a  circle  whose  radius  is  unity 
of  the  angles  GCB,  HCB,  etc.,  which  are  complements  of  the 
angles  at  C  (ACG,  ACH,  etc.),  which  we  are  considering,  and 
that  the  lines  upon  the  radius,  as  IC,  KC,  etc.,  are  parallel  and 
equal  to  them,  and  hence  vary  as  they  vary;  and  also  that  GI, 
H  K,  etc. — representing  every  possible  line  which  can  be  drawn 
parallel  to  the  radius  BC  in  the  same  quadrant, — are  the  sines 
of  the  varying  angles  at  C  (ACG,  AC  H,  etc.) ;  and  therefore 
equal  and  parallel  to  the  cosines  of  the  complements  to  these 
angles. 


WmSPEklXGS    OF    AX    OLD    PINE 


4S 


"But  these  sines  of  C,  GI,  H  K,  etc.,  are  the  half  chords  of 
the  arcs  GP,  HQ,  etc.,  and  therefore  proportional  to  those 
arcs,  and  also  proportional  to  the  halves  of  those  arcs,  and  their 
chords,  which  last  chords  are  the  sides  opposite  the  varying 
angles  at  C,  Ellen  uses  the  word  proportional  in  its  general 
sense. 

**It  follows  that  as  these  sines  GI,  H  K.  etc.,  vsiry  with  the 
angle  at  C.  the  sines  GM,  H-L,  etc,  of  the  complement  of  this 
angle,  which  are  parallel  and  equal  to  the  cosines  of  C  (IC, 
KC,  etc.),  will  vary  equally.  And  huncc  the  relationship  or 
proportion  between  them  is  always  the  same. 

**And  as  at  its  limit,  when  the  rcvolvint^  perpendicular  B  C 
(see  Figure,  page  40)  coincides  in  direction  with  the  base  AC, 
the  difference  betw^een  them,  if  any,  will  be  some  line  as  AK, 
which  will  represent  the  side  opposite  the  acute  angle  at  C. 

"Therefore  the  square  of  AK  (representing  the  difference 
between  the  two  quantities  AC  and  KC,  and  also  representing 
the  side  opposite  the  acute  angle),  equals  (AC)^ +  (KC)' — 
2ACXKC. 

♦'And  this  is  another  and  vxry  simple  demonstration  of  the 
proposition. 

"Thus,  if  the  perpendicular  and  base  are  both  four,  we 
shall  have,  when  they  coincide,  o2^(AC)^+(FC)-  — 2A  Cx 
FC^(4)^  +  (4)^-8X4=0. 

**  If  the  perpendicular  is  2  and  base  4  wc  will  have  2^ (side 
opposite  acute  angle)=:4^-l-22  — (4X2)X2=4, 

**  And  whichever  or  whatever  value  we  give  to  the  base  and 
perpendicular,  the  same  proportion  will  verify  again  at  the 
angle  of  60^,  at  the  right  angle,  and  at   the  angle    of    120^. 


46  ELLEN   OR 

But  this  is  entirely  unnecessary;  for,  as  Ellen  has  shown,  this 
proportion  holds  true  for  all  valves.     It's  dreadfully  funny!" 

"Ellen  is  a  very  busy  girl,"  I  replied,  "and  sports  with  math- 
ematics as  the  wind  tosses  (ne  foam  upon  the  ocean." 

"The  old  Pine  continues  to  flatter  Ellen,"  she  answered; 
*'  but  this  Ellen  thinks,  that  mind  is  able  to  sport  with  all  math- 
ematical principles.     For  these  are  comparatively  simple. 

"  By  continued  study  and  constant  familiarity  the  mind  comes 
to  consider  certain  mathematical  truths,  of  the  kind  that  we  call 
axioms,  as  self-evident.  But,  as  Ellen  thinks,  all  will  become 
equally  self-evident  as  the  mind  continues  to  study  them,  how- 
ever obscure  they  may  appear  at  first.  Nothing  is  self-evident 
until  one  has  had  an  opportunity  to  study  and  learn  it. 

PROPOsmoN  XX. 

*  The  bisector  of  an  angle  of  a  triangle  divides  the  opposite  side  into 
segments  which  are  proportional  to  the  other  two  sides.* 


"Because  of  the  uniform  divergence  of  the  sides  of  an  angle. 

''Thus  in  the  triangles  ABD  and  ADC,  the  side  AD  is 
common  and  the  angles  at  A  equal.  Therefore  BD  and  DC, 
whose  lengths  depend  upon  AB  and  AC,  will  be  proportional 
to  ABand  AC. 

"This  Ellen  has  explained  more  fully  in  Proposition  XIV. 


■ 

I 

^M 

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1 

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48  ELLEN   OR 

**  Ellen  would  combine  these  propositions  in  one,  with  two 
corollaries  as  follows : 

Proposition  I. 
"Two  rectangles  having  equal  bases  and  equal  altitudes  are 
equal. 


**  Because  in  every  respect  equal. 

"Corollary  I. — ^The  areas  of  two  rectangles  having  equal 
bases  arc  to  each  other  as  the  altitudes. 

**  Corollary  II. — ^The  areas  of  two  rectangles  having  equal 
altitudes  are  to  each  other  as  their  bases. 

PROPOsmoN  IV. 

'  The  area  of  a  rectangle  is  equal  to  the  product  of  its  base  and  alti- 
tude, prtwided  the  unit  of  area  is  a  square  whose  side  is  the  linear  unit.' 

"The  last  part  is  utterly  senseless.  The  area  of  a  rectangle 
is  equal  to  the  product  of  its  base  and  altitude  under  any  pos- 
sible circumstances. 

PROPOsmoN  V. 
*  The  area  of  a  parallelogram  is  equal  to  the  product  of  its  base  and 
altitude.' 

*'  Because,  this  represents  the  number  of  times  that  the  base> 
as  a  standard  of  measure,  is  contained  in  the  parallelogram. 


WHISPERINGS  OF  AN   OLD   PINE  49 

*CoROLLARV  I. — Parallelograms  having  equal  bases  and  equal  alti- 
tudes are  equivalent. 

'Corollary  II. — The  areas  of  any  two  parallelograms  are  to  each 
other  as  the  products  of  their  bases  and  altitudes. 


'Corollary  III. — The  areas  of  two  parallelograms  having  equal  bases 
are  to  each  other  as  their  altitudes ;  the  areas  of  two  parallelograms 
having  equal  altitudes  are  to  each  other  as  their  bases. 

Proposition  VI. 

*  The  area  of  a  triangle  is  equal  to  one-half  the  product  of  its  base 
and  altitude.* 

**  Because  it  is  half  a  rectangle  or  half  a  parallelogram  having 
equal  base  and  altitude. 

** Ellen  would  say:  The  area  of  a  triangle  is  equal  to  the 
product  of  the  line  drawn  parallel  to  the  base  and  connecting 
the  middle  points  of  the  other  two  sides,  by  the  altitude. 

**  Because  a  triangle  may  be  considered  to  be  composed  of  a 
series  of  contiguous  straight  lines,  each  uniformly  shorter  than 
the  preceding,  extending  from  the  base  to  the  apex,  so  that  the 
mean  or  average  line  would  be  situated  at  half  the  altitude. 

'Corollary  I. — Triangles  having  equal  bases  and  equal  altititudes 
are  equivalent. 

'Corollary  II. — ^The  areas  of  any  two  triangles  are  to  each  other  is 
the  product  of  their  bases  and  altitudes. 

'Corollary  III.— The  areas  of  two  triangles  having  equal  bases  are 


50  ELLEN   OR 

to  each  other  as  their  altitudes ;  the  areas  of  two  triangles  having  equal 
altitudes  are  to  each  other  as  their  bases. 

Proposition  VIL 
'  The  area  of  a  trapezoid  is  equal  to  the  product  of  its  altitude  and 
one  half  the  sum  of  its  bases.* 

**  Because  the  non-parallel  sides  arc  straight  lines,  and  there- 
fore one-half  the  sum  of  the  bases  represents  the  average 
length  of  the  bases. 

'Corollary. — The  area  of  a  trapezoid  is  equal  to  the  product  of  its 
altitude  and  the  line  joining  the  middle  points  of  the  non-parallel  sides.* 

"  Because  such  line  represents  the  average  length  of  the  par- 
allel sides  of  the  trapezoid. 

**  Ellen  would  make  the  corollary  the  proposition,  and  the 
proposition  the  corollary. 

**  Ellen  uses  lOO  words  in  demonstration  of  these  seven  proposi- 
tions; or  143  with  double  demonstration  of  the  sixth;  the 
book  617  directly  and  7277  in  propositions  referred  to,  or  in 
all  7894. 

PROPOsnioN  VIII. 

'The  areas  of  two  triangles  which  have  an  angle  of  one  equal  to  an 
angle  of  the  other  are  to  each  other  as  the  products  of  the  sides  includ- 
ing those  angles.' 

**  Because  the  area  of  every  triangle  consists  of  the  space  be- 
tween two  sides,  and  therefore  the  areas  of  two  triangles  which 
have  an  equal  angle  will  depend  upon  the  length  of  each  of  the 
sides  including  the  equal  angles,  and  hence  is  proportional  to 


^TIISPERINGS   OF  AN   OLD   PINE  5  I 

the  products  of  these  sides.  For  if  a  variable  depends  upon 
each  of  two  other  variables,  it  is  proportional  to  their  product. 
Thus  if  ten  boards  have  the  same  length,  but  different  width, 
their  area  will  be  proportional  to  the  one  variable  of  width ; 
but  if  each  board  varies  in  both  width  and  length,  its  area  will 
be  proportional  to  the  product  of  the  two  variables. 

pROPOsmoN  IX. 
'The  areas  of  two  similar  triangles  are  to  each   other  as  the  squares 
of  any  two  homologous  sides.* 

*'  Because  the  areas  are  to  each  other  as  the  products  of  their 
altitudes  and  bases,  since  they  consist  of  one-half  such  product ; 
and  their  homologous  sides  and  altitudes  are  proportional. 

PROPOsrrioN  X. 
'The  areas  of  two  similar  polygons  are  to  each  other  as  the  squares 
of  any  two  homologous  sides.' 

*•  Because  similar  triangles  are  in  such  proportion,  and  similar 
polygons  may  be  divided  into  similar  triangles. 

Proposftion  XI.  • 

*The  square  described  on  the  hypotenuse  of  a  right  [angle] 
triangle  is  equivalent  to  the  sum  of  the  squares  on  the  other  two  sides.' 

**  Because  it  is.  Try  it.  Let  the  sides  of  a  right  angle  tri- 
angle be  respectively  3,  4  and  5  inches.  Construct  squares  on 
these  sides.  They  will  consist  of  9,  16  and  25  square  inches. 
See  Figure,  page  28. 


52  ELLEN   OR 

"  If  once  so,  always  so,  because  of  the  universality  of  natural 
law. 

Corollary. — The  square  on  either  side  about  the  right  angle  is 
equivalent  to  the  difference  of  the  squares  on  the  hypotenuse  and  on 
the  other  side.' 

"  Ellen  uses  203  words  to  demonstrate  these  four  propositions, 
to  383  directly  and  4905  indirectly  in  the  book. 

**  In  Ellen's  discussion  of  Proposition  XIX,  Book  III,  which 
showed  that  the  side  opposite  an  acute  angle  was  equal  to  the 
square  of  the  other  two  sides  minus  twice  a  rectangle,  and  that 
opposite  an  obtuse  angle,  these  squares  plus  twice  a  rectangle, 
this  proposition  was  fully  demonstrated ;  it  following  of  neces- 
sity that  the  square  of  the  side  opposite  a  right  angle  was 
exactly  equal  to  the  squares  of  the  other  two. 


TKF  VFW  yr.-^i: 


l.L 


WHISPERINGS   OF  AN   OLD   TINE  53 


IV. 
BOOK   V. 

REGULAR   POLYGONS   AND   CIRCLES. 

•*  I.  A  regular  polygon  is  both  equilateral  and  equiangular; 
a  circle  may  be  circumscribed  about  it,  and  also  in  it. 

"2.  Similar  polygons  are  polygons  which  have  the  angles  of 
one  equal  to  the  angles  of  the  other,  each  to  each,  and  the  cor- 
responding or  homologous  sides  proportional. 

'•3.  The  common  centre  of  the  circumscribed  and  inscribed 
circles  is  the  point  from  which  the  sides  and  angles  of  a  regular 
polygon  are  equally  distant;  it  is  also  its  centre  of  gravity,  and 
is  called  the  centre  of  a  regular  polygon. 

"4.  The  angle  formed  by  drawing  lines  from  the  centre  to 
the  extremities  of  any  side  is  called  the  angle  at  the  centre.  It 
is  equal  to  four  right  angles  divided  by  the  number  of  sides 
of  the  polygon. 

**  5.  The  apothem  is  the  .shortest  distance  from  the  centre  to 
-any  side. 

**6.  The  apothem  is  equal  to  the  radius  of  the  inscribed 
circle. 

"  7.  The  approximate  value  of  the  ratio  of  a  diameter  to  its 
circumference  is  3.1 416,  and  is  called  tt. 

Propositions  L,  II. 
'•  Included  in  definitions. 


54  ELLEN   OR 

Proposition  III. 
'Two  regular  polygons  of  the  same  number  of  sides  are  similar/ 

"  Self  evident  from  definitions. 

Proposition  IV. 

'In  two  regular  polygons  of  the  same  number  of  sides,  two  corre- 
sponding sides  are  to  each  other  as  the  radii  or  as  the  apothems.' 


**  Because  these  sides  with  their  radii  and  apothems  form 
triangles  which  are  mutually  equiangular,  and  therefore  their 
homologous  sides  proportional. 

'Corollary  I. — The  perimeters  of  two  regular  polygons  of  the  same 
number  of  sides  are  to  each  other  as  their  radii  or  as  their  apothems.* 

**  Because  the  homologous  sides  are  in  this  ratio ;  the  perim- 
eter representing  the  whole,  of  which  a  side  is  a  part. 

'Corollary  II. — The  areas  of  two  regular  polygons,  of  the  same  num- 
ber of  sides,  are  to  each  other  as  the  squares  of  their  radii  or  as  the 
squares  of  their  apothems.' 

**  Because  they  are  to   each  other  as  the   product  of    their 


WHISPERINGS   OF  AN  OLD   PINE  55 

perimeters  by  their  apothems ;  and  their  perimeters  are  to  each 
other  as  their  radii  or  apothems. 

PROPOsmoN  V. 
'The  circumference  of  a  circle  is  greater  than  the  perimeter  of  an 
inscribed  polygon.' 

"  Because  the  arc  of  a  circle  is  longer  than  its  chord. 

PROPOsmoN  VI. 

*The  circumference  of  a  circle  is  less  than  the  perimeter  of  a  cir 
cumscribed  polygon  or  any  enveloping  line.' 

**  Because  contained  within  it. 

PROPOsmoN  VII. 
'I.  If  one  regular  inscribed  polygon  has  twice  as  many  sides  as 
another,  its  perimeter  and  area  are  greater  than  those  of  the  other.* 

•'The  perimeter  is  longer  because  two  sides  between  any  two 
points  are  longer  than  one ;  and  the  area  is  greater  because 
representing  more  space. 

*  II.  If  one  regular  circumscribed  polygon  has  twice  as  many  sides  as 
another,  its  perimeter  and  area  are  less  than  those  of  the  other.* 

•*  Vvr  similar  reasons  to  those  given  in  Case  I. 
**  ICllcn  uses  121  words  to  demonstrate  these  seven  propositions 
to  669  directly  and  2 161  indirectly  in  book. 

Proihjsition  VIII. 
'  By  doubling  an  indefinite  number  of  times  the  number  of  sides  ol  a 
regular  f>olygon  inscribed  in  a  given  circle  : 


56  ELLEN   OR 

(    *  I.  The  apothem  can  be  made  to  differ  from  the  radius  by  less  than 
any  assigned  quantity. 

'  IL  The  square  of  the  apothem  can  be  made  to  differ  from  the  square 
of  the  radius  by  less  than  any  assigned  quantity. 
{      .     ' 

Proposition  IX. 

'The  circumference  of  a  circle  is  the  limit  which  the  perimeters  of 
regular  inscribed  and  circumscribed  polygons  approach  when  the  num- 
ber of  their  sides  is  doubled  an  indefinite  number  of  times ;  and  the 
area  of  the  circle  is  the  limit  of  the  area  of  these  polygons.* 

**  In  the  demonstration  of  these  two  propositions  it  is  stated 
that  we  can  make  the  difference  *  less  than  any  assigned  quan- 
tity/ or,  *as  small  as  we  please.'  This  might  be  true  if  the 
quantity  assigned  was  large  enough,  or  if  we  didn't  please  to 
have  something  too  small.  These  propositions  are  entirely  un- 
intelligible as  illustrated  by  these  phrases.  Thus  if  anyone 
should  undertake  to  extract  the  square  root  of  2,  he  might 
spend  an  eternity  at  it  without  an  exact  result. 

"Let  the  old  Pine  consider  for  a  moment  what  Ellen  has 
before  suggested,  that  through  the  pupil  of  the  smallest  eye  the 
whole  material  universe  may  be  reflected,  and  he  may  perhaps 
begin  to  realize  that  the  infinitely  small  is  as  remarkable  and  as 
possible  as  the  infinitely  large.  Nor  does  Ellen  know  of  any 
reason  why  it  should  not  be ;  nor  does  she  know  where  the  prob- 
lem of  its  consideration  may  end,  or  in  what  manner. 

Proposition  X. 

*The  ratio  of  the  circumference  of  a  circle  to  its  diameter  is  the  same 
for  all  circles.' 


WHISPERINGS   OF  AN.  OLD   PINE  57 

"  Self-evident  from  the  nature  of  a  circle,  for  the  extremities, 
of  its  diameter  may  generate  its  circumference. 

PROPosmoN  XI. 
*  'ITic  area  of  a  regular  polygon  is  equal  to  one-half  the  product  of  its 
apothem  and  perimeter/ 


"  Because  composed  of  triangles  whose  altitude  is  the  apo- 
them, and  the  sum  of  whose  bases  is  the  perimeter  of  the 
polygon ;  and  because  the  area  of  a  triangle  equals  one-half  the 
product  of  its  base  and  altitude. 

••Fifty-four  words  for  two  propositions  to  175  directly  and 
3100  indirectly  in  book. 

Proposition  XII. 

'The  area  of  a  circle  is  equal  to  one-half  the  product  of  its  radius 
and  circumference.* 

•'  Ellen  would  say,  is  equal  to  the  product  of  its  average  cir- 
cumference by  the  radius. 

'•  Because  a  circle  may  be  considered  to  be  composed  of  a 
series  of  contiguous  circumferences,  decreasing  uniformly  in 
length,  and  therefore  whose  mean,  or  average  circumference, 
will  be  situated  at  half  the  distance  between  the  outside  and  the 
centre. 

"Thirty-nine  words  instead  of  2018  in  the  book,  including 


58  ELLEN   OR 

propositions  referred  to.  It  has,  too,  the  advantage  of  being 
within  the  scope  of  our  knowledge, — that  is,  of  being  true, — 
whilst  the  usual  line  of  demonstration  is  not.  Furthermore,  the 
demonstration  Ellen  gives  is  the  real  reason,  and  the  only  pos- 
sible reason  for  the  fact. 

Proposition  XIIL 

'  Given  the  radius  of  a  circle  and  the  side  of  a  regular  inscribed  poly- 
gon, to  find  the  side  of  a  regular  inscribed  polygon  of  twice  the  number 
of  sides.* 

**With  the  radius  generate  a  circumference,  bisect  the  arc 
subtending  the  side  given,  and  connect  its  ends  with  chords. 
These  chords  will  be  the  required  side. 

PROPOsmoN'  XIV. 

*  Given  the  radius  of  a  circle  and  a  side  of  a  regular  circumscribed 
polygon,  to  find  the  side  of  a  regular  circumscribed  polygon  of  twice 
the  number  of  sides.' 


*'With  the  radius  generate  a  circumference.  Complete  the 
circumscribed  polygon.  Draw  radii  to  the  points  of  tangency 
of  the  sides  of  this  polygon.  Bisect  the  arcs  included  between 
these  points,  and  at  the  points  of  division  draw  tangents  to  the 


WHISPERINGS   OF  AN  OLD   PINE 


59 


<ircu inference    intersecting    the   sides    of    the    circumscribed 
polygon.     The  polygon  thus  formed  will  be  the  one  required. 

**  Eighty-three  words  to  explain  the  two  propositions,  to  178 
-directly  and  1 349  in  propositions  referred  to.  or  1527  in  the  book. 

PROPosmoN  XV. 
*To  compute  the  ratio  of  the  circumference  of  a  circle  to  its  diameter 
approximately.' 

•*  Divide  the  circumference    of   any    circle  by  its   diameter. 
Eight  words  to  1624  in  book,  including  propositions  referred  to. 

"The  usual  modern  method  of  computation  condensed  is  as 

follows : 

c 


"With  O  as  a  centre  and  AO  as  a  radius,  describe  the  circle 
AHC.  Let  AB  be  a  side  of  a  regular  inscribed  hexagon, 
which  is  equal  to  the  radius.  Draw  OC  perpendicular  to  AB 
cutting  it  at  D;   join  AC  and  AO. 

Then    (AO)2=:(AD)2  +  (DO)2. 
(DO)2=(AO)2-(AD)2. 
DO=V(AOy^-(AD)2 
But       CD=CO-DO. 
And      (AC)2=(AD)2  +  (CD)2. 
Hence  AC=x^{AD)'^-f{CDy^. 


6o  ELLEN   OR 

"But  AC  equals  the  side  of  a  polygon  with  double  the  sides- 
of  length  AB.  This  process  of  thus  doubling  the  sides  of  the 
enclosed  polygon  may  be  indefinitely  continued,  and  if  the 
radius  is  known  the  length  of  <he  circumference  of  the  circle 
thus  approximately  obtained. 


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WHISPERINGS   OF  AN   OLD   PINE  6 1 


V. 

BOOK  VI. 
Planes,  Diedral  and  Polyedral  Angles, 

DEFINITIONS. 

"  I.  A  plane  is  a  surface  which  does  not  change  its  direction. 

"  2.  A  straight  line  is  perpendicular  to  a  plane,  and  the  plane 
to  a  straight  line  when  the  angles  formed  by  them  are  right 
angles. 

"3.  A  straight  line  is  parallel  to  a  plane,  and  a  plane  to  a 
straight  line,  when  they  are  everywhere  equally  distant  from 
each  other. 

'*4.  Two  planes  are  parallel,  when  if  continued  indefinitely 
they  would  never  meet.  Parallel  planes  are  everywhere  equally 
distant  from  each  other. 

**S.  A  diedral  angle  is  the  amount  of  divergence  of  two 
planes.  The  line  in  which  the  planes  meet  is  called  the  edge 
of  the  angle,  and  the  planes  themselves  are  called  faces  of  the 
angle. 

"  6.  The  measure  of  a  diedral  angle  is  the  same  as  that  of  a 
plane  angle  formed  by  two  straight  lines,  one  in  each  face,  and 
both  perpendicular  to  the  edge  at  the  same  point.  A  diedral 
angle  may  be  acute,  obtuse,  or  a  right  angle.  In  the  latter 
case,  the  faces  are  perpendicular  to  each  other. 

"  7.  A  polyedral  angle  is  the  amount  of  divergence  of  several 


62  ELLEN    OR 

planes  meeting  at  a  common  point.  This  point  is  called  the 
vertex  of  the  angle ;  the  lines  in  which  the  planes  meet  are 
called  edges  of  the  angle,  and  the  planes  lying  between  the 
edges,  faces  of  the  angle.     See  Figure,  page  70. 

**8.  A  polyedral  angle  which  has  but  three  faces,  is  called 
a  triedral  angle. 

**  Ellen  will  quote  in  this  book  the  Propositions  as  given  in 
Davies'  Legendre. 

Proposition  I. 

'  If  a  straight  line  has  two  of  its  points  in  a  plane,  it  lies  wholly  in 
that  plane.' 

"Because  neither  a  straight  line  or  a  plane  changes  its 
direction. 

**  Corollary. — ^Through  any  point  of  a  plane,  a  very  great 
number  of  straight  lines  may  be  drawn  which  lie  in  the  plane. 

"  Scholium. — A  very  great  number  of  planes  may  be  passed 
through  a  given  straight  line. 

Proposftion  II. 

'Through  three  points,  not  in  the  same  straight  line,  one  plane  can 
be  passed,  and  only  one.* 

**  Because  neither  a  plane  nor  a  straight  line  changes  its  direc- 
tion ;  and  therefore  if  a  plane  passes  through  a  straight  line  it 
cannot  change  its  direction  except  to  revolve  about  the  line. 
Let  it  revolve  until  it  passes  through  the  third  point  C.  If  it 
revolves  further,   it  will  not  contain  C,  and  therefore  a  straight 


WHISPERINGS   OF  AN   OLD   PINE 


63 


line   partially  determines  the   position  of  a  plane,  and  three 
points,  not  in  the  same  straight  line,  fully  determine  it. 

Proposition  III. 
'The  intersection  of  two  planes  is  a  straight  line.' 


"Because  common  to  both  planes,  and  neither  plane   can 
change  its  direction. 

PROPOsmoN  IV. 

'If  a  straight  line  is  perpendicular  to  two  straight  lines  at  their  point 
of  intersection,  it  is  perpendicular  to  the  plane  of  those  lines.' 


**  Because  the  direction  of  the  plane  must  be  the  same  as  that 
of  the  lines.  For  three  points  not  in  the  same  straight  line 
determine  the  direction  of  a  plane. 

'Corollary  i. — Only  one  perpendicular  can  be  drawn  to  a  plane 
from  a  point  without  the  plane. 

'Corollary  2. — Only  one  perpendicular  can  be  drawn  to  a  plane 
from  a  point  in  that  plane.' 


64 


ELLEN   OR 


"The  book  has  590  words  and  12  propositions  referred  to,  to 
demonstrate  these  self-evident  propositions;  Ellen,  53  words. 

Proposition  V. 

'  If  from  a  point  without  a  plane,  a  perpendicular  is  drawn  to  the 
plane,  and  oblique  lines  drawn  to  different  points  of  the  plane. 

*  I.  The  perpendicular  is  shorter  than  any  oblique  line  : 

'2.  Olique  lines  which  meet  the  plane  at  equal  distances  from  the 
foot  of  the  perpendicular,  are  equal : 

*3.  Of  two  oblique  lines  which  meet  the  plane  at  unequal  distances 
from  the  foot  of  the  perpendicular,  the  one  which  meets  it  at  the  greater 
distance  is  the  longer.' 

"Because  having  the  same  perpendicular  distance  and  a 
longer  horizontal  one. 


'  Scholium. — The  angle  A  B  P  is  called  the  inclination  of  the  oblique 
line  AB  to  the  plane  MN.  The  equal  oblique  lines  A B,  AC,  AD,  are 
all  equally  inclined  to  the  plane  M  N.  The  inclination  of  A  D  is  less 
than  the  inclination  of  any  shorter  line  A  E. 


WHISPERINGS   OF  AN   OLD   PINE 


65 


Proposition  VI. 
'If  from  the  foot  of  a  perpendicular  to  a  plane,  a  straight  line  is 
drawn  at  right  angles  to  any  straight  line  of  that  plane,  and  the  point 
of  intersection  joined  with  any  point  ot  the  perpendicular,  the  last  line 
13  perpendicular  to  the  given  line  of  the  plane.' 


"Because  by  construction  in  the  same  plane  as  the  line 
drawn  perpendicular  to  the  given  line.  See  remarks  under 
Proposition  XVII. 

*  Corollary. — ^The  given  line  BC  is  perpendicular  to  the  plane  of 
the  triangle  A  P  D ;  because  it  is  perpendicular  to  A  D  and  P  D,  at  D. 

Proposftion  VII. 

*  If  one  of  two  parallels  is  perpendicular  to  a  plane,  the  other  one  is 
also  perpendicular  to  the  same  plane.* 

**  Because  having  the  same  direction. 

*  Corollary. — If  two  straight  lines  are  parallel  to  a  third  line  they 
are  parallel  to  each  other. 

Proposition  VIII. 
'  If  a  straight  line  [outside  of  a  plane]  is  parallel  to  a  line  of  a  plane, 
it  is  parallel  to  that  plane.' 

*'  Because  the  plane  on  which  a  line  is  situated  has  the  same 
direction  as  the  line. 


66  ELLEN   OR 

Proposition  IX. 

*  If  two  planes  are  perpendicular  to  the  same  straight  line,  they  are 
parallel  to  each  other.' 

"Because  extending  in  same  direction. 

PROPosmoN  X. 
'  If  a  plane  intersects  two  parallel  planes,  the  lines  of  intersection  are 
parallel.' 

**  Because  equally  a  part  of  the  intersecting  plane,  and  the 
parallel  planes. 

PROPOsmoN  XL 
'  If  a  straight  line  is  perpendicular  to  one  of  two  parallel  planes,  it  is 
also  perpendicular  to  the  other.* 

"Because  the  planes  extend  in  the  same  direction. 

PROPOsmon  XII. 

*  Parallel  straight  lines  included  between  parallel  planes,  are  equal.* 

•*  Ellen  doesn't  understand  what  is  meant  by  'included.' 
"By  definition,  parallel  planes  are  everywhere  equally  distant 

from  each  other.     Then  will  parallel  lines  terminated  by  these 

be  equal. 

"Ellen  has  50  words  to  demonstrate  these  six  propositions; 

the  book,  369  directly,  and  800  more  or  less  indirectly.     Ellen 

gets  awfully  tired  counting  them. 

'  Corollary. — If  a  straight  line  is  parallel  to  any  plane,  then  can  a 
plane  be  passed  through  this  line  parallel  to  the  given  plane. 

Proposition  XIII. 
'  If  two  angles,  not  situated  in  the  same  plane,  have  their  sides  par- 


WHISPERINGS   OF  AN  OLD   PINE 


67 


allely  and  Ijdng  in  the  same  direction,  the  angles  are  equal  and  their 
planes  parallel. 

Proposition  XIV. 
*  If  three  straight  lines,  not  situated  in  the  same  plane,  are  equal  and 
parallel,  the  triangles  formed  by  joining  the  extremities  of  these  lines 
are  equal,  and  their  planes  are  parallel. 


IZ^ 


EMJ 


7 


Proposition  XV. 
*  If  two  straight  lines  are  cut  by  three  parallel  planes,  they  are  divided 
proportionately. 


r^3 


[^ 


S 


/:^7 


'Corollary  i. — If  two  straight  lines  are  cut  by  any  number  of  parallel 
planes,  they  are  divided  proportionally. 

'Corollary  2. — If  any  numbered  of  straight  lines  are  cut  by  three 
parallel  planes,  they  are  divided  proportionally.' 

"Because  the  parallel  planes  are  everywhere  equally  distant 
from  each  other. 


68  ELLEN    OR 

**  Eleven  words,  to  78  in  the  book,  and  250  more  in  proposi- 
tions referred  to. 

PROPOsniON  XVL 

*  If  a  straight  line  is  perpendicular  to  a  plane,  every  plane  passed 
through  the  line  is  also  perpendicular  to  that  plane.* 

**  Seventy-eight  words  are  wasted  upon  this  proposition, 
which  is  too  puerile  to  answer.  Propositions  XIII.,  XIV.  and 
XVII.  are  equally  self-evident. 

'Corollary.  If  three  lines  are  perpendicular  to  each  other  at  a 
common  point,  each  line  is  perpendicular  to  the  plane  of  the  two 
others,  and  the  three  planes  are  perpendicular  to  each  other. 

Proposition  XVII. 

*  If  two  planes  are  perpendicular  to  each  other,  a  straight  line  drawn 
in  one  of  them,  perpendicular  to  their  [line  of]  intersection,  is  perpen- 
dicular to  the  other.' 

**  Because  it  extends  in  the  same  direction  as  its  plane. 


PROPOsnioN  XVin. 

*  If  two  planes  cut  each  other,  and  are  perpendicular  to  a  third  plane 
their  intersection  is  also  perpendicular  to  that  plane.' 


WHISPERINGS   OF  AN  OLD    PINE 


69 


"  Because  it  is  a  part  of  both  planes  and  therefore  must 
extend  in  the  direction  common  to  the  two. 

Proposition  XIX. 

*  The  sum  of  any  two  of  the  plane  angles  formed  by  the  edges  of  a 
triedral  angle,  is  greater  than  the  third.' 


**  Because  of  the  relativity  of  sides  and  angles.  The  two  sides 
AC  and  CB,  being  two  lines,  are  longer  than  the  straight  line 
AB  between  the  same  points. 

Proposition  XX. 

'The  sum  of  the  plane  angles  formed  by  the  edges  of  any  polyedral 
angle  is  less  than  four  right  angles.' 

"As  has  been  shown,  the  sum  of  all  the  angles  in  a  plane 
formed  by  straight  lines  intersecting  at  a  point  is  four  right 
angles.  As  these  straight  lines  are  moved  out  of  a  plane  and 
approach  each  other,  as  they  must,  when  they  form  the  edges 


^o 


ELLEN   OR 


of  a  polyedral  angle,  their  difference  in  direction  is  diminished, 
and  hence  the  sum  of  the  angles  formed  by  them  will  be  less 
than  four  right  angles. 


"  Seventy-four  words,  to  294  in  book. 

Proposftion  XXL 

*If  the  plane  angles  [ASC,  DTP,  etc.]  formed  by  the  edges  of  two 
triedral  angles  are  equal,  each  to  each,  the  planes  of  the  equal  angles 
are  equally  inclined  to  each  other.* 

**  For,  if  the  plane  angles  are  equal,  there  is  the  same  differ- 
ence of  direction  in  the  lines  (AS,  CS,  BS  and  DT,  FT, 
ET),  forming  them,  but  these  lines  are  the  intersections  of  the 
planes.  And  therefore  the  planes  forming  these  intersections 
must  have  the  same  difference  of  direction. 

**  Forty-six  words,  to  238  in  book. 

"Corollary. — If  two  plane  angles  of  two  triedral  angles 
are  equal  each  to  each,  and  the  inclination  of  their  faces  is  the 
same,  then  are  the  remaining  plane  angles  equal  to  each  other. 


WHISPERINGS   OF  AN   OLD    PINE 


71 


*•  Because  the  lines  which  form  the  plane  angles  are  the  lines 
of  intersection  of  the  planes. 

"  Because  two  plane  angles  of  a  triedral  angle  and  the  inclina- 
tion of  their  faces  decide  the  third  plane  angle. 


*•  Ellen  omits  scholiums  in  regard  to  the  coincidence  of  angles, 
as  the  principles  upon  which  their  equality  depends  are  entirely 
independent  of  such  coincidence. 


72 


ELLEN   OR 


VI. 

BOOK  VII. 
POLYEDRONS. 

DEFINITIONS. 

**  I.  A  polyedron  is  a  figure  bounded  by  polygons. 

"The  bounding  polygons  are  the  faces  of  the  polyedron; 
where  these  polygons  meet,  its  edges;  where  the  edges  meet, 
its  vertices. 

"2.  A  prism  is  a  polyedron  two  of  whose  faces,  called  the 
bases,  are  equal  polygons,  having  their  homologous  sides  par- 


RE(;rijvR 

PYRAMID. 


FRUSTUM  OF 
PYRAMID. 


allel.  The  other  faces  are  formed  by  planes,  passing  through 
the  corresponding  sides  of  the  bases,  and  are  therefore  parallel- 
ograms. 

"The  parallelograms  form  the  lateral  or  convex  surface  of 
the  prism,  and  their  intersections  its  lateral  edges. 


w 

1 

I 

I 

K 

«                             1 

'  ^B 

1 

WHISPERINGS   OF   AN   OLD    I*1NE 


73 


"3.  The  altitude  of  a  prism  is  the  pcrpendicylar  distance 
betxi'een  the  planes  of  its  bases. 

'^4.  A  right  prism  is  one  whose  lateral  edges  are  perpendic- 
ular to  the  bases, 

•*  In  this  case,  any  lateral  edge  is  equal  to  the  altitude. 

•*  5»  An  obliqe  prism  is  one  whose  lateral  edges  are  oblique 
to  the  bases. 

"In  this  case,  any  lateral  edge  is  greater  than  its  altitude. 

•*6,  Prisms  are  named  from  the  number  of  sides  of  their 
bases;  a  triangular  prism  is  one  whose  bases  are  triangles;  a 
cntagonal  prism  is  one  whose  bases  are  pentagons,  etc. 

•*7*  A  parallelopiped  is  a  prism  whose  bases  are  parallelo- 
grams. 

**  A  right  parallelopiped  is  one  whose  lateral  edges  are  per- 
pendicular to  the  bases. 

**A  rectangular   parallelopiped  is   one  whose   faces  are  all 

:tangles, 

•*  A  cube  is  a  rectangular  parallelopiped  whose  faces  are 
squares. 

•*$•  A  pyramid  is  a  polyedron  whose  base  is  a  polygon  and 
whose  other  sides  are  triangles  which  meet  at  a  point,  called 
the  vertex  of  the  pyramid* 

"The  triangles  form  its  lateral  or  convex  surface ;  their  inter- 
sections its  lateral  edges, 

"9,  Pyramids  are  named  from  the  number  of  sides  of  their 
bases,  triangular,  quadrangular,  etc. 

"  10.  The  altitude  of  a  pyramid  is  the  perpendicular  distance 
from  the  vertex  to  the  plane  of  its  base. 

*'II.  A  regular  pyramid  is  one  whose  base  is  a  regular  poly- 


74  ELLEN   OR 

gon,  and  whose  perpendicular  passes  through  the  centre  of  the 
base. 

"This  perpendicular  is  called  the  axis  of  the  pyramid. 

"12.  The  slant  height  of  a  regular  pyramid,  is  the  altitude  of 
its  triangular  faces  drawn  from  the  vertex. 

"13.  A  truncated  pyramid  is  that  portion  of  a  pyramid 
included  between  the  base  and  any  plane  which  cuts  all  the 
lateral  edges. 

"When  the  cutting  plane  is  parallel  to  the  base,  the  truncated 
pyramid  is  called  a  frustum  of  a  pyramid,  and  the  intersection 
of  the  cutting  plane  with  the  pyramid  is  the  upper  base  of  the 
frustum ;   the  base  of  the  pyramid  its  lower  base. 

"  14.  The  altitude  of  a  frustum  of  a  pyramid  is  the  perpen- 
dicular distance  between  the  planes  of  its  bases. 

"15.  The  slant  height  of  a  frustum  of  a  regular  pyramid  is 
the  altitude  of  any  lateral  face  of  the  frustum. 

"  16.  The  lateral  area  of  a  pyramid  is  the  sum  of  the  areas 
of  its  lateral  faces. 

"  17.  Similar  polyedrons  are  those  which  are  bounded  by  the 
same  number  of  similar  polygons,  similarly  placed. 

**  Parts  which  are  similarly  placed,  whether  faces,  edges,  or 
angles,  are  called  homologous. 

"18.  A  diagonal  of  a  polyedron  is  a  straight  line  joining  the 
vertices  of  two  polyedral  angles  not  in  the  same  face. 

"  19.  The  volume  of  a  polyedron  is  the  space  which  it  occu- 
pies, and  is  generally  expressed  in  terms  of  another  solid  taken 
arbitrarily  as  the  unit  of  measure ;   as  a  cubic  foot,  yard,  or  mile. 

"  20.  Two  figures  are  equivalent  when  their  volumes  are 
equal. 


WHISPERINGS   OF  AN   OLD   PINE  75 

"These  definitions  are  very  complete,  but  as  the  more  recent 
geometry  has  endeavored  to  abbreviate  the  demonstrations,  and 
in  that  respect  to  make  them  more  sensible,  Ellen  will  again 
quote  its  propositions. 

Proposftion  I. 
'The  lateral  faces  of  a  prism  are  parallelograms.' 

'*  Because  they  lie  between  parallel  lines.  Included  in  defi- 
nitions. 

PROPOSmON  II. 

The  sections  of  a  prismatic  surface  made  by  two  parallel  planes  cut- 
ting its  edges  are  equal  polygons.' 

"  Because  mutually  equilateral  and  equiangular. 


Proposition  III. 

*.\ny  two  opposite  faces  of  a  parallelopiped  may  be  taken  as  its 
bases.' 

"Because  all  opposite  faces  are  parallelograms.     Included  in 
definitions. 


1e 


ELLEN   OR 
Proposition  IV. 


'The  lateral  area  of  a  prism  is  equal  to  the  product  of  the  perimeter 
of  a  right  section  and  a  lateral  edge.' 

"  Because  the  lateral  faces  are  parallelograms  whose  areas  are 
the  product  of  the  bases  by  the  altitude.  But  the  perimeter 
of  a  right  section  represents  the  altitude  of  the  lateral  faces, 
and  the  edges  their  bases. 

Corollary. — ^The  lateral  area  of  a  right  prism  is  equal  to  the  prod- 
uct of  the  perimeter  of  its  base  and  its  altitude. 

Proposition  V. 

*Two  right  truncated  prisms  are  equal,  if  three  lateral  edges  of  one  are 
equal  to  the  three  corresponding  edges  of  the  other,  and  the  bases  to 
which  they  are  respectively  perpendicular  are  equal.' 


**  Because  the  three  lateral  edges  determine  the  planes  of  the 
sections  which  complete  the  truncated  prisms. 

Proposition  VL 

*An  oblique  prism  is  equivalent  to  a  right  prism  whose  base  is  a  right 
section  of  the  oblique  prism,  and  whose  altitude  is  equal  to  a  lateral 
edge  of  the  oblique  prism.* 


'Because   by  construction    enclosing   equal   space   (having 


WHISPERINGS   OF  AN   OLD    PINE 


77 


equal  volume).     For  the  two  truncated   prisms  ABCDE-G 
and    A'B'C  D'E'-G'   having  mutually  equal   edges  and  the 


lower  and  upper  bases  of  each  being  mutually  equal  and  par- 
allel, are  equal,  and  the  intermediate  figure  FGNHK-C  is 
common. 

Proposition  VII. 

'The  plane  i)asse(l  through  two  diagonally  opposite  edges  of  a  par- 
allelopiped  divides  it  into  two  equivalent  triangular  prisms.' 

**  Because  dividing  it  into  prisms  having  equal  bases  and 
altitudes.     Sec  figure,  page  ^6. 

**  In  demonstrating  these  seven  propositions  Ellen  uses  124 
words;  the  book,  398  directly,  and  6492  in  propositions  re- 
ferred to. 

Proposition'  VIII. 

'Two  rectangular  parallelopipeds  having  ecpial  bases  are  to  each  other 
as  their  altitudes.' 

*'  Because  in  all  other  respects  they  arc  equal. 


78 


ELLEN   OR 
Proposition  IX. 


'Two  rectangular  parallelopipeds  which  have  one  dimension  in  com- 
mon are  to  each  other  as  the  products  of  the  two  other  dimensions. 


/; 

1- 

/ 

f~  ----, 


Proposition  X. 

*  Any  two  rectangular  parallelopipeds  are  to  each  other  as  the  products 
of  their  three  dimensions.* 


**  Because  the  volume  of  all  rectangular  parallelopipeds  is 
equal  to  the  product  of  their  three  dimensions. 

**  Ellen  makes  these  three  last  propositions  self-evident  in 
24  words.  The  geometry  she  quotes  has  succeeded  in  using 
directly  346,  plus  over  850  in  propositions  referred  to,  or  in  all 
over  1200,  or  fifty  times  as  many.  An  entirely  unnecessary 
performance,  and  alone  a  demonstration  that  the  present 
method  of  teaching  geometry  ought  to  be  and  will  be  super- 
seded. 

Proposition  XI. 

*The  volume  of  a  rectangular  parallelopiped  is  equal  to  the  product 
of  its  three  dimensions,  provided  the  unit  of  volume  is  a  cube  whose 
edge  is  the  linear  unit.' 


^^^^^^^^^^^^^^^^^^^^^^^^^^^r 

■ 

PUBLIC  LIBRARY                    ^^^H 

1 

BRINGS    OF   AN 

'Omitting  the  last  part»  which  is  superfluous,  for  always  its 
volume  is  the  pruduct  of  the  three  dimensions,  this  proposition 
is  self-evident. 

Propositiun  XII. 

'The  volume  of  any   parallelopipcd  is  equal  to  the  product  of  its 
base  and  altitude.' 


"Ellen  considers  this  self-evident  from  the  definitions  of  a 
parallelopiped  and  a  parallelogram.  For  the  volume  of  any- 
thing is  the  space  which  it  encloses,  and  this  is  as  true  of 
a  base  as  of  any  other  figure, 

**In  the  nature  of  things  the  product  of  its  sides  represents 
the  volume  contained  in  the  base,  and  this  multiplied  by  the 
altitude  of  a  parallelopiped  represents  the  number  of  times  such 
surface  or  volume,  for  these  terms  being  applied  to  the  base 
arc  synonymous,  is  contained  in  the  larger  figure. 

"TTicrc  is  so  much  of  this  thmg,  space,  oneway,  and  so  much 
the  other,  and  their  product,  thickness  being  regarded  as  uniu^ 
must  represent  the  total  amount  of  space  included  in  two 
dimensions,  that  is,  included  in  the  base,  of  a  rectangular  lit^ore 

"  Wc  sec  it  illustrated  on  a  larger  scale  in  rows  uf  bricks.     We 
111  suppose  tlierc  are  twelve  bricks  one  way  in  line,  and  ten  the 
"other;  then  there  are  in  the  base  twelve  bricks  taken  ten  times; 
that  i%  twelve  added  ten  times  equals  120,  or  twelve  multiplied 
by  ten  equals  120.      And  therefore  the  product  of  two  dimen- 
sions gives  the  amount  contained  in  them/* 

*^I|  gives  the  amount  of  brick,"  I  said. 

"It  gives  the  amount  of  anything  which  occupies  space/*  she 


8o  ELLEN   OR 

answered;  "and,  if  so,  it  must  give  the  amount  of  space  in 
whatever  space  consists. 

"The  volume,  then,  of  any  figure — that  is,  of  anything — is 
measured  by  the  product  of  its  average  dimensions. 

PROPosmoN  Xin. 

'The  volume  of  a  triangular  prism  is  equal  to  the  product  of  its  base 
and  altitude.' 


"Because   this  equals  the  number  of  times  that  the  base  is 
contained  in  the  altitude.     See  Proposition  XII. 

PROPOsmoN  XIV. 
*  The  volume  of  any  prism  is  equal  to  the  product  of  its  base  and 
altitude.' 

**  Because  this  represents  the  product  of  its  dimensions. 
"  Four  self-evident  corollaries  follow. 

Proposition  XV. 
'The  lateral  edges  of  a  regular  pyramid  are  equal.' 

"Because  they  pass  over  the  same  vertical,  and  equal  hori- 
zontal distances. 


WHISPERINGS   OF  AN   OLD    HNE  8 1 

*CoROLXARV  I. — ^The  lateral  faces  of  a  regular  pyramid  are  equal 
isosceles  triangles. 

'Corollary  II. — ^The  altitudes  of  the  lateral  faces  drawn  from  a  com- 
mon vertex  are  equal. 

PROPOsmoN  XVI. 
'The  lateral  area  of  a  regular  pyramid  is  equal  to  one-half  the  pro- 
duct of  the  perimeter  of  its  base  and  its  slant  height.' 

"Because  one-half  the  perimeter  of  its  base  represents  the 
average  width  of  the  triangles  which  compose  the  lateral  area, 
and  the  slant  height  their  altitude. 

Proposition  XVII. 

'The  lateral  faces  of  a  frustum  of  a  regular  pyramid  are  equal  trape- 
zoids.' 


"  By  construction. 

*  CoROLL\RV. — The  lateral  area  of  a  frustum  of  a  regular  pyramid  is 
equal  to  one-half  the  product  of  the  sum  of  the  perimeters  of  its  bases 
and  its  slant  height.' 

'*  Because  this  represents  the  average  width  of  the  trapezoids 
by  their  altitude. 


82  ELLEN   OR 

Proposition  XVIII. 

*  If  a  pyramid  is  cut  by  a  plane  parallel  to  its  base : 

'  I. — The  lateral  edges  and  the  altitude  are  divided  proportionally. 
*II. — ^The  section  is  a  polygon  similar  to  the  base.' 

**  Because,  parallel  planes  are  everywhere  equally  distant  from 
each  other;  and  because  of  the  uniform  divergence  of  the  sides 
of  each  angle  at  the  vertex. 

'Corollary  I. — The  areas  of  any  sections  of  a  pyramid  parallel  to  its 
base  are  proportional  to  the  squares  of  their  distances  from  the  vertex. 

'Corollary  II. — If  two  pyramids  having  equal  altitudes  are  cut  by 
planes  parallel  to  their  bases  at  equal  distances  from  their  vertices,  the 
sections  thus  formed  will  be  proportional  to  the  bases. 

*  Corollary  III. — If  two  pyramids  have  equal  altitudes  and  equivalent 
bases,  sections  parallel  to  their  bases  and  equally  distant  from  their  ver- 
tices are  equivalent. 

Proposition  XIX. 

*  The  volume  of  a  triangular  pyramid  is  the  limit  of  the  sum  of  the 
volumes  of  a  series  of  inscribed  or  circumscribed  prisms  of  equal  alti- 
tude, when  their  number  is  indefinitely  increased.' 

"Useless. 

Proposition  XX. 

'Two  triangular  pyramids  having  equal  altitudes  and  equivalent  bases 
are  equivalent.' 

**  Self-evident. 


WHISPERINGS   OF  AN   OLD    PINE 

Proposition  XXI. 


83 


•The  volume  of  a  triangular  pyramid  is  equal  to  one-third  the  product 
of  its  base  and  altitude.' 


**  Because  the  volume  of  a  triangular  prism  is  equal  to  its 
base  by  its  altitude,  and  such  prism  will  contain  three  triangular 
pyramids  each  equivalent  to  one  having  same  base  and  altitude 
as  the  prism. 

"Ellen  uses  134  words  in  demonstrating  the  last  nine  propo- 
sitions, the  book  839  directly,  and  several  thousand,  more  or 
less,  indirectly. 


84  ELLEN   OR 

VII. 

BOOK  VIII, 

CYLINDER,   CONE  AND   SPHERE. 

"  I .  A  curved  line  is  one  whose  direction  constantly  changes. 

"2.  A  cylinder  is  a  figure  bounded  by  a  circular  surface, 
called  its  lateral  surface,  which  terminates  in  two  lateral  planes, 
and  every  portion  of  which  is  equally  distant  from  a  line  within 
called  the  axis.  The  parallel  planes  are  the  bases  of  the  cylin- 
der, and  the  distance  between  them  its  altitude.  A  cylinder 
may  be  generated  by  a  rectangle  revolving  about  one  of  its 
sides. 

"3.  Similar  cylinders  are  those  which  may  be  generated 
by  similar  rectangles  revolving  about  homologous  sides. 

*'4.  A  prism  is  inscribed  in  a  cylinder  when  its  bases  are 
inscribed  in  the  bases  of  the  cylinder.  In  this  case  the  cylinder 
is  circumscribed  about  the  prism. 

**5.  A  prism  is  circumscribed  about  a  cylinder  when  its 
bases  are  circumscribed  about  the  bases  of  the  cylinder.  In 
this  case  the  cylinder  is  inscribed  in  the  prism. 

"6.  A  cone  is  a  solid  figure  bounded  by  a  surface  termi- 
nating at  one  end  in  a  point,  called  the  vertex  of  the  cone,  and 
at  the  other  in  a  circle  called  its  base.  The  perpendicular  from 
the  base,  at  its  centre,  to  the  vetex  is  called  the  axis  of  the  cone. 
The  distance  from  the  vertex  to  any  point  in  the  circumference 
cf  the  base  is  the  slant  height,  and  the  perpendicular  distance 
from  the  vertex  to  the  base  is  the  altitude  of  the  cone.     A  cone 


WHISihKi:N«o    OF  AN   OLD    PINE 


85 


fnay  be  generated  by  a  right  angle  triangle  revolving  about  one 
of  the  sides  adjacent  to  the  right  angle  as  an  axis. 

*'7.  A  truncated  cone  is  that  portion  of  a  cone  between  the 
base  and  any  plane  which  cuts  the  convex  surface. 

•'8*  Similar  cones  are  those  which  may  be  generated  by 
similar  right  angle  triangles  revolving  about  homologous  sides. 

**9»  A  pyramid  is  inscribed  in  a  cone  when  its  base  is 
inscribed  in  the  base  of  the  cone,  and  when  its  vertex  coincides 
^rith  that  of  the  cone, 

"  10.  A  pyramid  is  circumscribed  about  a  cone  when  its  base 
is  circumscribed  about  the  base  of  the  cone  and  when  its  vertex 
coincides  with  that  of  the  cone, 

**  1 1.  A  sphere  is  a  figure  bounded  by  a  curved  surface,  cvtry 
part  of  which  is  equally  distant  from  a  point  within  called 
the  centre.  A  sphere  may  be  generated  by  a  semicircle  revolv- 
ing about  its  diameter  as  an  axis. 

**  12.  A  radius  of  a  sphere  is  a  straight  line  drawn  from  the 
centre  to  any  point  of  the  surface.  A  diameter  is  a  straight 
line  through  the  centre,  limited  by  the  surface.  All  radii  and 
diameters  of  a  sphere  are  mutually  equal. 

**13.  A  circle  whose  plane  passes  through  the  centre  of  the 

licre  is  called  a  great  circle ;  one  whose  plane  does  not  so 
pass,  a  small  circle. 

*•  14.  The  poles  of  a  circle  are  the  extremities  of  its  axis. 

"15.  The  polar  distance  of  the  circle  of  a  sphere  is  the  arc 

a  great  circle  from  its  nearer  pole  to  any  point  in  its  circum- 
ference. 

**  16.  A  spherical  angle  is  the  angle  between  two  intersecting 
arcs  tA  great  circles. 


86  ELLEN   OR 

"17.  A  spherical  polygon  is  apart  of  a  spherical  surface 
bounded  by  three  or  more  arcs  of  great  circles. 

*'  18.  A  diagonal  of  a  spherical  polygon  is  an  arc  of  a  great 
circle  joining  two  vertices  not  adjacent. 

"19.  If  great  circles  are  described  from  the  vertices  of  a 
spherical  triangle  as  poles,  they  will  divide  the  spherical  sur- 
face into  eight  triangles.  One  of  these  is  the  polar  triangle  of 
the  given  triangle. 

**  20.  A  lune  is  a  part  of  a  spherical  surface  bounded  by  two 
semi-circumferences  of  great  circles. 

**2i.  The  spherical  excess  of  a  spherical  triangle  is  the 
excess  of  the  sum  of  its  angles  over  two  right  angles. 


"Ellen  has  given  the  usual  definition  of  a  curved  line,  but  a 
circumference  is  described  by  a  point  moving  so  as  to  make  a 
fixed  angle  with  the  radius  drawn  to  itself,  and  in  this  view 
always  moves  in  the  same  direction,  though  very  different  from 
that  of  a  straight  line. 

"  The  Yale  College  geometry,  in  begining  this  book,  intro- 
duces definitions  which  do  not  appear  in  Euclid,  Davies,  or 
Loomis,  and  as  Ellen  thinks,  are  entirely  undesirable. 

"To  avoid  these,  Ellen  omits  two  Propositions,  and  re-words 
a  third. 


WHISPERINGS   OF  AN   OLD    PINE  8/ 

Proposition  III. 

"  Every  section  of  a  cone  made  by  a  plane  parallel  to  its 
base  is  a  circle  whose  centre  is  a  part  of  the  axis. 

"Because  of  the  uniform  convergence  of  the  surface  of  a 
cone  from  its  base  to  its  vertex,  or  uniform  divergence  from  its 
vertex  to  its  base. 

PROPosmoN  IV. 
*  Every  section  of  a  sphere  made  by  a  plane  is  a  circle  whose  centre 
is  the  foot  of  the  perpendicular  from  the  centre  of  the  sphere  to  that 
plane.' 


**  Because  of  the  uniform  curvature  of  the  surface  of  the 
sphere.  For  a  sphere  may  be  supposed  to  be  composed  c;f 
parallel  circles  contiguous  to  each  other,  the  limits  being  from 
zero  to  a  great  circle  and  from  a  great  circle  to  zero ;  and  the 
perpendicular  to  which  from  the  centre  is  a  radius  or  diameter 
of  the  sphere. 

"Six  corollaries  follow,  all  self-evident,  from  Ellen's  ex- 
planation. 

'Corollary  VII. — Through  any  three  points  on  the  surface  of  !*. 
sphere  one  and  only  one  circle  can  be  drawn. 


88  ELLEN    OR 

'Corollary  VIII. — ^Through  any  two  points  on  the  surface  of  a 
sphere,  not  at  the  extremities  of  a  diameter,  one  and  only  one  great 
circle  can  be  drawn.' 

"  Because  three  points  decide  the  position  of  a  plane.  In  the 
last  corollary  the  third  point  would  be  the  centre  of  the  sphere 

Proposition  V. 

*  All  points  on  the  circumference  of  a  circle  of  a  sphere  are  equally 
distant  from  each  of  its  poles.' 

**  Because  of  the  uniform  curvature  of  the  surface  of  a 
sphere;   and  because  equal  arcs  are  subtended  by  equal  chords. 

Proposition  VL      . 

*  If  a  point  on  the  surface  of  a  sphere  is  at  a  quadrant's  distance  from 
two  points  on  that  surface  [not  at  the  extremities  of  a  diameter],  it  is 
the  pole  of  the  great  circle  passed  through  those  points.* 

"  Because  two  points  with  the  centre  decide  the  direction  of 
a  great  circle,  excepting  when  these  points  are  at  the  ends  of  a 
diameter;   and  because  of  the  uniform  curvature  of  a  sphere. 

Proposition  VII. 

*  The  angle  of  two  arcs  of  great  circles  on  a  spherical  surface  is 

*  I.  Equal  to  the  plane  angle  of  the  diedral  angle  formed  by  their 
planes. 

'  II.  Measured  by  the  arc  of  the  great  circle  described  with  its  vertex 
as  a  pole  and  included  between  its  sides,  produced  if  necessary.* 

**  This  is  a  very  peculiar  proposition,  and  the  demonstration 
of  it  a  most  extraordinary   one,  illustrating   in   a   remarkable 


hiLSrLRlNUb    O 


QLIf    I'hNi 


degree  the  ignorance  or  incompetency  of  the  authors.  For 
the  proof  given  is  a  definition,  and  the  principles  involved, 
although  special  and  remarkable  are  not  at  all  explained, 
nor  indeed  has  Ellen  seen  any  explanation  m  text-books. 
Apparently  indeed  almost  certainly  the  statement  that  they  are 
equal  is  simply  quoted  from  previous  books.  It  is  the  asser- 
tion of  ignorance*  and  absolutely  untrue.  They  are  subtended 
by  the  same  arc  upon  the  surface  of  the  sphere.  And  this  is 
true  not  because  they  are  equal,  but  because  they  are  nut 
equal;  for  if  they  were  equal  it  would  be  impossible  for  them 
to  be  subtended  by  the  same  arc,  being  at  very  different  dis- 
tances Irom  that  arc. 


«K- 


"In  the  case  of  the  spherical  angle  the  subtending  arc  is 
dways  upon  the  surface  of  the  sphere,  either  the  arc  of  a  great 
circle  described  from  the  vertex  of  the  angle  as  a  pole,  or  that 
of  a  small  circle  parallel  to  this;  whilst  the  arc  subtending  the 
plane  angle  of  the  diedral  angle  can  be  made  with  any  radius, 
and  may  or  may  not  be  upon  the  surface  of  the  sphere.  That 
the  spherical  angle  is  measured  by  the  arc  of  a  great  circle, 
described  with  its  vertex  as  a  pole,  is  a  misleading  if  not  inac- 


90  ELLEN    OR 

curate  statement.  It  is  subtended  by  this  arc ;  and  so  it  is  sub- 
tended, or  may  be,  by  an  infinite  number  of  arcs  of  small  circles 
parallel  to  this  great  circle ;  and  it  would  be  as  reasonable  to  say 
that  it  was  measured  by  each  and  all  of  these  last  arcs  as  that  it 
was  measured  by  the  arc  of  the  great  circle.  In  one  sense  it  is, 
but  not  in  the  sense  in  which  the  text-books  use  the  word. 
It  has  nothing  whatever  to  do  with  the  plane  angle  of  the 
diedral  angle,  belonging  to  an  entirely  different  order  of  magni- 
tudes. 

**  Any  spherical  angle  formed  upon  the  surface  of  a  sphere  is 
governed  by  its  own  laws,  which,  as  a  whole,  are  different  from 
those  governing  plane  angles. 

**Thus,  the  angle  of  two  arcs  of  great  circles  on  a  sphere  is 
formed  by  the  converging  of  these  arcs  together,  or  their 
diverging  from  each  other,  and  governed  by  the  laws  which 
control  great  circles  upon  a  sphere.  It  would  be  impossible 
for  these  laws  to  be  the  same,  as  those  which  govern  the  action 
of  straight  lines,  by  which  plane  angles  are  formed— -or  for 
their  effects  to  be  the  same.  This  is  self-evident,  and  -ought 
to  have  prevented  the  text-book  makers  from  making  such 
blundering  propositions. 

"Thus,  the  arcs  of  great  circles  always  curve,  and,  curve 
uniformly.  It  follows  that  the  angle  formed  by  them,  when 
their  planes  are  perpendicular  to  each  other,  is  less  than 
a  right  right  angle  by  the  amount  of  this  curvature.  For,  as 
r211en  has  shown  before,  the  angles  made  by  the  lines  crossing, 
which  vary  from  the  perpendicular,  are  as  much  less  than 
four  right  angles  as  the  lines  so  vary,  the  extremes  being  from 


WHISPERINGS    OF   AN    OLD    I'lNE 


91 


four  right  anglt^s  to  zero — from  an  umbrella  open  to  an  umbrella 
shut. 

•*It  ts  a  fact  that  the  planes  in  which  these  great  circles  lie 
make  the  same  angle  wherever  they  cross,  provided  each  plane 
is  bounded  by  parallel  lines.  In  the  case  of  the  great  circles 
ihcy  are  not  so  bounded^*  but  because  of  the  fact  that  the  angles 
would  be  the  same  11  the  planes  were  so  bounded,  or  rather 
because  the  sides  of  each  of  the  angles,  the  spherical  and  the 
dicdral,  lie  in  the  same  planes  extended,  they  mtist  at  some 
point  cross  each  other,  and  at  this  point  the  arc  of  the  great  cir- 
cle, which  on  one  side  subtends  the  diedral  angle  at  the  centre 
will,  on  another  side,  also  subtend  the  spherical  angle,  but.  as 
Ellen  has  said,  at  a  different  distance  from  the  vertex ;  and  at 
a  quadrant*s  distance,  or  at  the  point  where  the  difference  be- 
tween these  great  circle  arcs  is  the  greatest^  the  same  arc  uf  the 
sphere  will  subtend  the  spherical  angle  and  the  diedral  angle 
made  at  the  centre. 

**  And  this,  so  far  as  the  spherical  angle  is  concerned,  because 
of  the  uniform  curvature  of  the  sphere.  For  here  again  it  is 
jfcclf-evident  that  any  two  lines  which,  crossing  each  other, 
ivcrgc  evenly  and  then  converge  evenly  until  they  cross  again, 
must  be  at  the  greatest  distance  from  each  other  at  the  halt- 
way  station. 

**As  Ellen  has  said  thrs  sanic  arc  subtends  both  of  these 
angles  because  the  sides  of  both  lie  in  the  same  planes,  and 
from  the  nature  of  their  directions  at  some  point  must  cross 
each  otlter.  It  might  subtend  an  infinity  of  other  plane  angles 
with  sides  lying  in  different  planes. 

** Ellen  then  objects  to  the  word  'measures *  as  misleading 


94  ELLEN    OR 

rays  over  the  universe ;  whilst  its  sides  having  inaugurated  such 
a  remarkable  angle  are  satisfied  to  retreat  upon  themselves  and 
ever  after  to  continue  in  a  circle. 

"  The  old  Pine  will  remember  that  the  sides  of  a  plane  angle 
are  supposed  to  extend  forever  in  the  same  direction,  constantly 
increasing  the  space  between  their  sides.  Ellen  can  hardly 
imagine  how  there  could  be  two  kinds  of  angles  more  distinctly 
different  than  these. 

"By  the  text-book  definition  the  angle  of  two  curves  meet- 
ing at  a  common  point  is  the  angle  formed  by  the  two  tangents 
drawn  in  their  planes  to  the  curves  at  that  point.  But  in  the 
case  of  the  coins  the  tangents  are  one  and  the  same  straight 
line,  which  can  form  no  angle.  And  yet  the  touching  circum- 
ferences do  form  an  angle.*' 

*'And  yet/'  I  said,  **  Ellen,  the  so-called  spherical  angles 
would  appear  in  some  respects  to  resemble  plane  angles.  Thus 
certain  general  principles  in  regard  to  angles  and  their  sides  are 
true  of  both." 

"Yes,"  she  replied,  **they  are  governed  by  certain  laws  and 
those  laws  in  certain  respects  are  similar  to  those  which  govern 
plane  angles,  something  very  natural  as  all  are  angles. 

**  Thus  we  have  the  following  propositions  with  their  corol- 
laries : 

Proposition  XIL 

*  If  two  angles  of  a  spherical  triangle  are  equal,  the  opposite  sides  are 
equal. 

PpOIH)SITION   XIII. 

'  Any  side  of  a  spherical  triangle  is  less  than  the  sum  of  the  two  others. 


1 

■ 

THE  KEW  YORK 
PUBLIC  LIBRARY 

i^B 

« 

WHISPERINGS   OF  AN  OLD   PINE 
PRoPosnioN  XIV^ 


95 


*Two  triangles  on  the  same  sphere  are  equal : 

•*  !•  If  two  sides  and  the  included  angle  of  one  are  equal  respectively 
to  two  sides  and  the  included  angle  of  the  other. 

*2.  If  a  sitie  and  the  two  adjacent  angles  of  one  are  equal  respec- 
tively to  a  side  and  the  two  adjacent  angles  of  the  other. 

*3.  If  the  three  sides  of  one  are  equal  respectively  to  the  three  sides 
of  the  other. 

'  Provided  in  each  case  that  the  parts  given  equal  are  arranged  in  the 
same  order  in  both  triangles.' 

"These  propositions  show  that  in  respect  to  the  relative  size 
of  sides  and  angles  certain  laws  governing  spherical  and  plane 
angles  and  triangles  arc  the  same.  In  other  respects,  as  Ellen 
has  illustrated,  they  are  wholly  dissimilar. 

"Instead  of  the  'Proviso'  Ellen  would  prefer  to  have  the 
proposition  read  *  Two  triangles  on  the  same  sphere  arc  equal 
in  area,  etc.* 

*•  Ellen  will  now  explain  what  arc  called  polar  triangles.  And 
lo  assist  she  will  repeat  definitions. 

**  I.  The  poles  of  a  circle  are  the  extrcnrities  of  its  axis. 

**2.  If  with  the  vertices  of  a  spherical  triangle  as  poles,  great 
circles  arc  described,  these  circles  will  divide  the  spherical  sur- 
face into  eight  triangles.  One  of  these  is  the  polar  triangle  of 
the  given  triangle. 

** Triangles  so  related  that  any  vertex  of  either  is  the  pole  of 
'the  side  lying  opposite  it  in  the  other,  are  called  polar  tri- 
angles. 

♦*  Ellen  will  quote  again  from  the  Davies"  Legendre. 


96  ELLEN   OR 

Proposition  V. 

'  If  from  the  vertices  of  the  angles  of  a  spherical  triangle,  as  poles, 
arcs  be  described  forming  a  second  spherical  triangle,  the  vertices  of 
the  angles  of  this  second  triangle  are  respectively  poles  of  the  sides  of 
he  first.* 

*•  Because  the  arcs  described  from  two  vertices  of  the  first 
triangle  meet  at  a  vertex  of  the  second.  Therefore  each  vertex 
of  the  second  must  be  the  pole  of  an  arc  containing  two  vertices 
of  the  first.     Thus : 

**If  from  E  and  F  (see  Figure,  page  97),  two  vertices  of  the 
first  triangle  as  poles,  arcs  of  great  circles  are  described,  they 
will  intersect  at  A,  a  vertex  of  the  second  triangle ;  therefore, 
if  from  A  as  a  pole  an  arc  of  a  great  circle  is  described,  it  will 
pass  through  E  and  F  two  vertices  of  the  first  triangle. 

PROPosmoN  VI. 

'Any  angle  in  one  of  two  polar  triangles,  is  measured  by  a  semi- 
circumference,  minus  the  side  lying  opposite  to  it  in  the  other  triangle.* 

**  Ellen  will  re-word  this  so  as  to  make  it  intelligible.  Any 
angle  in  one  of  two  polar  triangles,  is  measured  by  a  semi-cir- 
cumference, minus  the  side  lying  opposite  to  its  corresponding 
angle  in  the  other  triangle. 

**The  angle  at  A  is  subtended  by  the  arc  GH  all  right,  and 
so,  too,  EH  and  GF  are  quadrants  and  hence  are  together 
equal  to  a  semi-circumference. 

**But  EG  being  equal  to  HF,  EH  and  GF  are  equafto  GH 
and  EF,  the  last  of  which  is  the  side  lying  opposite  to  D  in  the 
other  triangle.     And  therefore  the  spherical    angle  A  is  sub- 


WHISPERINGS   OF  AN   OLD    PINE 


97 


teiided  by  a  semi-circumference  minus  the  side  opposite  to  its 
corresponding  angle  in  its  polar  triangle. 


;^9. 


•*In  like  manner  it  may  be  shown  that  any  other  angle  in 
either  triangle  is  thus  subtended. 

**The  propositions  immediately  following  are  of  the  relativity 
of  sides  and  angles  of  spherical  triangles,  which  FJlen  has 
already  referred  to.     Then  follows, 

pRoposnioN  XIV, 

'The  sum  of  the  angles  of  a  spherical  triangle  is  less  than  six  right 
ingles,  and  greater  than  two  right  angles/ 

•^Because  the  chords  of  any  three  arcs  of  great  circles,  how- 
ever short,  form  a  triangle  that  contains  the  sum  of  two  right 
angles*  As  the  arcs  diverge  more  than  their  chords,  the  tri- 
angle contained  by  them,  although  the  smallest  possible  spheri- 
cal triangle,  will  contain  a  little  more  than  two  right  angles. 

**On  the  other  hand,  if  these  shortest  possible  arcs  are  con- 
tinuously increased,  the  triangles  made  by  them  will  be  con- 
tinuously enlarged,  until  they  become  the  circumference  of  a 


..iLii m^sm^ 


98  ELLEN    OR 

great  circle,  when  the  triangle  changes  to  the  surface  of  a  hemi- 
sphere. Just  before  this  change  the  arcs  at  each  vertex  ex- 
tend in  nearly  opposite  directions  thus  including  nearly  two 
right  angles,  or  nearly  six  in  the  triangle. 

'Corollary  L — The  sum  of  this  three  angles  of  a  spherical  triangle 
is  not  constant  like  that  of  the  angles  of  a  plane  triangle,  but  varies 
between  two  right  angles  and  six.  Two  angles  therefore  do  not  ser\'e 
to  determine  the  third. 

'Corollary  II. — A  spherical  triangle  may  have  two  or  even  three  of 
its  angles  right  angles ;  also  two  or  even  three  of  its  angles  obtuse. 

'Corollary  III. — If  a  triangle,  ABC  (See  Figure,  page  97),  is 
bi-rectangular,  that  is,  has  two  right  angles  B  and  C,  the  vertex  A  is  the 
pole  of  B  C,  and  A  B  and  A  C  will  be  quadrants. 

'For  since  the  arcs  AB  and  AC  are  perpendicular  to  BC,  each  must 
pass  through  its  pole ;  hence  their  intersection  is  that  pole,  and  A  B 
and  A  C  are  quadrants. 

'  If  the  angle  A  is  also  a  right  angle,  the  triangle  ABC  is  tri-rectan- 
gular ;  each  of  its  angles  is  a  right  angle,  and  its  sides  are  quadrants. 
Four  tri-rectangular  triangles  make  up  the  surface  of  a  hemisphere.' 

"  Kllen  has  given  the  corollaries  as  worded  in  the  book.  As 
we  have  seen,  the  four  angles  formed  by  two  arcs  of  great  circles 
intersecting  are  subtended  by  the  same  arcs,  but  otherwise  are 
entirely  different  in  their  character  from  four  right  angles  made 
by  straight  lines. 

'Scholium. — The  [spherical]  right  angle  is  taken  as  the  unit  of 
measure  of  spherical  angles,  and  is  denoted  by  i. 

'The  excess  of  the  sum  of  the  angles  of  a  spherical  triangle  over  two 
[spherical]  right  angles,  is  called  the  spherical  excess.     If  we  denote 
this  excess  by  E,  and  the  three  angles  by  A,  B,  and  C,  we  have 
E=A-|-B-f-C— 2  [spherical]  right  angles. 


WHISPERINGS    OF   AN   OLD    PINE  99 

*The  spherical  excess  of  any  spherical  polygon  is  equal  to  the  excess 
of  the  sum  of  its  angles  over  two  right  angles  taken  as  many  times,  less 
two,  as  the  polygon  has  sides.  If  we  denote  the  spherical  excess  by 
E,  the  sum  of  the  angles  by  S,  and  the  number  of  sides  by  n,  we  have, 

E=S— 2(n— 2)  right  angles  :^S— 2n  right  angles  -f-4  right  angles.' 

"  Ellen  has  given  the  corollaries  as  worded  in  the  book. 

Proposition  XV. 

'Any  lune  is  to  the  surface  of  the  sphere,  as  the  arc  which  measures 
its  angle  is  to  the  circumference  of  a  great  circle :  or,  as  the  angle  of 
the  lune  is  to  four  right  angles.* 


''Because  the  surface  of  each  hemisphere  is  included  between 
the  sides  of  four  spherical  right  angles,  and  the  circumference 
of  the  great  circle  subtending  these  angles ;  a  part  of  which  cir- 
cumference subtends  (measures)  the  angle  of  the  lune. 

Proi»<3sition  X\'I. 
'Symmetrical  triangles  are  eciual  in  area.* 

"Ikcause  they  inclose  equal  space. 

Proposition  XVII. 
'If  the  circumferences  of  two  great  circles  [as  MAPand  NAQ]  in- 
tersect on  the  surface  of  a  hemisphere,  the  sum  of  the  opposite  triangle 


25843tt 


lOO 


ELLEN   OR 


thus  formed  Is  equal  to  a  lune,  whose  angle  is  equal  to  that  formed  by 
the  circles.* 


•'Because  BMN  is  equal  to  PAQ  and  this  because  of  the 
uniform  curvature  of  the  surface  of  a  sphere.  If  equals  are 
subtracted  from  or  added  to  equals  the  results  will  be  equal. 

Proposition  XVIII. 

'The  area  of  a  spherical  triangle  is  equal  to  its  spherical  excess  mul- 
tiplied by  a  tri-rectangular  triangle. 

'  Definitions. — A  spherical  triangle  having  two  right  angles  is  a 
bi-rectangular  triangle. 

'A  spherical  triangle  having  three  right  angles  is  a  tri-rectangular 
triangle. 

Proposition  XIX. 

'The  area  of  a  spherical  polygon  is  equal  to  its  spherical  excess  mul- 
tiplied by  a  tri-rectangular  triangle.* 

**This  is  the  same  as  to  say  that  the  area  of  a  surface  depends 
upon  the  number  of  times  that  its  unit  of  measure  is  contained 
in  it,  it  being  absolutely  impossible  for  it  to  depend  on  anything 
else. 


WHISPERINGS   OF   AN   OLD   PTNE 


tOI 


*•  Ellen  thinks  that  propositions  of  this  character  need  dem- 
onstrations far  less  than  the  one  which  states  that  a  spherical 
angle  is  identical  with  one  made  by  straight  lines,  though  the 
schoolmen  use  several  pages  to  prove  the  first,  /*  e'.,  that 
area  is  in  proportion  to  extent,  but  are  satisfied  to  pt&vf  the 
last  by  a  definition. 

"Thus  the  Yale  College  Geometry  has; 

PROPOsmoN  VI L 

*The  angle  of  two  arcs  of  great  circles  on  a  spherical  surface  is 

•  I.  Equal  to  the  plane  angle  of  the  diedral  angle  formed  by  their 
^bjies. 

*».  Measured  by  the  arc  of  the  great  circle  described  with  its  vertex 
as  a  pole  and  included  between  its  sides,  produced  If  necessary. 

•Given  AB  and  AB'  two  arcs  of  great  circles  whose  planes  form  a 
diedral  angle  having  the  diameter  AD  for  an  edge.     (See  Figure,  page 

•With  A  as  a  pole  de£cribe  a  great  circle,  cutting  AB  and  AB^,  pro- 
ciucedp  if  necessary,  in  C  and  C. 

•l.  To pr&pe  the  angle  BAB'  is  equal  to  the  plane  angle  of  the  die- 
<lral  angle  BADE'. 

*Draw  AT  and  AT'  tangent  to  the  arcs  AB  and  AB'  respectively. 

*Thcn,  by  definition,  the  angles  BAB' and  TAT  are  identical — §75 1/ 

'•  SVc  turn  to  ,^751,  and  read : 


•Dkhkition. — The  angle  of  two  curves  meeting  in  a  common  point 
H  the  angle  formed  by  the  two  tangents  to  the  curves  at  that  point.* 

"And  this  is  given  as  t\ic proaf.'' 

*'And  why  do  they  not  discuss  the  proposition?**  I  asked. 


I02  ELLEN   OR 

"Presumably  because  they  know  nothing  about  it"'  she  re- 
plied, **  whether  it  is  so  or  whether  it  is  not. 

"The  Yale  College  Proposition  referring  to  the  proportion 

existing  between  a  spherical  triangle  and  its  spherical  excess  is 

as  follows : 

Proposition  XXIII. 

*  If  the  unit  angle  is  the  right  angle  and  the  unit  surfece  the  tri-rec- 
tangular  triangle,  the  area  of  a  spherical  triangle  is  measured  by  its 
spherical  excess.' " 

"And  why  is  it  measured  by  its  spherical  excess?**  I  asked. 

"  It  may  be  measured  by  any  appropriate  standard  of  meas- 
ure," she  answered.  "  A  natural  measure  for  the  surface  of  a 
sphere  is  a  tri-rectangular  triangle.  For  it  is  easily  shown  that 
this  includes  one-eighth  of  the  surface  of  the  sphere,  and  there- 
fore eight  of  these  make  the  surface  of  a  sphere  as  much  as 
four  pecks  make  a  bushel. 

"And  if  the  old  Pine  considers  he  will  see,  a  bi-rectangular 
triangle,  in  order  to  exist,  must  have  more  than  two  right  angles. 
The  definition,  then,  is  intended  to  mean  that  a  spherical  tri- 
angle having  two  separate  right  angles  is  called  a  bi-rectangular 
triangle.  As  Ellen  says,  it  cannot  have  these  and  no  more ;  to 
have  these  it  must  have  another  angle.  For  it  takes  three 
angles  to  make  a  triangle,  spherical  or  otherwise;  and,  too,  the 
sides  opposite  the  right  angles  are  equal  and  are  quadrants. 

"Well,  the  old  Pine  will  see  that  when  the  two  right  angles 
start,  another  angle  (MAN)  starts,  and  with  it — not  before — 
the  occupancy  of  space  upon  the  surface  of  the  sphere  by  this 
spherical  triangle.  As  the  angle  MAN  increases,  this  space  in- 
creases, until  the  bi-rectangular' triangle  becomes  a  tri-rectangu- 


WHISPERINGS  OF  AN   OLD   PINE 


103 


lai  triangle,  tliat  is,  a  spherical  triangle  ha\ang  three  separate 
right  angles,  and  occupying  one-eighth  of  the  surface  of  a  sphere, 

"The  old  Pine  will  now  see  why  the  measuring  process  by 
the  tri-rectangular  triangle  does  not  begin  except  with  what  is 
called  the  spherical  excess.  Ellen  doesn't  think  that  any  of  the 
modem  text  book  makers  ever  had  any  conception  in  regard 
to  it-  And  he  will  sec,  too,  that  beginning  with  the  smallest 
possible  third  angle  this  third  angle  increases  gradually,  or 
may  increase  gradually,  until  it  equals  every  possible  third  angle 
between  the  smallest  possible  angle,  and  a  right  angle,  inclusive, 

**As  this  excess  is  multiplied  by  the  tri-rectangular  triangle 
representing  unity,  we  shall  get  all  possible  dimensions  of  a 
spherical  triangle  from  the  smallest  to  half  the  surface  of  the 
sphere.  And  therefore  if  the  sum  of  the  three  angles  of  a 
spherical  triangle  equals  three  right  angles,  its  surface  will  be 
equal  to  the  tri*rectangular  triangle;  if  the  sum  is  equal  to 
lour  right  angles  the  surface  of  the  triangle  will  be  equal  to 
two  tri-rectangular  triangles.  If  the  sum  is  equal  to  five  right 
angles,  the  surface  will  be  equal  to  three  tri-rectangular  tri- 
angles. Or,  if  the  sum  is  equal  to  two  and  one-third  right 
angles,  or  two  and  one-thousandth,  or  any  other  sum,  the  sur* 
[ace  will  be  equal  to  one  third,  or  one  one-thousandth,  or  any 
other  fraction  of  a  tri-rectangular  triangle." 

'•But  why  isn't  all  this  explained  in  the  books?**  I  asked, 

•*  Presumably  because  those  who  made  them  didn't  know 
enough  to  explain  it.  Ignorance  of  some  kind  is  always  the 
cause  of  stupidity*  It  may  be  here  the  ignorance  of  a  fact,  or 
of  the  importance  of  explaining  a  fact,  or  how  to  explain  the 
fact»  or  all/' 


I04  ELLEN   OR 

"Well,"  I  said,  "Ellen  has  made  it  pretty  clear,  why,  if  the 
excess  of  the  sum  of  the  angles  of  a  spherical  triangle  over  two 
right  angles  is  called  its  spherical  excess,  the  area  of  a  spherical 
triangle  is  measured  by  thiS  /xcess.  But  the  old  Pine  has 
noticed  that  the  books  in  the  discussion  of  this  subject  give  the 
following  proportion : 

"  If  the  area  of  the  tri-rectangular  triangle  be  represented  by 
T,  the  surface  of  the  sphere  will  be  represented  by  8T.  Also 
if  we  take  the  right  angle  for  unity  and  represent  the  angle  of 
the  lune  by  A,  we  shall  have  the  proportion,  AREA  OF  THE 
LUNE  :  8T::  A  :  4.     Hence,  the  area  of  the   lune  is  equal  to 

8  AxT  -      _, 

,  or  2  AxT. 

4 

"This  proportion  is  very  evident,  but  why  does  it  follow  that 

8  A  X  T 

the  area  of  the  lune  is  equal  to  .     That  is,  why  in  such 

4 

proportion,  or  in  any  proportion,  is  the  product  of  the  extremes 
equal  to  that  of  the  means?" 

"  Because  the  four  magnitudes  are  proportionals,"  she  replied. 
"That  is,  the  first  is  contained  the  same  number  of  times  in  the 
•second  that  the  third  is  in  the  fourth.  This  being  so,  if  we 
multiply  the  first  by  the  fourth,  that  is,  take  the  number  of 
times  that  the  fourth  will  contain  the  first,  for  in  all  such  cases 
multiplication  is  addition,  the  product  must  equal  that  of  the 
second  by  the  third.  For  as  many  times  as  the  second  is 
larger  than  the  first,  the  third  is  smaller  than  the  fourth.  Thus, 
if  we  have  2  :  41:6  :  12,  we  shall  have  2X  12=4x6.  That  is, 
taking  2  twelve  times  is  most  evidently  the  same  as  taking  4, 
which  contains  2,  twice,  6  or  half  as  many  as  12  times. 


THl  FEW  7CFK 
PUBLIC  LIBRA  Rv 


WHISPERINGS   OF  AN    OLD    PINE 


lOS 


\7IL 


BOOK  IX. 

5UREMENT  OF  CYI-INDER,   CONE  AND   SPHERE. 

**  Ellen  will  return  to  the  Yale  College  geometry. 

Proposition  L 

*  If  the  number  of  lateral  faces  of  a  prism  inscribed  in  or  circum- 
iibcd  about  a  cylinder  be  indefinitely  increased  so  that  each  one 

becomes  indefinitely  small,  then 

*  I ,  Any  right  section  of  the  prism  approaches  a  right  section  of  the 
cylinder  as  a  limit 

'  IL  The  lateral  area  of  the  prism  approaches  the  lateral  area  of  the 
cylinder  as  a  limit. 

*in.  The  volume  of  the  prism  approaches  the  volume  of  the  cylinder 
;  a  limit/ 


*  Three  hundred  and  thirty-eight  words  are  used  directly, 
and  one  thou?»and,  more  or  less,  in  other  pruposittons  referred 
to,  to  demonstrate  this  proposition,  which  is  as  phin  as  to  say 
that  if  a  part  of  anything  is  taken  away,  the  remainder  will  be 
smaller  than  the  original  thing.  It  is  noticeable,  too,  that  the 
authors,  having  struck  something  which  they  understand,  enter 
into  iU  discussion  with  great  zest 


I06  ELLEN   OR       - 

Proposition  II. 

'The  convex  surface  of  a  cylinder  is  equal  to  the  circumference  of  its 
base  multiplied  by  its  altitude.' — Davies, 

"That  the  convex  surface  of  a  cylinder  is  equal  to  the 
product  of  its  circumference  and  altitude,  may  be  easily  and 
accurately  proven.  For  the  surface  of  a  sheet  of  writing  paper 
is  equal  to  the  product  of  its  length  and  width.  But  any  sheet 
of  writing  paper  may  make  the  convex  surface  of  a  cylindei,  in 
whi^h  the  length  of  the  paper  becomes  the  circumference  and 
the  width  the  altitude  of  the  cylinder.  And  therefore  the  lat- 
eral area  or  convex  surface  of  any  cylinder  will  be  equal  to  the 
product  of  its  circumference  and  altitude. 

"The  line  of  proof  offered  in  modern  geometries  is  to  inscribe 
in  a  cylinder  a  prism  whose  lateral  area  is  equal  to  its  perimeter 
multiplied  by  its  lateral  edge ;  then  increasing  indefinitely  the 
lateral  faces  of  the  prism,  and  assuming  that  it  finally  equals 
the  cylinder,  or  as  expressed  that  it  approaches  the  cylinder  as 
a  limit — which  is  true — and  that  therefore  the  lateral  area  of  the 
cylinder  equals  the  product  of  the  perimeter  of  a  right  section 
and  a  lateral  edge,  which,  whether  true  or  not,  is  not  true  for 
the  reason  given,  but  instead,  so  far  as  our  knowledge  extends, 
is  untrue.  Ellen  would  feel  very  badly  if  the  old  Pine  should 
ever  make  such  statements.  Because  she  can  sec  but  little 
difference  between  saying  a  thing  is  so  that  we  know  is  not,  or 
saying  that  a  thing  is  so  when  we  know  nothing  about  it. 

Proposition  IT  I. 
'The  volume  of  a  cylinder  is  equal  to  the  product  of  its  base  and 
altitude.' 


WHISrERINGS    OF   AN    OLD    I'lNE 


107 


lusc  this  represents  the  product  of  the  three  dimensions. 
And  it  is  also  true  that  the  volume  of  a  cylinder  is  equal  to  the 
mean  or  average  convex  surface  multiplied  b)-  its  radius,  or  its 
convex  surface  multiplied  by  half  its  radius.** 

'*And  what  does  Elten  mean  by  its  mean  nv  average  convex 
surface?*    I  asked. 

**  A  cylinder,"  she  replied,  "maybe  supposed  to  consist  of 
a  scries  of  contiguous  surfaces  having  the  same  altitude  and 
thickness  as  the  convex  surface,  but  each  shorter  proportionally 
to  Its  distance  from  the  axis,  the  length  of  the  first  being  the 
circumference  of  the  cylinder,  and  the  distance  from  the  axis 
tbQ  radius  of  this  circumference.  Because  of  this  proporliun 
the  surface  half  way  between  the  convex  surface  and  the  axis 
will  be  the  average  surface;  and  therefore  this  surface  multi- 
plied by  the  radius*  or  the  first  convex  surface  multiplied  by 
half  the  radius,  will  equal  the  volume  of  the  c}^linder. 

**  Proposition  IV\  is  simitar  to  Proposition  I, 

Prok»situ)N  v. 

*The  lateral  area  of  a  cone  is  equal  to  one-half  the  pro<lu€t  of  the 
cifcmnfcrence  of  its  base  and  its  slant  height/ 

•*  Because  of  the  uniform  convergence  of  the  surface  of  a  cone 
from  the  base  to  the  apex,  or  divergence  from  the  apex  to  the 
base. 

Prop*  Ksn  ION  VL 

*The  lateral  area  of  the  frustum  of  a  cone  is  equal  to  one-half  the 
l%nR  of  the  circumferences  of  its  bases  by  its  slam  height/ 

'•  Because  half  the  sum  of  the  circumferences  of  its  bases  rep- 
resents the  average  circumference. 


io8 


ELLEN  OR 


Proposition  VIL 

'The  volume  of  a  cone  is  equal  to  one- third  the  producut  of  its  base 
by  its  altitude ; 

'The  volume  of  a  cone  is  equal  to  its  base  multiplied  by  one-third  its 
altitude.' — Davids, 

**  Ellen  would  say :  *  The  volume  of  a  cone  is  equal  to  the  area 
of  its  average  circumference  by  its  altitude.' 

"Ellen  will  quote  at  once  the  remaining  five  propositions  of 
this,  the  last  book  of  the  Yale  College  geometry,  as  all  relate  to 
the  surfaces  and  volumes  of  cones  and  spheres,  and  therefore 
may  be  considered  together. 


Proposition  VIH. 

'The  area  of  the  surface  generated  by  a  straight  line  revolving  about 
an  axis  in  its  plane  (not  crossing  the  straight  line)  is  equal  to  the 
product  of  the  projection  of  the  line  on  the  axis  and  the  circumference 
of  the  circle  whose  radius  is  the  perpendicular  to  the  line  drawn  at  its 
middle  point  and  terminated  in  the  axis.* 

"If  used  at  all  Ellen  would  suggest  the  re-wording  of  this 
proposition  as  follows:  The  curved  surface  generated  by  a 
bi-rectangular  trapezoid,  revolving  about  the  f  ^'de  perpendicular 


WHISPERINGS   OF  AN   OLD   PINE 


109 


to  the  parallel  sides,  is  equal  to  the  product  of  the  side  used  as 
an  axis,  by  the  circumference  whose  radius  is  a  perpendicular  to 
the  oblique  side»  and  drawn  from  the  middle  point  of  this  side 
Jo  the  axis. 

Proposition  IX. 

♦The  area  of  a  zone  is  equal  to  the  product  of  its  altitude  and  the 
cifcumference  of  a  great  circle. 

Proposition  X. 

•The  volume  generated  by  a  triangle  revolving  about  an  axis,  in  its 
f^lane^  and  passing  llirough  its  vertex  without  crossing  its  surface,  is 
equal  to  the  provluct  of  one- third  the  altitude  and  the  area  generated 
by  the  base.* 

"The  English  of  this  is  execrable,  of  the  kind  that  is  alto- 
gether too  frequent  in  our  text-books.  As  Ellen  has  before 
said,  it  is  to  want  of  thoroughness,  in  those  who  undertake 
to  teach  that  the  difficulties  of  mathematics  are  largely  dut, 
the  remainder  being  to  errors  in  principles,  and  w^ant  of  more 
direct  methods  in  instruction.  For  there  is  no  reason  why 
mathematics,  the  w^hole  of  them,  shouldn't  be  as  plain  and  as 
easily  learned  as  geography  or  spelling,  excepting  the  inaccu- 
rate and  entirely  unnecessarily  stupid  way  in  which  they  are 
taught. 

"Ellen  will  re-write  the  proposition  to  make  it  more  under- 
standable : 

"The  irolume  generated  by  a  triangle  revolving  about  an  axis 
tn  its  planCp  which  axis  passes  through  a  vertex  of  the  triangle 
i-ithoul  crossing  its  surface,  is  equal,  etc. 


no 


ELLEN    OR 


"  In  this  geometry  the  determination  of  the  surface  of  a  zone 
or  sphere,  and  the  volume  of  a  sphere  or  its  segment,  is  made 
to  depend  upon  these  propositions ;  but  Ellen  will  investigate 
questions  concerning  a  sphere  upon  entirely  independent  lines. 

PROPOsrrroN  XL 
*  The  volume  of  a  spherical  sector  is  equal  to  the  product  of  the  area 
of  the  zone  which  forms  its  base  and  one-third  the  radius  of  the  sphere. 

**This  is  the  last  proposition  of  the  book. 

"It  is  evident  that  the  convex  surface  of  a  cone  is  composed 
of  a  series  of  circumferences  or  edges  of  circles,  solid  circles, 
Ellen  doesn't   care  how  thin  you  make  them,  whose  limits  are 


the  circle  forming  the  base  and  that  forming  the  apex.  Be 
cause  of  the  uniform  convergence  of  the  cone  from  the  base 
to  the  apex,  the  circumference  at  the  centre  is  a  mean  circum- 
ference ;  and  therefore,  and  for  no  other  possible  reason,  the 
convex  surface  of  the  cone  is  equal  to  this  multiplied  by  the 
slant  height,  or,  what  would  be  equivalent,  and  for  same  rea- 
son, the  circumference  of  its  base  by  one-half  its  slant  height." 
**But  why,"  I  asked,  "is  the  volume  of  a  cone  one-third  of 
that  of  a  cyHnder  of  equal  base?" 


WfflSPERINGS    OF   AN   niD    I'lNE 


I  1  [ 


**Tliat  is  very  evident,"  she  replsed.  Take  a  plane  surface 
that  of  a  cone  divided  longitudinally  through  its  centre.  The 
figure  would  be  a  triangle.  Because  of  the  uniform  diver- 
gence of  its  sides  A  B  and  A  C»  the  line  of  average  length 
connecting  them  will  be  parallel  to  BC,  and  half  way  between 
A  and  BC.  Let  DE  represent  this  line.  Then  the  area  of 
ABC  will  beUExAF.  For  AF  represents  the  number  i>r 
lines,  AS  DE,  between  A  and  BC  inclusive.  Because  of  the 
uniform  divergence  of  A  B  and  Ad  as  we  have  seen,  there  will 
be  the  same  number  of  lines  between  A  and  DE  as  between 
OE  and  BC,  and  in  succession  these  will  be  exactly  as  much 
shorter  on  one  side  as  they  are  longer  on  the  other ;  and  there- 
fore DE  will  be  their  average  length.  And  hence,  and  for  no 
other  reason,  the  area  of  this  triangle  will  be  DEx;\I\  iti 
average  base  or  length,  by  its  altitude." 

**But,*'  I  said,  **the  statement  in  geometries  is  tliat  tlie  area 
is*  BC  multiplied  by  half  AF/' 

"Yes/*  she  said,  "because  that  represents  the  same  amount, 
and  for  the  same  reason. 

"  But  whiUt  these  amounts  are  the  same,  as  Ellen  has  said 
before,  statements  in  mathematics  ought  not  to  be  made  differ- 
ent from  the  order  in  which  they  occur.  From  doing  this  has 
perhaps  come  the  inconceivably  absurd  suggestion  that  things 
ha%'C  no  beginnings  or  endings.  For  we  may  suppose  of  just 
«och  h'nes  as  DEof  whatever  size  that  be  taken,  different  in 
length,  but  parallel  and  otherwise  the  same,  is  the  surface  or  are.i 
oi  any  triangle  ABC  composed  ;  and  of  similar  lines  we  may  sup- 
pose c%'er>*  other  plane  figure  to  be  composed  Surely  the  old 
Pine  didn't  suppose  that  everything  was  created  simr'^aneotisl) 


I  12  ELLEN    OR 

in  all  its  parts;  thus,  that  a  house, — cellar,  chimneys,  studs, 
joice,  rafters,  boarding,  roofing,  lath,  stairs,  doors,  windows. 
blinds,  and  the  finishing — all  went  together  at  the  same  instant. 
And  if  a  house,  so  everything  else  from  an  orange  to  a  sphere. 
That  is,  that  there  are  no  such  things  as  beginnings  and  end- 
ings, or,  as  modern  geometricians  assert,  no  such  things  as 
points,  lines  and  superficies?" 

'*  Oh  no,  not  at  all,"  I  said.  ''The  old  Pine  knows  that  every- 
thing, so  far  as  he  has  ever  observed,  is  made  on  ver}'  different 
principles;  consists  of  certain  parts  supplied  in  order,  which 
order,  perhaps,  admits  of  some  variety,  but  not  very  much,  cer- 
tainly not  except  with  much  extra  effort.  He  never  was  at  all 
disturbed  by  the  folly  of  those  who  seemed  to  assume  other- 
wise ; — that  was  their  matter,  and  not  his." 

'*  No,  indeed,"  she  continued  ;  **  there  was  never  a  thing  made 
all  at  once.  The  universal  law  is  that  all  construction,  from  the 
least  to  the  greatest,  is  a  process  of  time, — a  thing  of  growth. 
And  therefore  again,  points,  lines,  and  superficies  are  both  a 
fact  and  a  necessity. 

'*  Ellen  thinks  now  the  old  Pine  can  see  why,  when  we  have 
to  do  with  two  dimensions,  we  take  the  length  at  one-half  the 
height.  For  all  the  material  in  the  other  half  will  make  the 
half  taken  of  uniform  length. 

*•  But  when  we  have  three  dimensions,  thickness  as  well  as 
length  and  height,  we  cannot  do  this,  for  now  we  have  two 
dimensions  to  make  uniform  from  the  remaining  material. 

*'And  in  a  cone,  because  of  the  uniform  character  of  its 
curved  surface,  instead  of  the  upper  half  to  make  the  other 
half  a  parallelogram,  as  in   a  triangle,   it  will  require  the  two 


upper  thirds  to  make  the  lower  third  a  cylinder;  an  equal 
amoant  being  used  for  each  dimcosion.  And  therefore  the 
volume  of  a  cone  is  equal  to  one-third  that  of  a  cylinder  with 
the  ^mc  base  and  altitude. 

"The  difference  of  ratio  between  things  of  two  dimensions 
and  those  having  three  may  be  illustrated  in  circles  and  sphcrer 
Thus  a  circle  surrounding  any  point  as  a  center  constantly 
ificfeases  with  the  length  of  its  radius^  the  proportion  of  increase 
being  not  as  the  radii  but  as  their  squares.  If  a  radius  of  2  is 
iacreasccl  to  4  the  proportion  of  the  circles  will  be  as  4  to  16. 
That  is  the  larger  circle  is  four  times  as  large  as  the  first*  and 
not  twice  as  is  its  radius.  This  is  the  law  of  circles;  that  is,  it 
is  the  taw  of  similar  surfaces;  but  when  volume  is  considered, 
am  in  spheres,  the  proportion  is  as  the  cubes  of  the  radfi.  Thus, 
if  one  sphere  has  a  radius  of  2,  and  another  a  radius  of  4,  the 
proportion  of  surface  will  be  as  4  to  16 ;  but  uf  volume  as  8  to 
64;  that  is,  the  second  sphere  will  have  8  times  the  volume  of 
the  first,  although  but  4  times  the  surface." 
*•  And  why  is  this?**  I  asked. 

"Because  of  the  nature  of  space;  nor  can  Ellen  see  how  it 
atxild  be  different. 

"The  surfaces  then  of  circles  are  as  the  squares  of  their 
ladii.  And  so  similar  surfaces  are  as  the  squares,  and  similar 
volumes  as  the  cubes  of  Ihetr  homologous  dimensions. 

** There  might  be  an  infinite  number  of  cylinders  with  differ- 
ent bases  and  different  heights,  the  volume  of  each  of  which 
would  be  equal  to  the  volume  of  this  cone,  or  whose  volume 
the  volume  of  the  cone  would  equaL  Thus,  as  we  have  seen, 
the  volume  of  the  cone  is  equivalent  to  that  of  a  cylinder  upon 


114  ELLEN    OR 

the  same  base,  and  one  third  the  height  of  the  cone.  It  is  also 
equivalent  to  that  of  a  cylinder  two  thirds  the  height  of  the 
cone,  and  whose  base  is  half  that  of  the  cone.  And  it  is  equiv- 
alent to  that  of  a  cylinder  of  same  height,  and  with  base  one 
third  that  of  the  cone. 

**  Of  the  old  methods  of  proof,  that  the  volume  of  a  cone  is 
one  third  that  of  a  cylinder  with  same  base  and  altitude,  Ellen 
much  prefers  the  demonstration  given  by  Euclid,  an  unusually 
brilliant  one,  if  things  are  to  be  proven  indirectly,  as  follows : 

Proposftion  XVIII.  (Playfair's  Euclid,  Book  III.,  Supplement.) 
^  If  a  cone  and  cylinder  have  the  same  base  and  the  same  altitude^ 
the  cone  is  the  third  part  of  the  cylinder, 

'Let  the  cone  A  BCD,  and  the  cylinder  BFKG  have  the  same  base, 
viz.,  the  circle  BCD,  and  the  same  altitude,  viz.,  the  perpendicular 
from  fhe  point  A  upon  the  plane  BCD,  the  cone  A B C D  is  the  third 
part  of  the  cylinder  BFKG.     (See  figure,  page  io8). 

*If  not,  let  the  cone  ABCD  be  the  third  part  of  another  cylinder 
LMNO,  having  the  same  altitude  with  the  cylinder  BFKG,  but  let 
the  bases  BCD  and  LIM  be  unequal;  and  first,  let  BCD  be  greater 
than  LIM. 

'Then,  because  the  circle  BCD  is  greater  than  the  circle  LIM,  a 
polygon  may  be  inscribed  in  BCD,  that  shall  differ  from  it  less  than 
LIM  does  (4,1.,  Supplement),  and  which,  therefore,  will  be  greater 
than  LIxM.  Let  this  be  the  polygon  BECFD;  and  upon  BECFD 
let  there  be  constituted  the  pyramid  A  BECFD,  and  the  prism 
BCFKIIG. 

'Because  the  polygon  BECFD  is  greater  than  the  circle  LIM,  the 
prism  B  C  F  K  H  G  is  greater  than  the  cylinder  LMNO,  for  they  have 
the  same  altitude,  but  the  prism  has  the  greater  base.     But  the  p)rramid 


WHISPEKINC.S    OK   AN    uLU    MNE 


IIS 


ABECFD  is  the  ihird  part  of  the  prism  (15,  3,  Supplement)  BCFK 
HG,  therefore  it  is  greater  than  the  third  part  of  the  cylinder  LM  N  O. 
Now,  the  cone  ABEC  FD  is,  by  hypothesis,  the  third  part  of  the  cyl- 
io< lex  LM  NO,  therefore  the  pyramid  ABECFDis  greater  than  the 
cone  A  BCD,  and  it  is  also  less,  because  it  is  inscribed  in  the  cone, 
which  is  impossible.  Therefore,  the  cone  A  B  C  D  is  not  less  than  the 
ihiril  part  of  the  cylinder  BFKG  :    And  in  the  same  manner,  by  cir- 


S 


'1,1 


Ko 


^F 


]M 


k •idHMCribtng  a  polygon  about  the  circle  BCD,  it  may  be  shov^ii  that  the 
cone  A  BCD  is  not  greater  than  the  third  part  of  the  cylinder  BFKG; 
fberefore,  it  is  equal  to  the  third  part  of  that  cylinder.* 

**Il  was  a  great  master  that  conceived  this  demonstration  of 
the  volume  of  a  cone.  And  yet,  as  Ellen  has  shown,  this  may  be 
demonstrated  directly  and  by  simpler  principles. 

'*  We  have  seen  by  the  experiment  with  the  sheet  of  paper  that 
the  convex  surface  of  a  cylinder  equals  its  circumference  by  its 
altttiidc.  And  this  because  this  convex  surface  represents  two 
dimensions,  the  length  and  width,  of  a  rectilinear  plane  sur- 
face.    And  so  any  spherical  surface  is  equivalent  to  the  sur- 


1  1 6  ELLEN   OR 

face  of  some  rectilinear  plane  figure.  And  so,  too,  the  volume 
of  every  figure  is  equivalent  to  that  of  some  rectilinear  figure. 
And  as  it  is  impossible  to  conceive  of  matter, — of  a  single 
particle  of  matter, — which  does  not  consist  of  the  three  dimen- 
sions, so  it  is  impossible  to  conceive  of  any  figure  which  does 
not  so  consist.  It  is  possible  to  conceive  of  one  of  the  dimen- 
sions of  a  figure  so  reduced,  in  proportion  to  the  others,  that 
it  might  be  ignored.  It  is  in  such  cases  as  these  that  we  speak 
of  a  thing  as  having  one  or  two  dimensions,  but  accurately 
stated  the  three  dimensions  arc  as  one,  neither  of  them  being 
possible  except  when  united  with  the  other  two.  That's  awfully 
funny,  too." 

"Why,  yes,"  I  said,  "that's  a  fundamental  principle,  cer- 
tainly." 

**We  consider  a  superficies,"  she  continued,  *'and  speak  of  it 
as  having  but  two  dimensions,  though  in  reality  it  has  three, 
just  as  much  as  the  greatest  tower  that  was  ever  built.  And  so 
it  is  with  a  line  or  with  a  point." 

'*  But",  I  said,  **  Ellen  admits  that  these  conditions  shade  into 
the  infinite." 

*'Ycs,"  she  answered,  "from  the  standpoint  that  we  occupy, 
or  with  the  facilities  that  we  have  to  analyze  matter,  the  particles, 
or  parts  of  it,  which  we  use,  may  become  indistinguishable, 
and  undcfinable." 

"  What,  then,  is  a  point,"  I  asked,  "  or  a  line,  or  superficies?" 

"They  admit  of  very  great  differences,"  she  replied,  "but,  as 
ICUen  has  said  before,  a  point  is  any  small  amount  of  matter, 
according  to  the  measure  of  our  vision.  Change  the  vision 
and  the  point  becomes  a  globe.     The  same  is  true  of  a  line  or 


WHISPERINGS    OF   AN   OLD    PINE  II  / 

of  a  superficies,  only  a  line  and  superficies  would  be  of  a  differ- 
ent shape  from  the  globe. 

"Ellen  doesn't  know  when  this  division  of  matter  stops.  It  is 
a  will-o'-the-wisp  that  she  doesn't  propose  to  spend  her  time  in 
chasing ;  certainly  not  at  present,  when  there  are  so  many  other 
things  of  more  immediate  importance  to  be  considered. 

"But  this  is  most  evident,  that  points,  lines,  and  super- 
ficies are  each  a  basis  of  measurement  adapted  to  our 
vision.  They  represent  the  beginnings  and  the  end  of  every 
conceivable  figure.  They  are,  too,  the  usual  standards  of 
measure,  which,  whether  knowingly  or  not,  we  always  use. 
Thus  a  plane  surface  consists  of  matter  arranged  in  more 
or  less  of  length  and  width,  but  little  thickness.  That  is,  it 
consists  of  a  superficies,  which,  as  Ellen  has  observed  before, 
may  be  composed  of  lines,  and  they  of  points.  This  is 
the  base,  and  the  volume  of  a  cylinder  or  any  rectangular 
figure  constructed  upon  it  will  be  the  number  of  times 
that  this  standard  of  measure,  call  it  what  you  will — point, 
line,  base,  superficies,  or  any  other  possible  name, — is  con- 
tained in  the  structure,  and  as  with  our  ability  of  perception 
it  would  be  impossible  for  us  to  give  this  in  numbers — ^just  as 
it  would  be  impossible  for  us  to  tell  the  number  of  drops  in  an 
ocean, — ^wedoit  approximately  by  measurement,  and  therefore, 
and  for  no  other  reason,  no  other  possible  reason,  we  say  that 
the  volume  of  a  cylinder  is  its  base  mutiplicd  by  its  altitude ;  or 
the  volume  of  a  sphere  the  surface  multiplied  by  a  third  of  the 
radius. 

"In  all  cases,  then,  surfaces  consist  of  the  product  of  two 
dimensions,  and  volume  of  the  product  of  three ;   so  that  the 


Il8  ELLEN    OR 

only  question  is  the  dimensions  to  be  used.  If  a  surface  or 
solid  is  rectangular  its  length  and  breadth,  or  length,  breadth» 
and  thickness,  are  the  factors  to  be  used ;  if  of  irregular  shape 
some  proportional  of  these  must  be  taken,  but  always,  and 
always  in  one  of  these  two  ways,  the  surface  of  anything  con- 
sists of  the  product  of  two  of  these  factors,  and  the  volume  of 
the  three. 

"The  old  Pine  never  would  have  thought  to  fix  things  up 
this  way,  would  he?  Ellen  thinks  that  he  would  never  have 
got  beyond  straight  lines,  but  this  creation  that  we  have  abounds 
in  curves,  and  the  curved  line  is  the  line  of  beauty. 

"The  surface,  then,  or  the  volume  of  any  rectangular  solid  is 
very  easily  determined ;  or  of  any  solid  not  rectangular  if  we 
can  discover,  or  as  we  discover,  the  relationship  which  the  fig- 
ure bears  to  a  rectangle. 

**  Ellen  will  now  consider  the  area  and  volume  of  a  sphere. 
5he  will  start  with  the  figure  of  a  silver  dollar. 

H 


o 


B 

"Omitting  its  edges  twice  the  plane  surface  ABCD  will  en- 
close the  dollar. 

"  Ellen  will  call  attention  also  to  the  fact  that  twice  the  plane 
surface  ABCD  will  enclose  the  ends  of  any  cylinder,  however 
long  it  may  be,  having  the  same  circumference  as  the  dollar. 


WHfS!*ERfNas   Of   AN   OLD    m 


!  19 


And  equally  in  the  ^ame  directions  twice  this  same  surface  must 
enclose,  and  therefore  be  equivalent  to  the  half  surface  of  any 
sphere  whose  circumference  is  equal  to  that  of  the  dollar. 

"But  Ellen  thinks  the  old  Pine  can  see  that,  if  this  cylinder  is 
changed  into  a  sphere  having  equal  circumference,  two  sur- 
faces would  cover  it  in  two  directions,  which  we  will  call  east 
and  west^  and  two  more  equal  surfaces  in  the  other  two  direc- 
tions, which  we  will  call  north  and  south.  And  therefore  the 
surface  of  a  sphere  is  equal  to  that  of  four  ^reat  circles  of  the 
sphere." 

"The  old  Pine  isn*t  quite  certain  that  he  understands  this/*  I 

Wild/' 


•♦Tlien  Ellen  will  explain  it  more  fully;'*  she  replied*  **by 
changing  this  figure  into  a  sphere  ;  that  is  she  will  make  a  sphere 
having  the  same  circumference,  and  enclose  it  in  a  cylinder. 

**  It  looks  awfully  pretty.  Well,  Ellen  can  see,  and  the  old 
Pine  will  see,  that  it  must  take  more  to  cover  the  sphere  than 
it  did  the  dollar.  Ellen  can  see,  and  the  old  Pine  will  scei 
that  it  must  take  just  as  much  to  cover  this  sphere  east  and 
west,  or  in  the  direction  AC,  as  it  did  the  dollar,  and  no  more,  for 


I20  ELLEN    OR 

this  distance  is  neither  increased  or  lessened.  But  the  figure 
has  increased.  It  extends  now  north  and  south  just  as  much 
as  it  did  east  and  west;  and  therefore  it  will  take  just  as  much 
to  cover  it  in  those  directions  as  it  did  to  cover  the  dollar,  just 
as  much  and  no  more.  And  this  because  of  the  absolute  equal- 
ity of  its  different  hemispheies. 

"In  such  a  sphere,  or  such  a  circle,  or  in  any  figure,  the 
amount  of  surface  in  any  one  direction,  north,  south,  east,  west 
depends  upon  the  dimensions  of  the  figure  in  that  direction. 
Nor  will  it  make  any  difference  in  amount  where  this  surface 
comes;  that  is,  whether  all  in  a  plane  surface,  or  distributed  in 
different  planes.  This  is  true  of  square  surfaces  as  well  aa 
spherical  surfaces.     It  is  true  of  all  surfaces. 

**Thus,  take  a  brick  wall  8  feet  long,  6  feet  high,  and  4  inches 
thick,  built  north  and  south.  It  will  have  two  surfaces 
east  and  west,  though  these  will  both  be  a  part  of  the  same 
b»'icks  and  their  extent  will  be  6  X  8=48  feet  each.  If  the  brick 
are  2  by  4  by  8  inches,  the  surface  of  this  wall  north  and 
south  will  be  4  inches  the  width  of  the  brick,  multiplied  by 
6  feet,  the  heij^ht  of  the  wall,  multiplied  by  2=576  square 
inches,  or  4  square  feet. 

"Ellen  will  widen  this  wall  by  making  it  two  bricks  thick. 
There  remains  the  same  surface  east  and  west  as  before,  but 
that  north  and  south  is  doubled.  And  so  indefinitely,  if  she 
extends  the  width  of  the  wall,  or  as  she  extends  its  width,  the 
original  surfaces  east  and  west  will  remain  the  same,  whilst 
those  north  and  south  will  be  constantly  increased. 

**  Suppose,  now,  Ellen  increases  the  thickness  of  a  part  of  the 
wall,  beginning  at  the  distance  of  a  brick  from  each  end,  the 


WHISPERINGS    tu     AN    oLI*    ViS\L 


sSmce  of  the  wall  east  and  west  will  remain  the  same,  though 
extended  irregularly,  that  is,  no  longer  a  plain  surface;  but 
llic  other  surfaces  north  and  south  will  be  again  increased  by 
the  width  of  a  brick,  although  extended  irregularly,  that  is. 
although  they,  too,  are  no  longer  plain  surfaces.  And  if  we 
continue  the  structure  in  this  manner^  dropping  two  bricks  in 
Tfi^h  at  each  additional  layer  unt"!  we  reach  ibc  limit  of  one 
'l>rick,  the  same  principles  will  hold  trite.  There  will  still  be 
just  as  "much  and  no  more  surface  east  and  west,  whilst  that 
north  and  south  has  been  constantly  increased, 

•*In  other  words  the  aggregate  surfaces  parallel  to  any  given 
surface,  and  representing  all  the  parts  of  that  surface,  are  equal 
to  it,  no  more,  no  less;  no  matter  what  their  number  may  be, 
or  at  what  distance  they  may  be  placed  from  the  given  surface. 

**Thus,  the  bases  of  a  cylinder  will  be  the  same  whether  the 
length  of  it  13  increased  or  shortened. 

•*  Every  sphere  may  be  divided  into  eastern  and  western  or 
northern  and  southern  hemispheres,  but  no  sphere  can  exist 
without  extending  in  four  directions,  north,  south,  cast  and 
west.  The  covering  or  surface  east  and  west,  as  we  have  seen, 
will  require  two  great  circles,  and  so,  too,  with  its  extension 
north  and  south;  and  this  is  all.  And,  as  Ellen  has  said,  it 
makes  no  difference  whether  these  coverings  north  and  south 
or  cast  and  west  are  made  at  on.'^e  in  plane  surfaces,  as  in  a  great 
circle,  or  distributed  over  the  distance  of  two  radii,  when  such 
great  circle  is  changed  to  a  sphere.  In  this  last  the  old  Pine 
will  see  that  it  will  require  four  great  circles  to  effect  the  cover- 
ing; two  for  that  part  of  the  sphere  which  extends  east  and 
west,  and  two  for  that  part  which  extends  north  and  south. 


122  KLLEN    OR 

"The  old  Pine  cannot  help  but  see  that  these  principles  muse 
hold  equally  true  with  curved  figures  or  surfaces,  the  only  dif- 
ference being  in  the  frequency  of  the  changes  of  the  plane  sur- 
faces of  the  wall. 

**And  he  will  see,  too,  that  in  a  sphere  we  will  come  to  our 
limits  in  both  directions,  when  there  will  be  precisely  as  much 
surface  north  and  south  as  east  and  west,  that  is  in  both  hemi- 
spheres, the  last  of  which  has  been  created  by  extending  two 
plane  surfaces,  but  the  first  of  which  has  been  neither  increased  or 
diminished  a  particle,  although  differently  placed.  That  is,  it  is 
no  longer  a  plane  surface,  but  distributed  over  a  spherical  one. 

*'Thus  in  the  plane  figure  A  BCD,  [page  1 19]  in  which  is  in- 
scribed the  great  circle  of  a  sphere,  should  the  sides  of  the  square 
which  enclose  the  circle  be  continually  doubled,  they  would 
approach  nearer  and  nearer  to  the  circumference  of  the  sphere, 
and  finally  to  our  apprehensions  equal  it,  or  become  merged 
in  it. 

*'The  combination  of  the  two  makes  the  apparently  curved 
lines,  and  that's  all  there  is  in  the  surface  of  a  sphere.  And 
therefore  they  make  or  equal  the  surface. 

**  And  therefore  the  surface  of  a  sphere  equals  that  of  four 
great  circles. 

"The  demonstration  is  complete,  first,  that  the  material  in  the 
surfaces  of  four  great  circles,  if  distributed  over  innumerable 
parallel  planes,  is  sufficient  to  cover  the  surface  of  a  sphere  of 
which  they  are  the  circles ;   and  second,  that  they  do  do  it." 

"Then,"  I  said,  "Ellen  admits  that  the  constant  division  of 
a  straight  line  will  produce  a  curved  line." 

"She  admits  nothing  of  the  kind,"  she   answered.     "The 


nilSPEklM.s    ul-    AN    OLD    PINE 


,  she  will  admit  is  that  it  practically  operates  in  that  manner. 
As  Ellen  has  said  before,  what  she  especially  objects  to  in  this 
method  of  demonstration  is  the  stupid,  blundering  manner  in 
which  the  proposition  is  stated  i  first,  that  such  a  limit  'S  some- 
thing which  can  always  be  approached,  but  ne/er  reached ;  and 
second,  that  by  constant  division  the  approaching  straight  line 
finally  becomes  identical  with  the  limit  Certainly  if  it  does,  it 
is  not  true  that  the  limit  can  never  be  reached.  The  principle 
for  all  practical  purposes,  or  at  least  for  all  ordinary,  practical 
purposes,  Ellen  accepts;  but  it  doesn't  at  all  follow  that  a  differ- 
<mce  doesn't  exist  because  we  cannot  perceiv^e  it.  And  so, 
^galn.  such  imperceptible  difference  to  us,  in  its  own  order  of 
differences,  might  be  of  infinite  moment.  Thus,  a  crack  almost 
or  quite  imperceptible  to  us,  might  be,  to  certain  animals,  a 
ravine  impossible  to  be  crossed ;  for  the  microscope  demon- 
strates that  such  orders  of  animals  exist,  Ellen  recognizes  the 
infinite  in  every  direction.  She  recognizes  that  there  ma}'  be, 
and  indeed  thinks  must  be,  innumerable  vistas  of  existence,  and 
therefore  of  knowledge,  of  which  we  have  no  perception  what- 
ever,** 

"But.  how  would  Ellen  explain  this  apparent  forming  of 
cttrved  lines  or  spherical  surfaces  by  the  constant  division  of 
straight  lines?" 

**  She  thinks  that  the  whole  operation  is  delusive.  That  is, 
that  it*s  a  mere  effect  of  vision.  No  such  combination  is  made; 
but  by  the  limitation  of  vision — in  the  limitation  of  vision — 
such  appearances  take  place." 

**Thcn  Ellen  thinks  that  the  limits  of  the  straight  lines  are 
Mtreached?'* 


124  ELLEN   OR 

•**  Ellen  thinks  that  they  have  no  limits.  Thus  we  suppose 
blood,  all  of  blood,  to  be  red ;  but  when  the  limits  of  our  vision 
are  extended  by  a  microscope  we  see  that  only  a  minimum  part 
of  the  blood  is  red, — small  particles,  whilst  the  greater  part  of  it 
is  colorless.  But  Ellen  thinks  that  the  straight  lines  thus  com- 
bined include  the  necessary  material  to  cover  the  surface  of  the 
sphere. 

"And  therefore  the  surface  of  a  sphere  is  equal  to  that  of 
four  of  its  great  circles. 

"  And  as  the  surface  of  a  circle  is  equal  to  its  mean  circum- 
ference by  its  radius,  the  surface  of  the  sphere  will  be  equal  to 
four  times  this,  which  would  be  the  mean  circumference  by  two 
diameters;  or,  as  usually  stated  in  geometries — ^because  the 
mean  circumference  is  at  half  the  radius,  and  for  no  other  rea- 
on,  no  other  possible  reason, — the  circumference  by  the 
diameter. 

**A11  that  Ellen  lacks  now,  in  the  consideration  of  these 
spherical  figures,  is  the  direct  principle  for  obtaining  the  vol- 
ume of  a  sphere,  and  this  she  thinks  the  hobble  bush  will  find 
out,  for  he  is  awfully  pretty  and  gave  Ellen  once  a  beautiful 
leaf  to  eat  her  strawberries  on." 

"The  hobble  bush  is  a  very  sprawling  and  disagreeable  kind 
of  a  bush,"  I  said. 

**  He  never  gave  the  old  Pine  a  leaf  to  eat  his  strawberries 
on,"  she  answered.  "  Ellen  thinks  he  is  lovely,  has  the  most 
beautiful,  oval  leaves  and  the  prettiest  of  red  berries.  The  old 
Pine  is  jealous  of  him." 

•*The  old  Pine  doesn't  like  him  at  all,"  I  answered;  and  if 
he  doesn't  mind  his  business  he  will  throw  him  over  the  moun- 


WHISPERINGS   OF  AN   OLD   PINE 


125 


tain  down  in  the  valley  with  the  sheep  and  the  cows,  who  will 
eat  him  up/* 

'*Thc  old  Pine  will  have  quite  a  job/*  she  replied^  **for  Ellen 
knows  more  than  ten  thousand  hobble  bushes  on  these  moun- 
tains. They  are  in  all  the  woods,  in  every  shaded  dell,  and  all 
the  sunshine  they  get  is  that  which  falls  down  among  them 
from  between  the  trees. 

••And  Ellen  thinks  ever>'thing  of  them,  because  with  their 
white  flowers,  big  sober  leaves,  shy  mannersi  and  pretty  berries, 
they  ornament  the  woods  from  the  earliest  spring  to  the  latest 
autumn. 

••  But  if  the  old  Pine  is  so  jealous,  Ellen  will  find  out  for  her- 
self about  the  sphere, 

"The  volume  of  a  sphere  consists  of  the  surface  multiplied 
by  the  number  of  times  it  is  taken,  this  number  of  times  being 
expressed  in  terms  of  the  radius, 

"In  the  great  circle  of  a  sphere,  which  is  composed  of  two 
dimensions  and  which  may  be  supposed  to  be  formed  of  con- 
tiguous circumferences  from  the  outside  to  the  centre  each 
uniformly  shorter  than  the  preceding,  the  surface  is  equal  to 
the  average  circumference  by  the  radius,  or  the  outside  circum- 
ference by  half  the  radius.  For,  at  the  middle  point,  the 
interior  half  will  supplement  the  exterior  half  of  the  circum- 
ferences, so  as  to  make  them  all  of  equal  length,  when  their 
thickness  or  altitude  can  be  measured  by  the  radius. 

•*But  in  the  sphere  we  will  have  three  dimensions.  And  it 
requires  as  much  to  extend  the  sphere  north  and  south  as  east 
and  wesL  And  therefore  instead  of  half  and  half  as  in  a  circle 
or  in  a  cylinder,  which,  similarly  to  a  circle,  may  be  considered 


125  ELLEN   OR 

to  be  composed  of  a  series  of  convex  surfaces  each  shorter  than 
the  preceding,  as  Ellen  has  before  illustrated,  we  will  want  two- 
thirds  to  complete  one-third,  one-third  for  each  dimension  as  in 
the  cone ;  and  therefore  the  volume  of  a  sphere  will  equal  its 
surface  by  one-third  its  radius. 

*'  That  is  to  say,  it  will  take  its  surface  the  thickness  of  one- 
third  the  radius  to  make  the  volume  of  the  sphere." 

"But  cannot  Ellen  demonstrate  this  in  any  other  way?"  I  asked 

**She  thinks  she  can,"  she  answered. 

**The  surface  is  equal  to  that  of  four  great  circles  of  the 
sphere.  Ellen  will  take  one  great  circle  and  place  it  upon  the 
ground.  But  the  next  surface  to  the  first,  or  second  surface, — 
for  we  can  suppose  the  sphere,  every  sphere,  to  be  composed  of 
a  series  of  surfaces  enclosed  within  each  other, — will  also  equal 
four  great  circles  of  the  sphere  of  which  it  is  the  surface,  whose 
diameter,  and  therefore  whose  surface  and  volume,  is  just  the 
least  little  tiny  bit  smaller  than  the  previous,  or  first  surface. 
Ellen  will  take  this  great  circle  and  lay  it  very  carefully  upon 
the  first  one.  And  then  she  will  take  the  third  surface,  which 
will  be  the  surface  of  the  third  sphere  just  the  least  tiny  little 
bit  smaller  than  the  surface  of  the  second  sphere  and  which 
surface  will  also  be  equal  to  four  of  its  great  circles,  and  she 
will  place  one  of  these  circles  just  the  least  little  tiny  bit  smaller 
than  the  second,  which  was  just  such  another  little  tiny  bit 
smaller  than  the  first,  upon  the  second.  And  Ellen  will  keep 
awfully  busy  and  continue  to  gather  the  circles  together  of  each 
succeeding  sphere,  every  one  of  them  just  the  least  little  bit 
smaller  than  the  one  preceding  until  she  comes  to  the  last  one 
which  will  represent  zero,  or  be  dreadfully  near  it. 


WHISPERINGS   OF  AN    OLD    PINE 


127 


"And  the  old  Pine  will  see  that  she  will  have  a  cone.  ABC 
t>E,  —  a  prett>'' flat  kind  of  a  cone  with  a  right  angle  at  A,  but 
^il  the  more  substantial,  it  would  be  almost  impossible  to  blow 
it  over, — whose  volume  represents  one-fourth  of  the  volume  of 
the  sphere,  a  great  circle  of  which  is  the  base  of  the  cone,  and 
its  radius  the  altitude  of  the  cone. 


5f-r  --\-  1^ 


•*But  the  volume  of  a  cone,  as  w^e  have  seen,  is  its  base  by 
one^third  its  altitude.  And  therefore,  the  v^olume  of  a  sphere 
IS  its  surface  multiplied  by  one-third  of  its  radius." 

•*  And  where  will  what  Ellen  calls  the  average  surface  come?'* 
I  asked.     **VVill  that  be  at  one-third  the  radius?" 

'*  No  it  will  not»"  she  answered,  "for  in  the  double  division  of 
material  this  material  is  too  much  mixed  up.  Where  there  are 
but  two  dimensionsi  it  is  plainly  evident  where  such  average  is 
situated.  But  where  another  dimension  is  added,  this  is  not 
thus  self-evident;   but  it  can  be  found  by  computation. 

'•Construct  the  pyramid  O  — A  BCD;  and,  from  its  apex,  draw 
OH  perpendicular  to  the  base.  Also  at  one-third  the  distance 
OH  from  the  apex  make  a  new  base  abed  parallel  to  A  BCD. 

**  Because  of  the  uniform  divergence  of  the  sides  of  each  angle 
ttO  wc  will  have  O a  :  OA  ;:  Ob  :  OB  ::Oc  :  OC  :  Od  : 
OD::ab  :  AB::bc  :  BC::cd  :  CD::da:  DA:  Oh:  OH 
::ah;  AH::bh  :  BH::ch  :  CH::hd  ;  HD. 


128  ELLEN   OR 

"  But  if  certain  distances  as  2  and  4  are  proportionals  with 
other  distances  as  3  and  6  their  squares  will  be  proportionals." 

"  And  why  is  that,"  I  asked. 

**  Because  in  such  case  each  proportion  is  made  proportion- 
ally larger. 

"And  therefore  AB^  :  ab^  ::  0H2  :  Oh^.  That  is,  the  area 
of  the  base  AB CD  :  area  of  base  abcdirOH^  :  Oh^. 


"Suppose  the  base  of  a  pyramid  OABCD  to  be  3x6= 
18  feet.  The  apex  will  be  zero.  And  because  of  the  uniform 
divergence  of  a  pyramid  from  the  apex  to  the  base,  at  one- 
third  from  the  apex  the  dimensions  will  be  1X2=2  feet,  and 
at  two-thirds  from  the  vertex,  or  one-third  from  the  base, 
2X4=8  feet.  At  half  the  distance  from  the  apex  it  will  be 
i^X3=4j  feet.  But  the  average  base  will  be  6  feet,  and 
therefore  lies  between  one-third  and  one  half  from  the  base  to 
the  apex. 

"  In  the  case  of  the  pyramid,  the  base  is  to  the  average  base 
as  the  square  of  the  altitude  of  the  pyramid  is  to  the  square  of 


WHISPERINGS   OF  AS  OLD   PINE 


129 


the  distance  of  the  average  base  from  the  apex  of  the  pyramid* 
And  as  the  average  base  by  hypothesis  is  one-third  the  base,  the 
proportion  of  the  square  of  the  altitude  and  the  square  of  the 
distance  from  the  average  base  to  the  apex  must  be  one-third. 

**Thus:  If  the  base  of  the  pyramid  O— A  BCD  is  3  by  6 
and  the  altitude  12,  we  will  have  the  base  18  is  to  6,  the  average 
base,  as  144,  the  square  of  the  altitude  of  the  pyramid,  is  to  the 
square  of  the  ahitudc  of  the  pyramid,  O— a  bed.  Or  18  :  6 :: 
144  :  to  tlie  square  of  the  altitude  sought.  This  is  a  simple 
example  in  the  rule  of  three,  and  the  answer  is  48,  the  square 
root  ol  which  is  6.9282 +;  and  hence,  the  average  base  will 
be  6*9282 +feet  from  the  apex. 

••  In  the  same  way  will  we  get  the  proportions  of  the  surfaces 
of  spheres,  their  altitudes  being  expressed  by  the  radius.  Thus, 
the  surface  is  to  the  average  surface,  as  the  square  of  the 
radius  to  the  square  of  the  distance  from  the  average  surface  to 
the  centre  of  the  sphere. 

**  But  as  by  hypothesis  the  surface  of  the  given  sphere  is  three 
times  the  average  surface,  the  square  of  the  radius  must  be  three 
times  the  square  of  the  radius  of  the  sphere  having  the  average 
surface. 

*' Ellen  thus  hastily  has  outlined  to  the  old  Pine  a  new  geom- 
etry* If  put  into  a  text-book  it  will  want  to  be  more  thoroughly 
illustrated,  and  in  places  somewhat  more  fully  explained,  but 
this  is  easily  done,  and  then  the  science  will  be  taught  in  at 
least  one-third  the  space  or  time — and  Ellen  thinks  in  much 
less  than  that — and  far  more  intelligently. 

**For  EUen*s  geometry  is  based  on  principles  and  not  on 
specifications.     Thus  taught,  the  w^hole  nature  of  construction 


I30  ELLEN   OR 

becomes  familiar  to  both  scholar  and  teacher,  and  a  great 
advance  will  be  made  in  knowledge.  Nor  is  it  possible  to  make 
this  in  any  other  way." 

She  arose,  as  if  to  go. 

The  sun  still  reigned  supreme  in  the  heavens.  .  "Surely/*  I 
said,  **  Ellen  will  not  return  in  the  heat  of  the  day." 

**Thcn,"  she  said,  *'she  will  take  a  good  sleep,  and  the  old 
Pine  must  watch  over  her  and  call  her  when  it  is  time  for  her 
to  start." 

She  threw  herself  again  under  my  branches  and  soon  was 
quietly  sleeping.  When  she  awoke  the  day  had  passed  through 
its  changing  cycles  as  the  years  do,  and  as  the  centuries,  carry- 
ing us,  too,  in  their  onward  course. 

**  Didn't  the  old  Pine  think  it  was  time  for  Ellen  to  go  home?  " 
she  asked. 

"The  old  Pine  was  just  going  to  wake  Ellen,"  I  said 
"although  the  sun  is  yet  over  an  hour  high,  and  he  knows  that 
Ellen  can  reach  the  meadow  in  half  that  time." 

"  But  Ellen  didn't  want  to  hurry  to-day,"  she  answered 
"She  has  done  quite  a  little  bit  of  thinking  to  teach  the  old 
Pine  a  sound  geometry,  and  wants  rest." 

"The  old  Pine  thought  of  that,"  I  said,  "and  whilst  Ellen  has 
been  so  sweetly  sleeping  he  has  recognized  full  well  that  she 
both  needed  and  had  earned  the  rest.  For  accomplishment  is 
always  preceded  by  effort,  and  this  is  equally  true  morally  and 
intellectually,  as  physically.  Repose  follows  as  naturally  as 
night  follows  day." 

"Yes,"  she  said,  "and  this  is  another  most  wonderful  illus- 
tration of  the  intimate  connection,  which  seems  to  amount  to 


WHtSI^ERlNGS    OF   AN    OLD    TINE 


I  si 


lenttcy,  between  the  physical,  intellectual,  and  moral.  For 
repObc  is  of  a  similar  character  whether  from  physical,  or  moral, 
or  intellectual  action;  but  this  is  very  easily  explained,  as  Ellen 
thinks,  for  whatever  the  action  nia\'  have  been,  whether  ph}'S- 
fcal  or  intellectual,  it  is  the  spirit  which  has  performed  it ;  and 
it  is  the  spiritual — the  soul — which  experiences  the  rest. 

"  But  Ellen  now  must  bid  all  her  friends  upon  the  mountain 
good-bye.  For,  as  she  has  said,  she  does  not  want  lo  hurry, 
but  walking  leisurely  reach  her  home  before  the  last  rays  of  the 
setting  sun  disappear." 

Something  over  an  hour  after,  Ellen,  and  the  beautiful 
shadows  of  the  night,  which  apparently  had  flocked  to  her  in 
the  woods,  emerged  together  upon  the  meadow,  and  continued 
together  lo  the  cottage  upon  the  hilL 

•*  It*s  a  weird  company  that  she's  gathered  to  her  now,"  I 
said,  •*  nor  can  she  well  get  rid  of  them  until  the  morning 
light*  But  when  the  morning  breaks,  Ellen  will  arise  with  fresh 
strength  to  seek  other  triumphs;  to  renew  the  pleasures  ^vhich 
come  from  achievement,  and  the  joys  which  follow  duties 
accomplished* 

'On  every  height  there  is  reijose,*** 


132  ELLEN   OR   THE 


IX. 


IT  was  in  the  late  autumn;  the  leaves  were  largely  fallen  from 
*  the  trees  and  the  sighing  winds  wandered  over  hill  and 
meadow,  whistling  amidst  the  dried  grasses,  and  creeping  into 
ever>'  dell  and  along  each  brookside.  Upon  the  mountains  the 
gray  of  winter  began  to  appear,  whilst  still  more  demonstrative 
in  the  higher  heavens  vast  armies  of  clouds  were  gathered : 

"  In  ranks  and  squadrons  and  right  form  of  war." 

At  such  a  time,  when  the  northern  blasts  were  prospecting 
for  their  winter  homes,  and  all  the  country  proclaimed  the 
transformation  of  the  seasons,  Ellen  made  her  next  visit  upon 
our  mountain. 

** Ellen  has  come,"  she  said,  "to  teach  the  old  Pine  Trigo- 
nometry." 

"But  the  winds  are  cold,"  I  said,  "and  the  clouds  are  dark." 
•  "And  Ellen  cares  but  little  for  the  cold  winds  and  not  at  all 
for  the  dark  clouds.  Eor  the  sun  is  her  friend,  and  he  is  still 
high  in  the  heavens,  l^ut  she  is  anxious  to  conclude  with  the 
old  Pine  the  study  of  mathematics,  so  that  from  that  higher 
plane  of  knowledge  they  can  make  further  discovery  into  the 
laws  which  govern  the  universe,  for,  as  Ellen  thinks,  all  of  these, 
spiritual  or  material,  may  be  understood. 

**But  the  old  Pine  must  remember  that  only  those  things 
are  sure,  which  are  accomplished ;  and  therefore  obey  Christ's 
command  to  *  Work  whilst  it  is  yet  day.' 


1 

■ 

THB  HBW  YORK 
FQBUC  UBRART 

VIUIM  routtitAiiatth 
K                      >• 

^W 

WHISPERINGS   OF  AN   OLD   PINE  1 33 

"The  text-books,  generally,  so  far  as  Ellen  has  seen,  begin 
Trigonometry  with  a  discussion  of  logarithms;  but  Ellen  prefers 
to  give  that  later.  For  logarithms  are  not  absolutely  necessary 
to  the  science,  although,  with  sufficient  practice  a  decided  help ; 
the  help  being  in  the  use  of  work  already  done,  by  which 
we  are  enabled  to  employ  addition  and  subtraction,  instead  of 
multiplication  and  division.  The  old  Pine  will  find  tables 
enough  in  Trigonometry  aside  from  those  of  logarithms,  and 
very  valuable  ones  they  are,  of  the  natural  sines  and  tangents, 
cosines  and  cotangents,  secants  and  cosecants,  and  others, 
giving  the  lengths  of  those  lines  for  different  angles  in  a  circle 
whose  radius  is  unity,  which  may  be  adapted  to  a  circle  of  any 
radius  by  multiplying  these  values  by  the  new  radius. 

"Ellen  will  begin  with 

PLANE  TRIGONOMETRY. 

"  Trigonometry  shows  how  to  find  the  remaining  parts  of  a 
triangle  when  certain  parts  are  given. 

"Plane  Trigonometry  treats  of  plane  triangles;  Spherical 
Trigonometry  of  spherical  triangles. 

"The  circumference  of  every  circle  is  supposed  to  consist  of 
360  equal  parts  called  degrees ;  each  degree  of  60  minutes,  and 
each  minute  of  60  seconds. 

"Considering  an  angle  at  the  centre  of  a  circle  to  be  measured 
by  the  arc  intercepted  by  its  sides,  a  right  angle  is  measured  by 
90^,  two  right  angles  by  180^  and  four  by  360^. 

"The  complement  of  an  arc  is  90^  minus  the  arc.  Thus  the 
arc  CF  is  the  complement  of  BF;  the  complement  of  20^  30' 
is  69^  30',  or  of  100°  is— 10°.     In  a  right  angle  triangle  the 


134 


ELLEN   OR  THE 


two  acute  angles  are  equal  to  a  right  angle  and  therefore  com- 
plements of  each  other. 

"The  supplement  of  an  arc  is  i8o^  minus  the  arc.  Thus  the 
arc  DCF  is  the  supplement  of  BF.  The  supplement  of  25^ 
15'  is  154^  45'.  In  general,  if  we  represent  any  arc  by  A,  its 
supplement  is  180— A.  Hence  if  an  arc  is  greater  than  180^ 
its  supplement  must  be  negative.  Thus  the  supplement  of 
200°  is— 20^.  In  any  plane  triangle  the  sum  of  the  angles  is 
180°  and  therefore  each  angle  is  the  supplement  of  the  sum  of 
the  other  two. 

"  The  sine  of  an  arc  is  a  line  drawn  perpendicular  from  one 
extremity,  to  the  diameter  passing  through  the  other  extrem- 
ity. Thus  FG  is  the  sine  of  the  arc  BF  or  of  the  angle 
BAF.     Every  sine  is  half  the  chord  of  double  the  arc. 


•*The  cosine  of  an  arc  is  that  part  of  the  diameter  which  lies 
between  the  foot  of  the  sine  and  the  centre  of  the  circle.  It  is 
also  equal  to  the  sine  of  the  complement  of  the  arc.  Thus 
AG  is  the  cosine  of  the  arc  BF  or  of  the  angle  BAF  and 
equals  FK,  the  sine  of  CF. 


WHISPERINGS    OF    AN   OLD    PINE  1 35 

"The  tangent  of  an  arc  is  the  line  which  touches  it  at  one 
extremity  and  is  terminated  by  a  line  drawn  from  the  centre 
through  the  other  extremity.  Thus  BI  is  the  tangent  of  the 
arc  BF  or  of  the  angle  BAF. 

**  The  cotangent  of  an  arc  is  the  tangent  of  the  complement 
of  that  arc.  Thus  CL  is  the  tangent  of  the  arc  CF  or  the 
cotangent  of  the  arc  B  F. 

"The  secant  of  an  arc  is  the  line  drawn  from  the  centre  of 
the  circle  through  one  extremity  of  the  arc  and  is  limited  by 
the  tangent  drawn  to  the  other  extremity.  Thus  A I  is  the 
secant  of  the  arc  BF  or  the  angle  BAF.  The  cosecant  of  an 
arc  is  the  secant  of  the  complement  of  that  arc.  Thus  AL  is 
the  secant  of  C  F  or  cosecant  of  B  F. 

**The  versed  sine  of  an  arc  is  that  part  of  the  diameter  which 
lies  between  the  foot  of  the  sine  and  the  arc.  The  coversed 
sine  of  an  arc  is  the  versed  sine  of  the  complement  of  that  arc. 
Thus  BG  is  the  versed  sine  of  the  arc  BF  or  the  coversed 
sine  of  the  arc  CF.  The  versed  sine  of  the  acute  angle  BAF 
is  the  radius  minus  the  cosine  AG,  and  of  the  obtuse  angle 
DAF  the  radius  plus  the  cosine  AG. 

"  Since  the  acute  angles  in  a  right  angle  triangle  are  comple- 
ments of  each  other,  the  sine,  tangent  and  secant  of  one  are  the 
cosine,  cotangent  and  cosecant  of  the  other. 

"  The  sine,  tangent  and  secant  of  one  arc  are  equal  to  the 
sine,  tangent  and  secant  of  its  supplement.  Thus  F  G  is  the  sine 
of  BF  or  of  its  supplement  DC F.  Also  BI  the  tangent  of 
BF  is  equal  to  DM  the  tangent  of  DCF.  And  A  I,  the 
secant  of  BF  is  equal  to  A M,  the  secant  of  DCF. 

"The  relations  of  the  sine,  cosine,  etc.,  to  each  other  may  be 


136  ELLEN    OR  THE 

obtained  from  the  principle  of  the  uniform  divergence  of  the 
sides  of  angles.  Thus  in  the  mutually  equiangular  right  angle 
triangles  AGF  and  ABI,  AG  :  GF::  AB  :  BI;  or,— repre- 
senting the  arc  BF  by  A  and  the  radius,  assumed  to  be  unity, 
by  R, — cos.  A  :  sine  A ::  R  :  tan.  A. 

R  sine  A 
Whence  tangent  A= -r- 

COS.  J\ 

FG:AG::AC:CL;  or  sine  A  :  cos.  A ::  R  :  cot.  A 

„„  .       Rcos.  A 

Whence  cotangent  A  =  — ; r— 

**  sme  A 

AG  :  AF::  AB  :  AI;  or  cos.  A  :  R::R  :  secant  A. 

R2 

Whence  secant  A= x 

COS.  A 

FG  :  AF::  AC  :  AL;  or  sine  A  :  R::  R  :  cosec.  A 

Whence  cosecant  A=-. ^ 

sme  A 

BI  :  BA::AC  :  CL;  or  tan.  A  :  R::  R  :  cot.  A 

R2  R2 

Whence  tane^ent  A= — — -«-  or  cot.  A^=i r* 

^  cot.  A  tan.  A 

"Also  in  the  right-angled  triangle  A  GF,(GF)2-t-  (A  G)2  = 

(AF)2,  or  sine  2  A  -f-cos.^  Az=R2  ;    that  is  the  square  of  the 

sine  of  an  arc  plus  the  square  of  its  cosine  equals  the  square  of 

the  radius. 

Whence  sine  A=dt\/^^~'Cos.2  A 


And  cosine  A  =  db\/^^~sinc2  A 
"And  as  the  old  Pine  and  Ellen  proceed  they  will  want  to 
become  familar  with  all  of  these  functions  of  the  circle  to  know: 
First,  that  it  is  impossible  for  one  of  them  to  change  without 
their  all  changing;  second,  that  of  necessity  if  the  movement  of 
one  is  continuous  the  movement  of  all  will  be  continuous ;  third, 


WHISPERINGS   OF   AN   OLD   PINE  ^  1 37 

the  change  of  each  is  a  fixed  quantity,  so  that  any  change  in 
any  angle  will  always  produce  a  particular  change  in  each 
function ;  fourth,  in  arriving  at  any  point  from  any  other  point, 
when  the  movement  is  continuous,  all  intermediate  distances 
must  be  passed  through ;  and  hence,  there  is  between  every  line, 
and  also  between  its  different  parts,  a  fixed  relationship ;  the 
last  being  just  as  true  as  the  first,  and  of  equal  importance  in 
the  consideration  of  this  subject. 

"Thus  let  the  sine,  tangent  or  secant  increase  continuously, 
and  it  is  impossible  for  one  of  them  to  increase  without  the 
others  increasing  correspondingly,  the  cosine,  cotangent  and 
cosecant  will  decrease  continuously;  the  limits  being  between 
zero  and  one,  with  the  sine,  and  one  and  zero  with  the  cosine; 
zero  and  infinity  and  infinity  and  zero,  with  tangent  and  cotan- 
gent; and  one  and  infinity  or  infinity  and  one,  with  secant 
and  cosecant.  In  every  case  it  being  true,  that,  in  passing  con- 
tinuously from  either  extreme  to  the  other,  or  from  any  point 
to  another  point,  all  intermediate  values  must  be  passed 
through.  The  old  Pine  must  see  that  everything  here  is  abso- 
lutely fixed  so  that  always  if  one  of  these  functions  is  changed 
the  others  are  changed  correspondingly.  And  that  means  that 
at  any  intermediate  value  they  always  have  the  same  relative 
positions.  And  therefore  if  four  of  these  functions,  including 
radius,  arc  proportionals  for  two  consecutive  values,  they  will 
continue  to  be  proportionals  throughout  their"  existence." 

"But  why  two,'*  I  asked;  "why  if  they  are  proportionals  at 
one  value  will  they  not  continue  to  be  proportionals?" 

*'  Because  it  is  possible  for  them  to  become  proportionals  at 
a  single  point  when  crossing  the  line  of  equality. 


138 


ELLEN   OR*  THE 


Thus,  in  the  angle  of  45° : 

Cosine  (.707107)  :  tang.  (i)::sine  (.707107)  ::  R  (i) ; 
but  this  proportion  does  not  hold  at  44^  or  46^. 

"It's  an  accidental  proportion  which  the  four  proportionals 
had  been  approaching  from  their  start,  and  recede  from  in  their 
continued  course. 


"At  the  angle 

of  44'' 

Cosine 

=   .719340 

Tangent 
Sine 

=   .965689 
=   .694658 

Radius 

=  1 

And  at  46° 

Cosine     • 

=   .694658 

Tangent 

=  1.03553 

Sine 

=    .719340 

Radius 

=  1.  

X. 


**The  old  Pine  aad  Ellen  will  now  further  examine  the  relation- 
ship which  exists  between  these  different  functions;  and  first 
between  the  sine  and  cosine,  beginning  at  the  angle  of  i^/' 

*'This  will  be  at  the  point  where  the  circle  is  nearest  to  a 
straight  line?"  I  said, 

••Not  at  all/*  she  replied.  "The  curvature  of  the  same  or 
eqti^  circles  is  the  same  at  all  points.  And  therefore  the 
assumption  that  anywhere  it  can  make  angles  the  same  or  simi- 
htt,  whether  with  another  curve  or  with  a  straight  line,  to  those 
made  by  two  straight  lines,  is  impossible. 

•^Ellcn  is  vtry  sorry  that  these  tables  of  sines,  cosines,  etc., 
~  not  accurate^  The  ones  that  she  uses  are  carried  out  to 
decimals.  They  have  been  carried  out  several  more  deci- 
mals, but  it  would  appear  to  be  impossible  that  any  can  be 
accurate.  The  inaccuracy  is  with  those  of  the  smaller  arcs, 
but  AS  the  others  are  based  upon  these,  it  is  carried  on  through 
the  whole.  Thus  it  is  assumed  that  the  sine  of  any  arc  less  than 
iric^  but  little  from  its  arc,  and  in  our  usual  estimate 
ui  valties  this  may  be  true,  but,  as  Ellen  has  said  before, 
all  size  is  relative  to  the  beholder  as  w^ll  as  the  thing  beholden. 
Il  is  also  relative  to  the  position  of  the  thing  beholden  as  well  as 
to  the  thing,  for  as  things  are  removed  from  us  they  grow  small, 
so  that  even  the  largest,  as  a  sphere,  will  decrease,  until  it  dis- 


^^^j^ 


I40  ELLEN   OR  THE 

appears.  This  should  be  a  complete  lesson  to  us  that  size  is 
relative  to  the  beholder,  or  that  real  size  and  apparent  size  are 
different,  this  difference  being  affected  largely  by  location,  and 
also  affected  by  other  causes  as  the  clearness  of  the  atmosphere ; 
but  Ellen  does  not  know,  as  she  has  said  before,  why  all  of 
these  different  causes  are  not  relative  to,  or  concerned  with,  the 
nature  of  vision,  rather  than  with  the  object  seen. 

'*And  indeed  it  is  certain  that  all  perception  or  vision  has 
to  do  with  the  thing  which  perceives  rather  than  with  the  thing 
perceived." 

"Could  it  not  have  to  do  equally  with  each  ?"  I  asked. 

"Possibly  it  might,"  she  replied,  "but  the  perception  of  the 
beauty  or  fragrance  of  a  sweet  pea  is  by  spirit,  that  is,  it  is  the 
effect  of  the  sweet  pea  upon  spiritual  existence." 

"And  yet,"  I  said,  "the  sweet  pea  exists,  must  exist,  in- 
dependent of  any  particular  spiritual  existence,  unless  it  is  the* 
highest,  that  which  has  made  it.  Then  certainly  the  old  Pine 
thinks  it  has  a  defined  existence,  otherwise  it  could  not  affect 
different  spiritual  existences  in  the  same  manner  and  at  differ- 
ent times,  as  we  know  that  it  practically  does." 

"But,"  she  said,  "  its  effect  upon  us  is  in  accordance  with  its 
relative  position  to  us  and  may  be  in  accordance  with  many 
other  things.  Thus  blood,  as  Ellen  has  suggested  before, 
appears  red  to  us  as  seen  by  the  natural  vision,  but  looked  at 
through  a  microscope  only  a  small  part  of  it  is  red." 

"And  yet,"  I  said  "the  sweet  pea  is  none  the  less  real." 

"  Very  possibly  not,"  she  replied.  "  Ellen  cannot  say,  but 
it's  awfully  evanescent.  It  may  last  for  a  day,  but,  as  Ellen 
thinks,  it  is  all  the  time  changing,  in  the  first  place  developing 


WHISPERINGS   OF   AN   OLD     FINE 


141 


a^  to  impress  us  with  a  higher  beauty,  and  then  fading. 
"But  our  estimate  of  it,  as  lillen  has  said,  in  cither  case,  is  more 
or  less  a  mistaken  one. 

"And  yet  EUcn  must  admit  that  it  plays  its  part  independent 
of  her;  nor  would  she  be  able  to  deny  its  fixedness.  By  the 
great  Creator  is  it  made  whether  directly  or  indirectly.  It  is 
the  product  of  mind,  and  made  for  the  uses  of  mind,  whether 
inhabited  by  or  connected  with  an  independent  spiritual  exist- 
ence she  does  not  know. 

"For  whilst  Ellen  cannot  deny  that  things  must  exist  and 
be  different^  and  whilst  we  may  be  able  to  a  certain  extent 
to  define  that  difference,  showing,  perhaps,  that  these  things 
consist  in  essentially  different  (orms  or  qualities  of  matter, 
the  great  fact  must  still  be  true  that  our  estimate  of  them  is 
due  to  their  effect  upon  uSp  and  is  therefore  rather  the  iiiflu- 
eoce  of  matter  upon  spirit, — perhaps  all  spirit,  perhaps  only 
our  own,  but  Ellen  thinks  universal  spirit* — than  the  essential 
nature  of  matter.  Indeed  Ellen  doesn't  know  that  matter 
has  any  essential  nature,  for  it  is  inconceivable  to  her  that 
matter  should  exist  without  spirit.  For  as  it  was  created  by 
spirit,  so  it  must  depend  upon  spirit  for  its  continued  exist- 
ence. Its  influence  upon  spirit  is  another  question,  in  which 
consists,  so  far  as  r-lien  c«»n  see,  our  present  existence.  For 
except  for  such  inrtuence,  so  far  as  Ellen  can  see,  that  exist- 
ed nr**  would  be 

'A  blank  my  lord/ 

**  But  Ellen  must  return  to  the  discussion  of  the  Trigonometry 
for  she  wants  to  finish  it  to-day,  and  the  winds  are  cold  and  the 


142  ELLEN    OR   THE 

clouds  dark,  and  look  as  if  they  were  gathering  for  an  attack 
upon  Ellen  and  going  to  destroy  her." 

*' And  Ellen  would  better  go  home,"  I  said. 

**  And  Ellen  isn't  going  home,  but  is  going  to  stay  up  here 
with  the  old  Pine  and  the  winds,  and  the  clouds,  and  the  old 
Pine  must  take  care  of  her." 

**  He  is  trying  to,"  I  said,  "trying  to  send  her  home." 

**  And  Ellen  won't  go  home,  until  she  is  through.  She  has 
brought  her  luncheon  with  her  again,  and  her  shawl,  and  is 
going  to  teach  the  old  Pine  the  whole  of  Trigonometry  before 
she  goes  back.  That's  what  she  came  for.  And  the  old  Pine 
must  take  care  of  her  here. 

*'To  return  to  the  increments: 

*  Many  a  mickle  makes  a  muckle.' 

**And  besides  if  the  circle  was  big  enough  this  little  would 
be  evident  enough,  and  might  seem,  even  to  us,  as  large.  And 
thus,  as  the  old  Pine  will  see,  all  mathematics  are  filled  with 
inaccuracies;  but  taking  what  we  have  as  a  basis  Ellen  has 
constructed  the  following  tables : 

"  First  a  table  of  sines  and  cosines,  illustrating  more  fully  the 
differences  between  them. 

"The  first  column  gives  the  length  of  the  arcs;  the  second 
the  natural  cosines  of  these  arcs  in  a  circle  whose  radius  is 
unity.  The  third  shows  the  difference  between  these  cosines, 
and  the  fourth  is  a  table  of  second  differences,  being  the  differ- 
ences between  the  differences  of  the  cosines. 

*' There  is  a  fifth  table  of  the  third  order  of  differences,  lacking 
uniformity,  because  obtained  from  values  which  are  not  complete. 


WHISPERINGS  OF  AN   OLD   PINE 


143 


Value  of            Valui 

•  of  Cosines  for 

First  Order 

Second  Order 

Third  Order 

Arcs                 a  A\ 

idiu:  of  Unity 

of  Differences 

of  Differences 

of  Differences 

qO       I 

.000000 

1° 

.999848 

.000152 

2° 

999391 

.000457 

•305 

3° 

998630 

.000761 

304 

I 

4° 

997564 

.001066 

30s 

—  I 

5° 

99619s 

.001369 

303 

2 

6° 

994522 

.001673 

304 

—  I 

7° 

992546 

.001976 

303 

I 

8° 

990268 

.002278 

302 

i 

90 

987688 

.002580 

302 

0 

•10° 

984808 

.002880 

300 

2 

11° 

981627 

.003181 

301 

—  I 

12° 

978148 

.003479 

298 

3 

13° 

974370 

.003778 

299 

—  I 

14° 

970296 

.004074 

296 

3 

15^ 

965926 

.004370 

296 

0 

16" 

961262 

.004664 

294 

2 

17° 

956305 

.004957 

293 

I 

18° 

951057 

.005248 

291 

2 

19° 

945519 

.005538 

290 

I 

20° 

939693 

.005826 

288 

2 

210 

933580 

.006113 

287 

I 

320 

927184 

.006396 

283 

4 

230 

920505 

.006679 

283 

0 

24<^ 

91354s 

.006960 

281 

2 

25^ 

906308 

.007237 

277 

4 

26° 

898794 

.007514 

277 

0 

27° 

891007 

.007787 

273 

4 

28^ 

.882948 

.008059 

272 

I 

290 

874620 

.008328 

269 

3 

30° 

866025 

.008595 

267 

2 

44 

ELLEN  OR  THE 

31° 

.857167 

.008858 

263 

4 

32° 

.848048 

.009119 

261 

2 

33° 

.838671 

.009377 

258 

3 

34° 

.829038 

.009633 

256 

2 

35° 

.819152 

.009886 

253 

3 

36° 

.809017 

.010135 

249 

4 

37° 

.798636 

.010381 

246 

3 

38° 

.78801 1 

.010625 

244 

2 

39° 

.777146 

.010865 

240 

4 

40° 

.766044 

.011102 

237 

3 

41° 

.754710 

•01 1334 

232 

5 

42° 

.743145 

.011565 

231 

I 

43° 

•731354 

.011791 

226 

5 

44° 

•719340 

.012014 

223 

3 

45° 

.707107 

.012233 

219 

4 

46° 

.694658 

.012449 

216 

3 

47° 

.681998 

.012660 

211 

5 

48° 

.669131 

.012867 

207 

4 

49° 

.656059 

.013072 

205 

2 

5o° 

.6^788 

.013271 

199 

6 

51° 

.629320 

.013468 

197 

2 

52° 

.615661 

.013659 

191 

6 

53° 

.601815 

.013846 

187 

54° 

.587785 

.014030 

184 

55° 

•573576 

.oi4?09 

179 

56° 

•559193 

.014383 

174 

57° 

•544639 

•014554 

171 

58° 

.529919 

.014720 

166 

59° 

.515038 

.014881 

161 

60° 

.500000 

.015038 

157 

61° 

.484810 

.015190 

152 

62° 

•469472 

•015338 

148 

63° 

•453990 

.01  5482 

144 

WHISPERINGS   OF  AN   OLD    PINE  145 


<>4'> 

•438371 

.015619 

137 

7 

*5° 

.422618 

.015753 

134 

3 

«P 

.406737 

.015881 

128 

6 

6f 

.390731 

.016006 

125 

3 

68*^ 

.374607 

.016124 

118 

7 

69« 

.358368 

.016239 

"5 

3 

70° 

.342020 

.016348 

109 

6 

71° 

.325568 

.016452 

104 

5 

72° 

.309017 

.016551 

99 

5 

73° 

.292372 

.016645 

94 

5 

74° 

.275637 

.016735 

90 

4 

75° 

.258819 

.016818 

83 

7 

76° 

.241922 

.016897 

79 

4 

77° 

.224951 

.016971 

74 

5 

78° 

.207912 

.017039 

68 

6 

79° 

.190809 

.017103 

64 

4 

800 

.173648 

.017161 

58 

6 

810 

.156434 

.017214 

53 

5 

82° 

.139173 

.017261 

47 

6 

83° 

.121869 

.017304 

43 

4 

84° 

.104528 

.017341 

37 

6 

85^ 

.087156 

.017372 

31 

6 

86" 

.069756 

.017400 

28 

3 

87° 

.052336 

.017420 

20 

8 

88<5 

.034899 

•017437 

17 

3 

89° 

.017452 

.017447 

10 

7 

900 

.000000 

.017452 

5 

5 

•  These  differences  represent  millionths  but  for  convenience  the  decimal  j)oinl 
wd  the  c>i>hcTS  that  immediately  follow  are  omitted. 

"  It  will  be  seen  that  there  are  very  considerable  differences  in 
the  cosines.  And  these  must  represent  the  spaces  in  which 
intermediate  sines  may  be  extended  from  the  cur\'ed  roof  above. 


146  ELLEN   OR  THE 

*'  Here  we  have  the  natural  sines  as  given  in  the  tables,  con- 
sisting of  degrees  and  minutes.  And  between  them  are  other 
spaces  in  which  might  be  sines  consisting  of  degrees,  minutes, 
and  seconds,  very  readily  estimated.  After  them  there  would 
be  an  infinite  succession  of  sines  which  we  may  suppose  to  con- 
sist of  degrees,  minutes,  seconds,  and  a  further  corresponding 
division  to  be  followed  by  other  sines  including  a  similar 
additional  division  to  infinity. 

"  And  in  all  these  cases,  so  far  as  they  might  extend,  each 
sine  will  be  distinct  and  separate  from  its  inception  to  its  termi- 
nation, the  accurate  expression  of  this  last  artificially,  being  im- 
possible. 

"There  would  be,  then,  to  be  added  to  each  of  these  sines  as 
obtained  artificially,  what  would  appear  to  be  an  infinite  series 
of  numbers,  which  of  necessity  must  represent  the  space  exist- 
ing between  the  lower  extremity  of  the  sine  and  the  cosine." 

*'Then  Ellen  admits  of  inaccurate  conditions  in  different 
directions,"  I  said. 

"She  admits  of  them  in  length  and  number,"  she  replied; 
**  that  is,  they  are  all  inaccurate  as  to  length,  nor  is  there  any 
possible  expression  for  their  number." 

'*  But,"  I  said,  **  the  usual  tables  as  given  are  accurate  to  six 
figures  are  they  not?" 

"No  they  are  not,"  she  replied.  "  Ellen  knows  that  the 
ordinary  form  of  statement  is  that  they  are  accurate  to  six 
figures,  and  this  might  be  true  if  it  was  true,  but  it  isn't. 

**That  is,  the  custom  is  to  leave  the  last  figure  given  accurate 
if  the  next  (not  given)  would  be  4  or  under,  but  if  this  next 
is  5  or  over  the  last  figure  is  made  one  larger  which  would 


WHISPERINGS   OF   AN    OLD    PINE  I47 

nullify  the  statement  that  the  whole  was  accurate  to  six  figures, 
the  truth  then  being  that  it  was  accurate  only  to  five. 

**The  eminent  Italian  mathematician  Cavalieri  considered 
lines  to  consist  of  an  infinite  number  of  small  points ;  surfaces 
of  an  infinite  number  of  parallel  lines,  the  breadths  of  which  are 
indefinitely  small ;  and  solids  of  an  infinite  number  of  parallel 
planes,  or  rather  of  indefinitely  thin  plates  or  laminae. 

'*Mr.  Elias  Loomis  in  one  of  his  Mathematical  works  says: 

'According  to  Newton  all  bodies  are  supposed  to  be  generated 
by  continuous  motion;  a  line  by  the  motion  of  a  point;  a  surface 
by  the  motion  of  a  line,  either  constant  or  variable ;  and  a  solid  by  the 
motion  of  a  plane  which  either  retains  the  same  magnitude,  or  varies 
according  to  a  certain  law.  All  other  quantities,  in  whatever  way  they 
may  be  expressed,  are  conceived  to  be  generated  in  a  similar  manner. 
The  relative  rates  of  velocities  with  which  magnitudes,  and  the  variables 
on  which  they  depend,  are  increasing  at  any  instant,  are  termed  their 
fluxions;  and  the  whole  quantities  generated  in  consequence  of  such 
velocities  of  increase  are  termed  the  fluents' 

**With  such  an  illustration  of  comprehensive  and  accurate 
thought,  it  is  most  remarkable  that  the  modern  text-book 
makers  should  preface  their  work  with  the  most  extraordinary 
statement  that  there  was  no  such  thing  as  a  point.  They  might 
as  well  assert  that  there  is  no  material  thing.  For  the  smallest 
and  the  largest  are  all  made  of  matter.  Else  it  would  be  a  sham ; 
and  it  is  no  sham.  It  is  tremendously  real.  For  everything  is 
equally  a  part  of  creation.  Nor,  as  Ellen  thinks,  would  it  be 
possible  for  anything  to  be,  if  it  was  not  a  desirable  part,  and 
if  desirable,  important. 


148 


ELLEN   OR  THE 


XL 


SOLUTION  OF  RIGHT-ANGLED  TRIANGLES. 

Theorem  I.  ' 

"  /;/  any  right-angled  triangle,  the  radius  is  to  tlu  hypotenuse 
as  the  sine  of  either  aeute  angle  is  to  the  opposite  side^  or  the 
cosine  of  either  acute  angle  to  the  adjacent  side. 


**Let  the  triangle  ABC  be  right  angled  at  C,  then  will 
R  :  A B::  sine  A  :  BC::cos.  A  :  AC. 

'•From  the  point  A  as  a  center,  with  a  radius  equal  to  unity 
describe  the  arc  DE,  and  on  AC  draw  the  perpendicular  EF^ 
Then  EF  will  be  the  sine,  and  AF  the  cosine  of  the  angle  A. 
Because  of  the  uniform  divergence  of  the  sides  of  an  angle, 

AE  :  AB::EF  :  BC, 
or  R  :  A  B::  sine  A  :  BC. 

Also,  AE  :  AB::AF  :  AC, 

or  R  :  AB::cos.  A  :  AC. 


■ 

^^^^^^^H 

THE  NEW  \ 
PDBLIC  LlHl 

llL01ltC  fOUNPATLOIil 

^^1 

WHISPERINGS   OF   AN    OLD   PINE  1 49 

Theorem  II. 

**In  any  right-angled  triangle  the  radius  is  to  either  side  as 
the  tangent  of  the  adjacent  acute  angle  is  to  the  opposite  side^  or 
the  secant  of  the  same  angle  to  the  hypotenuse. 

"Let  the  triangle  ABC(page  148)  be  right  angled  at  C,  then 
R  :  AC:: tang.  A  :  BC::sec.  A  :  AB. 

"From  the  point  A  as  a  center,  with  a  radius  equal  to  unity, 
describe  the  arc  DE,  and  from  the  point  D  draw  DG  perpen- 
dicular to  AC.  Then  DG  will  be  the  tangent,  and  AG  the 
secant  of  the  angle  A.  Because  of  the  uniform  divergence  of 
the  sides  of  an  angle, 

AD  :  AC::DG  :  BC, 
or  R  :  AC::  tang.  A  :  BC. 

Also,  AD  :  AC::  AG  :  AB, 

or  R  :  AC::  sec.  A  :  AB. 

"  In  every  plane  triangle  there  are  six  parts :  three  sides  and 
three  angles.  Of  these,  any  three  being  given,  provided  one  of 
them  is  a  side,  the  others  may  be  determined.  In  a  right- 
angled  triangle,  the  right  angle  is  always  given ;  and  if  one  of 
the  acute  angles  is  given,  the  other,  being  its  complement,  is 
known.  Hence  the  number  of  parts  to  be  considered  in  a 
right-angled  triangle  is  reduced  to  four,  any  two  of  which  being 
given,  the  others  may  be  found. 

"  It  is  desirable  to  have  appropriate  names  by  which  to  des- 
ignate each  of  the  parts  of  a  triangle.  In  a  right-angled  trian- 
gle one  of  the  sides  adjacent  to  the  right  angle  is  called  the 
base,  the  other  the  perpendicular.     The  three  sides  will  then  be 


ISO  ELLEN   OR  THE 

called  the   hypotenuse,  base  and  perpendicular.     Of  the  two 

acute  angles,  that  which  is  adjacent  to  the  base  is  called  the 

angle  at  the  base,  and  the  other  the  angle  at  the  perpendicular. 

**  We  therefore,  have  four  cases,  according  as  there  are  given, 

1.  The  hypotenuse  and  the  angles; 

2.  The  hypotenuse  and  base  or  perpendicular; 

3.  The  base  or  perpendicular  and  the  angles;  or, 

4.  Base  and  perpendicular. 

All  of  these  may  be  solved  by  the  preceding  theorems. 

Case  I. 

'*  Given  the  hypotenuse  and  the  angles,  to  find  the  base  and 
perpendicular, 

"This  is  solved  by  Theorem  I. 

**  Radius  :  hypotenuse ::  sine  of  the  angle  at  the  base  :  perpen- 
dicular \\  cosine  of  the  angle  at  the  base  :  base, 

"Ex.  I.  Given  the  hypotenuse  275,  and  the  angle  at  the  base 
57°  23',  to  find  the  base  and  perpendicular. 

The  natural  sine  of  57^  23'  is  .842296; 

"         cosine         "  .539016. 

Hence  i  :  275  ::  .842296  :  231.631  =AB. 

I  :  275  ::  .539016  :  I48.229=AC. 

''This  is  by  natural  numbers.     By  logarithms,  we  will  have 

Radius,  i  log.  .000000 

Is  to  the  hypotenuse  275  log.  2.439333 

As  the  sine  of  C  57°  23'  log.  sine  9.925465 


To  the  perpendicular  231.63  log.  2.364798 


WHISPERINGS    OF   AX   OLD    PINE  I51 

'•Ten  is  dropped  from  the  characteristic  of  the  logarithm  of 
the  perpendicular,  because  the  logarithms  of  the  sines  in  the 
table  are  ten  too  large. 

Also,  Radius,  i  log.  .000000 

Is  to  the  hypotenuse  275  log.  2.439333 

As  the  cosine  of  C  57°  23'       log.  cos.  9.731602 


To  the  base  148.23  log.   2.170935 

Case  II. 

*  Given  the  hypotenuse  and  one  other  side,  to  find  the  angles  and  the 
remaining  side.* 

"By  Theorem  I. 

'  Hypotenuse  :  radius : :  base  :  cosine  of  the  angle  at  the  base.     Radius 
:  hypotenuse:: sine  of  the  angle  at  the  base  :  perpendicular.' 

"When  the  perpendicular  is  given,  perpendicular  must   be 
substituted  for  base  in  this  proportion. 

Case  III. 

'Given  base  or  perpendicular  and  the  angles,  to  find  the  other  sides. 

"By  Theorem  II. 

'Radius  :  base:: tangent  of   the   angle  at  the  base  :  perpendicular.' 
::  secant  of  the  angle  at  the  base  :  hypotenuse. 

"When  the  perpendicular  is  given,  perpendicular  must  be 
substituted  for  base  in  this  proportion. 

Case  IV. 
'Given  base  and  perpendicular,  to  find  the  angles  and  hypotenuse.' 


152 


ELLEN   OR  THE 


•'By  Theorem  II. 


*  Base  :  radius : :  perpendicular  :  tangent  of  the  angle  at  the  base. 
Radius  :  base : :  secant  of  the  angle  at  the  base  :  hypotenuse.' 

SOLUTION  OF  OBLIQUE-ANGLED  TRIANGLES. 


Law  of  Sines.    Theorem  I. 

*In  any  plane  triangle,  the  sides  are  proportional  to  the  sines  of  the 
opposite  angles.* 

"  Ellen  will  illustrate  this  by  an  awfully  pretty  figure  which 
will  also  show  how  arcs  may  be  drawn  using  the  opposite 
angles  of  triangles  as  centres.     Thus : 

'*  Draw  the  straight  line  A  C,  bisecting  it  at  D.  With  the  equal 
radii  AD  and  CD  describe  the  two  arcs  DNE  and  DMF. 
From  D  draw  the  perpendicular  line  DI.  Take  B  at  the  low- 
est possible  point  on  DI,  draw  AB  and  BC.  Then  will  ABC 
be  an  isosceles  triangle  having  the  greatest  possible  obtuse 
angle  at  B.  Because  this  triangle  is  isosceles  we  shall  have 
AB  :  BC ::  sine  of  angle  at  C  :  sine  of  angle  at  A. 

'/ 


r  c  LJ 

** Ellen  will  now  increase  continuously  the  side  AB  of  the  tri- 
angle, letting  BC  remain  equal  to  the  radius.  We  will  then  have 
an  infinite  succession  of  triangles  asAKC,  ALC,  AMC,AOC, 
until  they  disappear  when  AB  and  BC  coincide  with  AF.     Let 


WHISPERINGS   OF  AN   OLD   PINE  1 53 

MC  and  HJ  be  perpendicular  to  AC,  HJ  being  drawn  from 
the  intersection  of  AM  with  DNE. 

"In  all  of  these  triangles  the  proposition  holds  true  and  if  in 
these  in  any, — for  should  we  lengthen  the  side  BC,  letting  AB 
remain  constant,  we  would  have  precisely  similar  results  only 
reversed. 

•'For,  because  of  the  uniform  divergence  of  the  sides  of  an 
angle,  we  have  side  AM  (of  triangle  AMC)  :  AH ::  sine 
MC  :  sine  HJ.  But  MC  and  AH  are  equal,  being  radii  of 
equal  circles.  And  therefore  side  AM  :  side  MC::  MC,  sine 
of  angle  at  C  :  H  J,  sine  of  angle  at  A. 

**But  primarily  this  principle  is  true  because  of  the  relation- 
ship which  the  sides  bear  to  their  opposite  angles,  and  they  to 
their  sines.  In  estimating  this  relationship  it  is  necessary  that 
the  circle  or  circles  to  which  the  sines  belong  be  drawn  with 
the  same  radius.  This  will  appear  in  the  above  figure,  where 
the  sines  of  the  second  angle  will  be  the  radius  of  the  first, 
only  when  the  two  circles  are  equal.  With  this  condition  it  is 
impossible  for  them  not  to  be. 

**  And  indeed  Ellen  can  see  without  demonstration,  that  such 
relationship  must  exist.  It  couldn't  possibly  be  otherwise. 
For  as  appears  in  the  figure  given,  the  sines  are  equal  when 
the  sides  are  equal,  and  constantly  vary  with  their  sides.  If 
AB  and  CB,  the  two  equal  sides  of  the  triangle  ABC,  were 
evenly  increased  the  sines  would  be  evenly  increased,  and  the 
relationship  would  remain  the  same.  That  is,  one  side  would 
be  to  the  other  as  the  sines  of  their  opposite  angles. 

"  Ellen  has  given  the  old  Pine  an  entirely  new  demonstration 
of  this  very  important  proposition  and  a  demonstration,  which 


154  ELLEN   OR  THE 

she  much  prefers  to  the  usual  one  in  text-books,  or  to  any  that 
she  has  hitherto  seen.  For,  as  Ellen  intends  that  all  her  demon- 
strations shall,  it  uses  principles,  and  illustrates  from  the  condi- 
tions as  they  exist  in  nature,  and  thus  throws  light  not  only 
upon  the  circle  and  its  functions  but  also  upon  methods  by 
which  the  universe  is  constructed.  This  cannot  be  done  by  a 
demonstration  which  depends  upon  the  manipulation  of  sym- 
bols. And,  as  Ellen  has  suggested  before,  the  difference  in 
final  results  becomes  world  wide,  it  being  the  difference  of  the 
whole  subject,  whether  the  scholar  becomes  a  master  of  mathe- 
matics, or  whether  he  does  not ;  very  probably,  as  frequently 
the  case  with  those  who  are  the  most  capable,  quitting  them  in 
disgust. 

Law  of  Tanceni^.    Theorem  IL 

*  In  any  plane  triangle,  the  sum  of  any  two  sides  is  to  their  differ- 
ence, as  the  tangent  of  half  the  sum  of  the  opposite  angles  is  to  the 
tangent  of  half  their  difference.* 

**  Because  the  sum  of  these  two  sides  represents  the  secant  of 
the  angle  which  represents  half  the  sum  of  the  opposite  angles, 
and  the  third  side,  the  secant  of  the  angle  representing  half 
their  difference. 

**Thus  let  ABC  be  any  triangle.  Extend  AC  until  CD  is 
equal  to  CB.  Then  will  AD  represent  the  sum  of  the  two 
sides  C  A  and  CB. 

**  Connect  BD,  and  with  AF,  drawn  perpendicularly  to  BD, 
as  a  radius,  describe  an  arc.  Then  will  FD  be  the  tangent  of 
the  angle  FAD;   and  FB  that  of  BAF. 

**0n  the  side  CB  draw  CE   equal  to  CA.     E  will  then  fall 


** And  Iherelorc  EAC»  or  FAD,  equals  half  of  the  sum  of 
the  angles  CAB  and  CBA;  and  FAB  half  the  difference. 
because  if  from  the  greater  of  two  magnitudes  half  the  sum  is 
taken,  the  remainder  equals  half  the  difference, 

"And    because  of  the  uniform   divergence   of  the    sides  of 
equal  angles,  in  the  triangles  FAD  and  FEB  we  have 
AD  :  BE::D1-  ;  FB 


CB+C  A  :  CH-CA::tan. 


A+B 


tan. 


A-R 


**TTiis  i^  a  shorter  ana  more  perspicuous  demonstration  than 
any  Ellen  has  seen,  and  this  mainly  because  of  the  use  of  the 
principle  of  the  uniform  divergence  of  the  sides  of  an  angle; 
that  is,  that  two  straight  lines  forming  an  angle  by  crossing, 


Jk 


156 


ELLEN   OR  THE 


from  the  moment  they  cross,  if  extended,  diverge  uniformly  to 
infinity,  and  this  because  neither  can  change  its  direction. 

"  This  principle  almost  any  scholar  can  learn  very  quickly^ 
and  will  never  forget,  whilst  by  its  use  mathematics  may  be 
much  simplified.  That  is  because  of  it,  sides,  of  the  same  or 
equal  angles,  together  with  corresponding  segments  cut  off  by- 
parallel  lines,  and  such  parallel  lines,  are  proportional  to  each 
other.  Thus  in  the  angle  ACB,  with  parallel  lines  as  AB,  FF', 
HD',  connecting  its  sides, 

AC  :  BC::FC  :  F'C::  AB  :  FF':: 
AF  :  BF'::FH  :  F'D',  etc. 

"  Here  a  principle  of  increments  enters,  the  sides  continuing 
to  increase  uniformly;  that  is,  with  the  ratio  of  the  correspond- 
ing increments  constant. 


Theorem  IIL 

*If  from  any  angle  of  a  triangle  a  perpendicular  is  drawn  to  the 
opposite  side  or  base,  the  wliole  base  will  be  to  the  sum  of  the  other 
two  sides,  as  the  differ^,  nee  of  t'.iose  two  sides  is  to  the  difference  of  the 
segments  of  the  base.' 

**  Because  the  length  of  the  segments  of  the  base  is  determined 
by  the  length  of  the  other  two  sides  of  the  original  triangle ; 


UNGS   OP  AN   OLD    PINE 


155 


that  is,  is  proportional  to  them.  And  this  because  of  the  imi- 
form  dtvcrgcficc  of  the  sides  of  an  angle. 

"In  every  plane  triangle  three  parts  must  be  given,  and  at 
Iciist  one  of  these  must  be  a  side,  to  determine  the  other  parts 
of  tlie  triangle.  This  is  evident  because  any  number  of  triangles 
may  be  equiangular  but  not  necessarily  equal  to  each  other. 

*' Under  obhque  triangles  we  may  have  given, 

1,  Two  angles  and  a  side. 

2.  Two  sides  and  an  angle  opposite  one  of  them. 

3.  Two  sides  and  the  included  angle. 

4,  The  three  sides. 
**  1.  Given    two    angles    and    a    sidu.     The    remaining  angle 

'equals  180*^  minus  the  sum  of  the  other  two  angles.  The  re- 
ni^iining  sides  are  found  by  Theorem  I. 

"2.  Given  two  sides  and  an  angle  opposite  one  of  them. 
The  angle  opposite  the  other  given  side  is  found  by  Theorem  I. 
The  third  angle  would  then  be  found  as  in  the  first  case,  also 
the  third  side  asjn  first  case. 

"5.  Given  two  sides  and  the  included  angle.  The  sum  of 
the  other  angles  equals  iSo^  minus  the  given  angle.  The 
difference  of  these  angles  is  found  by  Theorem  II.  Half  the 
the  difference  plus  half  the  sum  gives  the  greater  angle^  and 
hiilf  the  sum  less  half  the  difference,  the  smaller.  The  third 
side  is  then  found  by  Theorem  I. 

**4.  Given  three  sides.  Draw  upon  the  longest  side  a  perpen- 
dicular from  the  opposite  angle,  dividing  the  given  triangle  into 
two  right-angled  triangles.  The  segments  of  the  base  may  be 
found  by  Theorem  III.  There  will  then  be  given  the  hypothe- 
nusc  and  one  side  of  a  right-angled  triangle  to  find  the  angles. 


IS8 


ELLEN   OR  THE 


XII. 


TRIGONOMETRICAL  FORMULAS. 


'  Expressions  for  the  sine  and  cosine  of  the  sum  and  difference  of  two 
arcs/ 


•'Let  BC  and  CD  represent  any  two  given  arcs;  take  CE 
equal  to  CD  :  it  is  required  to  find  an  expression  for  the  sine 
of  BD.  the  sum,  and  of  BE,  the  difference  of  these  arcs. 


WHISPERINGS   OF  AN   OLD    PINE  1 59 

"Let  BC=tf,  and  CD=*;  then  BD=^+iJ,  and  BE=^— *. 
Draw  the  chord  D  E,  and  the  radius  A  C,  which  may  be  repre- 
sented by  R.  Since  DC  is  by  construction  equal  to  CE,  DF 
is  equal  to  FE,  and  DE  is  perpendicular  to  AC.  Draw  EG, 
CH,  FI,  and  DK  all  perpendicular  to  AB,  also  EL,  and  FM 
parallel    to  AB. 

"  Because  of  the  uniform  divergence  of  the  sides  of  an  angle, 
the  triangles  ACH,  AFI  being  equiangular,  we  have 

AC  :  AF::CH  :  FI;  or  R  :  cos.  *::sine  a.  :  FL 

Therefore,  FI='-^"^-^^^-^'^ 

•'Also,  AC  :  AF  ::  AH  :  AI ;  or  R  :  cos.  h  ::  cos.  ^  :  AI 

Therefore.  A  l=^":''"J^'''^. 
K 

••The  triangles  DF  M,  AC  H,  having  their  sides  perpendicular 

each  to  each,  are  equiangular  and  give  the  proportions, 

A  C  :  DF  ::  A  H  :  D  M  ;  or  R  :  sine  »  ::  cos.  ^r  :  D  M. 

i-r  i-kii/i     COS.  a  sine  b 

Hence  DM= - 

K 

"Also,  AC  :  DF::  CH  :  FM  ;   or  R  :   sine  b\\  sine  a  :  FM. 

„  T-Ti;f     sine  rt- sine  ^ 

Hence  FM  = -^ 

K 

Bur    FI+DM=DK=sine  (^+*); 

and   A  I— FM=AK=cos.  {a-\-b). 

Also.  FI-FL=EG=sine  {a-b)\ 

and    AI+EL  =  AG=cos.  {a-^b). 

•  -  .       I     X  i\     sine  ^  cos.  ^+cos.  ^  sine  ^      ..>, 

Hence,  sine  (rt-+-/^)  = ^ .    (1) 

K 

.     ,  ,  V      COS.  a  COS.  ^— sine  a  sine  b     ,  .. 
cos.  (^+*)  = g--  , — .    (2) 


l60  ELLEN   OR  THE 

/        ,v      sine  a  cos.  b — cos.  a  sine^     ,ox 
sine(^-*)= ^ .    (3) 

.        ,x     COS.  a  COS.  b  +  sine  a  sine  b    /-v 
•       COS.  {a-b)= ^     ^.  (4) 

^'F^L  being  equal  to  DM  and  EL  to  FM. 

**  Ellen  quotes  mainly  from  the  book,  although  she  prefers 
her  arrangement  of  letters,  placing  A  at  the  centre,  because,  as 
she  thinks,  it  gives  a  better  order  of  letters  in  the  demonstration. 
She  also  makes  several  other  minor  alterations ;  and  never  means 
to  forget  to  teach,  that  is  to  take  the  lead]  For  she  has  no  use 
for  any  teacher  who,  or  text-book  of  mathematics  which,  shirks 
upon  the  scholar,  or  tries  to,  explanations  and  demonstrations, 
that  the  teacher  or  writer  is  supposed  to  know,  and  the  scholar 
not." 

"And  does  Ellen  think  that  teachers  and  text-books  thus 
neglect  to  lead  ?  " 

**She  knows  that  they  are  constantly  doing  it." 

**And  why?"  I    asked. 

*'  Ellen  doesn't  know  whether  from  laziness,  shiftlessness, 
ignorance,  or  design,  but  supposes  a  mixture  of  all." 

**  Laziness,  shiftlessness  and  ignorance  are  easily  en.)ugh 
explained,"  I  said,  "but  what  does  Ellen  mean  by  des  gn?* 

"She  means  that  if  an  instructor  taught  all  he  knew,  suppos- 
ing he  did  know,  his  scholar  might  soon  know  as  much  as 
he,  and  his  prestige  if  not  vocation  might  be  in  d  mger. 

"Now  Ellen  doesn't  suppose  that,  ii  such  is  the  explanation, 
the  instructor  reasons  it  out,  but  that  involuntarily  and  instinct- 
ively he  thus  may  magnify  his  vocation.  But  whatever  the 
cause  the  books  are  full  of  this  kind  of  incompetency,  so  that 
as  Ellen  has  repeatedly  said,  because  of  poor  teaching  more 


WHISPERINGS     OF   AN   OLD    PINE  l6l 

than  from  any  other  cause,  or  all  other  causes,  but  ^tw  become 
proficient  in  mathematics." 

"But  doesn't  Ellen  think,"  I  asked,  '*that  it  is  better  for  the 
scholar  to  depend  upon  himself?  Will  he  not  learn  better  and 
remember  longer?" 

**  Possibly  so,  if  he  learns.  But  when  the  trouble  is  that  he 
doesn't  learn,  the  assumption  is  fatal.  The  teacher  is  all  right. 
He  has  intrenched  himself  so  that  his  assistance  is  still  needed, 
and  has  avoided  work. 

"As  Ellen  thinks,  mathematics  might  be  taught  so  that  nearly 
all  scholars  would  become  proficient  in  them;  but  very  few 
scholars  do ;  and  therefore  it  is  evident  that  what  is  needed  is 
more,  or  else  a  better  method  of  teaching,  for  the  scholar, 
instead  of  less." 

"  But,"  I  said,  **  more  teaching  carried  out  means  a  pony,  does 
It  not?" 

"  Possibly  it  may,"  she  answered ;  "  but  a  pony  oqly  means  the 
plainest  possible  exposition  of  the  subject  taught,  which  Ellen 
thinks  may  be,  and  indeed  ought  to  be,  and  will  be,  if  the 
scholar  uses  it  correctly,  that  is,  if  he  uses  it  in  studying  more, 
and  this  intelligently,  rather  than  less,  the  best  possible  instruc- 
tion— that  which  produces  the  greatest  results  with  the  least 
labor  and  time. 

** There  is  enough  to  learn,  then  why  should  there  be  waste 
of  either  labor  or  time?     For  with  the  longest  life  as  with  the 
shortest,  at  the  end  the  aphorism  is  equally  true : 
'So  much  to  do,  and  so  little  done.' " 

"But,"  I  said,  "this  gives  unfair  advantage  to  scholars,  unless 
all  use  the  pony ;  so  that  the  system  of  marking  would  become 
very  unfair." 


1 62  ELLEN   OR  THE 

"The  system  of  marking  is  the  cheapest  possible  incentive," 
she  replied,  **and  naturally  connects  with  inferior  instruction. 

"  Ellen  accepts  the  great  principles  of  rewards  and  punish- 
ments, which  rule  in  the  economy  of  the  universe ;  but  this 
doesn't  mean  that  any  one  should  substitute  an  inferior  for  a 
superior  reward.  Plainly  this  is  the  path  of  folly.  The  highest 
of  all  rewards,  for  nature  makes  no  mistakes  in  her  systems  of 
operation,  is  that  approval  of  our  inner  consciousness,  which 
follows  duties  accomplished.  Then  come  the  more  material 
rewards  of  scholarship,  just  remuneration  and  honorable  posi- 
tions, also  arranged  for  in  nature's  economies,  and  Ellen  thinks 
we  can  well  dispense  with  the  kind  of  incentives  which  depend 
upon  rivalry  among  scholars,  for  a  better  system  of  teaching. 

**  Ellen  certainly  would  build  up  her  principles  of  instruction 
upon  broader  foundations,  letting  nature  with  her  infinitely 
greater  opportunities  and  wisdom,  take  care  of  rewards  and 
punishments.  Or  she  would  adopt  some  system  of  rewards 
outside  of  rivalry,  as  giving  all  her  scholars  an  excursion,  or  buy- 
ing for  their  general  use  a  small  library,  as  good  as  Ellen's 
means  would  permit." 

*•  In  that  case,"  I  said,  "Ellen  would  follow  the  precedent  of 
the  rain  and  the  sunshine,  which  fall  equally  upon  all.  " 

**  Ves,'  she  answered,  "the  great  system  of  rewards  and  pun- 
ishment, is  very  thoroughly  and  adequately  arranged  for,  so 
that  one  need  not  bother  about  that.  There  remains  the 
highest    of    all   motives,    the  doing  a  thing  because    it's  best. 

"Ellen  is  very  sure  that  in  teaching,  as  in  everything  else, 
the  most  thorough  possible  svstcm  is  the  best.  But  certainly 
the  best  teaching  must  be  best  for  scholars . 


WUISI'ERINCS   OF   AN    OI-l:i    I'lXE 


163 


'•  But  frequently  the  trouble  is  that  the  teacher  doesii*t  know 
himself.  Many  a  teacher  uses  a  pony.  Indeed  the  ponies  are 
largely  made  for  them»  because  they  would  not  use  a  text- 
book without  tliem.  Nor  does  Ellen  care  how  many  ponies 
they  have  if  they  will  intelligently  explain  to  the  scholar,  who 
*loesn't  have  a  pony»  the  lesson,  whatever  it  is,  until  he  under- 
stands it.     To  learn  as  Ellen  thinks  is  to  know. 

"  Suppose  the  thing  to  be  learned  was  a  language.  Could 
there  be  any  so  good  way  to  learn  it  as  that  in  which  it  cuuld  be 
done  in  the  quickest  time,  and  the  most  thoroughly?  And 
so*  as  EUen  thinks,  it  is  with  everything.  Knowledge  is  power, 
and  with  the  infinite  to  learn,  surely  the  quickest  way  to  learn 
is  the  best,'* 

"Then  Ellen  doesn't  think  that  it's  the  exercise  of  teaming 
hat  gives  power.'* 

"Not  a  bit.  she  knows  that  it  is  not,  any  more  than  the 
gathering  of  supplies  in  an  army  or  anywhere,  gives  the  ad- 
vantages which  come  from  thcm«  It  is  knowledge  that  gives 
power,  nor  can  there  be  too  much  of  it.  And  therefore, 
ag;&in  would  Ellen  hasten  the  pace  of  teaching. 

**  When  teaching  is  not  to  be  had,  the  field  of  sclf*instruction 
remains ;  but  here  the  text-books  should  offer  every  encourage- 
fitent,  especially  those  of  mathematics,  but  they  do  not.  The 
paths  are  blocked  in  all  directions,  and  the  great  majority,  with 
limited  time  as  well  as  opportunities  at  command,  are  forced  to 
turn  back;  at  least  do  turn  back,  whilst  the  few  more  favored 
who  succeed  in  getting  a  partial  comprehension  of  mathematics, 
»ooo  lose  themselves  in  the  higher  branches,  and  blunder  away 
in  a  worse  than  futile  attempt  a  perfectly  ludicrous  attempt,  to 


l64  ELLEN   OR   THE 

demonstrate  the  imposssible  in  physics  by  the  unknown  in 
mathematics.  But  this  sort  of  thing  is  growing  less  and  less, 
and  Ellen  thinks  in  time  will  be  entirely  abandoned.  If  either 
mathematics  or  physics  had  been  more  generally  understood  it 
could  never  have  occurred. 

'Expressions  for  sine  and  cosine  of  a  double  arc* 

"  If,  in  preceding  formulas,  b  equals  a^  the  first  and  second 
will  become 

2  sine  a  cos.  a 
suie  2a=^  -     — , 

COS. 2  a  —  sinc2  a 

COS.  2a=. — . 

K. 

**  Making  radius  equal  to  unity,  and  dividing  both  numerator 
and  denominator  of  1st  equation  by  cos.  '^a^  and  substituting 
COS.  2  +  **^i"G  ^  for  unity,  wc  have 

2    sine   a   cos.   a 
2  sine  a  cos   a  cos.-    a 


sme  2^7=               J 

"  —                1 

COS.-    a 

2  sine  a 

COS.  a 

_  2  tang,  a             __ 

cos.2^7-|-sinc2^ 

cos.**^^?  ,  sine^^ 

COS.-r/       OOS.^rt' 

cos.'^a 

2  tang,  d    

I 

,    sine-   a 
■^  cos.'-i   a 

2  tang,  a 

1    +   tang.*^   a 

since  the  sine  over  the  cosine  is  equal  to  the  tangent. 


WHISPERINGS   OF  AN   OLD   PINE  1 65 

•*  Similarly  the  cosine  of  2a  may  be  shown  to  equal 

I— tang. 2  a 
i+tang.2  a 

'Expressions  for  sine  and  cosine  of  half  a  given  arc' 

••If  we   substitute  \a  for  a  in   the  preceding  equations  wc 
will  have 

2   sine  ^a  cos.   ]fa  .    . 

sme  ^= 2^^ 5..,  (5) 

COS.  ^— -        — 2 —  .2  ^5) 

••Also,  since  the  sum  of  the  squares  of  the  sine  and  cosine  is 
equal  to  the  square  of  radius,  we  have : 

C0S.2  ia-^-sine^  i^=R2. 
And  from  equation  6, 

COS.2  ^^  — sine^  i^^zz:R  cos.  a. 
Subtracting, 

2  sinc^  iya=R^  —  R  cos.  a. 
Adding, 

2  COS.2  ^rt=:R2-f-R  cos.  a. 

Hence, 

sine  ^a=\^  h  R^—^  R  cos.   a. 
COS.   U=V^W+h  KTcos"/. 

'Kxpressions  for  the  products  of  sines  and  cosines.' 

•*By  adding  and  subtracting  the  sine  and  cosine  of  the  sum 
and  difference  of  two  arcs  we  obtain  (sec  pages  159.  160)  : 

sine  (ii-^b)  +  sine  ((i—b)'=^^  sine  a  cos.  d. 


l56  KLLEN   OR   THE 

sine  {t7+fj)  —sine  (a—d)  =^  cos.  a  sine  d. 

COS.  (<?  +  /')  +  COS.   {a—fi)  =:^   COS    r?  COS.*. 

K 

-> 

COS.  (ii—lf)  —  COS.  (^7+/^)  =J^  sine/?  sine  d. 

K 

**If.  in  these  formulas,  we  make  ^7+*=A,  and  a—d=zB;  then 
adding  and  subtracting  and  dividing  by  2,  ^=i  (A+B),  and 
/;z=i  (.A— B).  and  we  have 

sineA+sincBzz:  ^  .sine  A  (A+B)cos.  i  (A  — B).  (7) 
sine  A-sineB=  ^  sine  },  (A-B)  cos.A  (A  +  B)..  (8) 
cos.A  +  cos.  Bz:=^  COS.  ^(A+B)  cos.  I  (A-B).    (9) 

cos.B-cos.  A=  ^  sinei  (A  +  B)  sine^(A  — B).  ( lO) 

**  Dividin,cj    formula    (7)     by     (8).     and    considering   that 

sine  (7      tancr.  it         , 

—  :=      p- — ,  we  have 
COS.  (I  K 

sineA+sinrB__sincJr(A  +  B)cos.  ^(A  — B)_tang.^(A  +  B)^ 
sine  A —sine  B     sine  ^(  A"-"B)  cos.  i(  A  +  B)  "tang!  I  { A  — B) ' 

that  is, 

*The  Sinn  of  the  sines  of  two  arcs  is  to  their  difference,  as  the 
tangent  of  half  the  sum  of  those  arcs  is  to  the  tangent  of  half  their 
difference.' 

cos 
'*  Dividing  formula  (9)  by  (10).  and  considering  that     -- = 

cot.      •  R        ,  ,^v  I 

,,   —  (see  page  136),  we  have 

K       tan<:. 


WHISPERINGS   OF   AN   OLD    FINE  167 

cos.A+cos.B_.cos.  ^(A+B)cos.  ^(A— B)__CGt.   '^{A+B) 
cos/B—  COS.  A     sine  J(A+B)sine  i(A  — B)     tang.J(A— B)  * 

that  is, 

'The  sum  of  the  cosines  of  two  arcs  is  to  their  difference,  as  the 
cotangent  of  half  the  sum  of  those  arcs  is  to  the  tangent  of  hah' 
their  difference.' 

••From  formula  (5),  by  substituting  A+B  for  a  wc  have 

sine(A+B)==l-«!l!^(A+B)  X  cos.  i  (A+B). 

K 
"Dividing  formula  (7)  by  this  we  obtain, 

2  sine  \  (A+B)  cos.  i  (A-B) 
sine  A+sine  B__  R  _ 

sine  ^A  +  Bl         2  sine  jr  (A+B)  cos,   i  (  A+B)"" 

R  '" 

sine  j^  (A  +  B)  cos.  \  (A— B)_co$.  Jr  (A-B) 
sine  r"(A+B)  cos;r(A+B)""cos.  V(A  +  B) 

that  is, 

*'lhe  sum  of  ihe  sines  of  two  arcs  is  to  the  sine  of  their  sum, 
as  the  cosine  of  half  the  difference  of  those  arcs  is  to  the  cosine  of 
half  their  sum.' 

••  If  we  divide  equation  (i)  by  equation  (3),  wc  shall  have 
sine  a  cos.  /;  +  cos.  a  sine  /; 
sine  (^?+/>)_  R  _ 

sine  (a—b)     sine  a  cos.  h  —  cos.  a  sine  ^~ 

R 

sine  (a-\-h) sine  a  cos.  /;  +  cos.  a  sine  b 

sine  (a—b)     sine  a  cos.  b  —  cos.  a  sine  b 

*•  By  dividing  both  numerator  and  denominator  of  the  second 

member  bv  cos.  /?  cos.  b,  and    substitutint^     *,,  '   for  (sec 

^      R  cos.  ^ 

page  1 36 J,  we  obtain 


l68  ELLEN    OR  THE 

sinert:  COS.  /^     cos.  a  sine^ 
sine(/?-f-^)__cos.  ^  cos.  ^  '  cos.^;  cos._^_ 
sine  (^ — b)     sine  ^?  cos.  b     cos.. a  sine^ 

COS.  a  COS.  b     COS.  a  cos.  b 

tang.  ^+tang.  b 

_  ^_    _      __tang.  ^-|-tang.  ^  R _ 

tang.  ^— -tang.  b~~  R  tang,  ^f— tang,  b 

R 

sine^(^+^)__tang.  a  +  tang,  b^ 
sine(rt'— ^)     tang,  rt-  —  tang.  ^* 

the  cos.  a  cos.  b  and  the  R's  cancelling  out,  that  is, 

'The  sine  of  the  sum  of  two  arcs  is  to  the  sine  of  their  differ- 
ence, as  the  sum  of  the  tangents  of  those  arcs  is  to  the  difference 
of  the  tangents.* 

"From  equation  (3),  dividing  each  member  by  cos.  a  cos.  b, 
and  remembering  that  sine-7-cos.=:tan.-7-R  we  obtain 
sine  (^— /^)  __sine  a  cos.  ^— cos.  a  sine  b ^ 
COS.  a  cos.  /;~  R  cos.  a  cos.  b  ~~ 

sine  a  cos.  /;  cos.  a  sine  ^ tang,  rt:— tang,  b , 

R  COS.  a  COS.  /;       R  cos.  a  cos.  b  R'^ 

that  is, 

'The  sine  of  the  difference  of  two  arcs  is  to  the  product  of  their 

cosines,  as  the  difference  of  their  tangents  is  to  the  square  of  radius. 

'Expressions  for  the  tangents  of  arcs.' 

"  If  we  take  the  expression  tang.  (^i'-f-^)=  1  Tr     *^"^ 

substitute  for  sine  {a-^b)  and  cos.  {a-^b)  their  values  given  in 

formulas  (i)  and  (2)  and  multiply  numerator  and  denominator 

by  R ;   wc  shall  find 

/     I  /\      R  (sine^  COS.  /;+cos.  ^7  sine^) 

tang.(^+/;)=:  -    ,    — •        — . /• 

^  cos.  a  cos.  ^— sme  a  sme  b 


WHISPERINGS   OF   AN   OLD    TINE  169 

IX  ^    .  COS. /?tane. «       ,   .       ,     cos.  A  tang. />>  /  ,,^x 

Hutsine/i=  ^ — ^-,andsine^=  o  (P^gc  136). 

K  K 

•*  If  we  substitute  these  values  in  the  preceding  equation,  and 

divide  all  the  terms  by  cos.  a  and  cos.  b,  we  shall  have 

P  .  COS.  a  tang,  a  cos.  ^     cos.  a  cos.  ^  tang,  b ) 

tang.  (/?+^)=: —       -       ,-  , 

"^                             ,      cos.  ^  tang,  rt' COS.  ^tancr /? 
COS. ^  COS.  a  —  — "02 

COS.  a  COS.  b  tang.  ^-|-cos.  a  cos.  b  tang,  b 

,         COS.  a  COS.  b  tang,  r?  tang,  b 

COS.  rt  COS.  ^  — — U2  — ^^ 

__cos.  b  tang,  rt'     +      cos.  b  tang.  ^ 

,  COS.  b  tang.  </  tang,  b 

COS.  /^  —  R2"  " 

tang.  ^  +  J?i?g-  * 

~  tang.  ^  tang.  ^ 

I        -  ^.^ 

"And  multiplying  by  R^  we  have 

/      I  A  V      R^  (tang,  a  +  tang.  /;)  .. 

tang.  ( ^?+^ )  =i5o-^    .  \         r    '  (*0 

&    V      •      /      R2   _  |;ang.  ^z  tang.  /; 

"In  like  manner  we  shall  find 

.        ,,      R2  (tang,  ^r— tang. /;) 

tang.     (^— /0  =  o-o-^,    .  .       -7 

^      ^  R^  +  tang,  a  tang.  /; 

Thus, 

,x      R(sine  ^  cos.  ^  — sine/;  COS.  ^) 
tang,    {a—b  )=  ,     -  .  , 

COS.  a  COS.  /;+smc  a  sine  ^ 

r>  .co$.  a  COS.  ^  tang.  ^/     cos.  a  cos.  /;tang.  ^ 

_    _    "    _K'  ~       '''     1^ 

,       ,       cos.  a  COS.  ^  tang  a  tang.  /^ 
COS.  rtr  COS.  ^      + R2 ^ — 

tang,  a     —      tang,  b     _ 
■^  "^""  tang.  ^7  tang,  b 

•  "^  R« 


I/O  ELLEN   OR   THE 

_R^  (tang,  a  —  tang.^) 
""R*-*    +   tang,  a  tang,  b 
•* Suppose  b=a  in  equation  (i  i),  then 

tang.2^  =  ?,J^'t^"g::^ 
^  R2  —  tang.2  a 

"Suppose  ^=2  ay  then 

tang,  la^^^^^'''^^'  ^_  +  ^^"^-  ?^). 
R2    —  tang,  a   tang.  2^ 

In  the  same  manner  by  dividing  equation  (2)  by  (i)we  find 

.     f     ,  is      cot.  a  cot*  b  —  R2  J    J-  -J-       -/.x   u     /<,\ 

cot.    (^+/^):=  ^   A   L    -.      :   and   dividmg  <4)  by  (3) 

cot.  O  -f-   cot.  <7 


4.      /  L\       cot.  rtr  cot.  ^  +   R 

cot.    (a—b)=  -      ,  - 

cot.  b  —  cot.  a 


When  the  three  sides  of  a  triangle  are  given,  the  angles  may 
be  found  by  the  formula 

.in.^A=Rv/<^-%f--^). 

where  S  represents  half  the  sum  of  the  sides  a,  b,  and  c, 

DEMONSTRATION. 


Let  A  H  C  be  any  triangle ;  then,  because  in  any  triangle  the 
square  of  a  side  opposite  an  acute  angle  is  equal  to  the  square 
of  the  other  two  sides  minus  twice  the  product  of  one  of  these 
sides  by  the  projection  of  the  other  side  upon  it, 


WHISPERINGS   OF  AN  OLD    I'INE  17I 

BC»=AB«+ACa-2  ABxAD. 

Hence.      Ap^AB' +  A^^BC^ 

2  AB 

But  in  the  right-angled  triangle  A  C  D  we  have 
R(AE)  :  AC:: COS.  A(AF;  :  AD 

„  .      RXAD. 

Hence.      cos.  A= — ^-^ — » 
A  v^ 

or  by  substituting  the  value  of  AD, 

cos  A-R  X  AB'+AO-BC« 
COS.  A_K  X 2ABXAC        ' 

Let  a,  by  c  represent  the  sides  opposite  the  angles  A,  B,  C, 
then, 

cos.  A=R  X     — ~-T 

2  b  c 

But  2  sin.  2  \  A=R2  — R  cos.  A. 

Substituting  for  cos.  A.  its  value  given  above,  we  obtain 

2  sine  *  Jt  A=:  R2— R2  X     - -, zzR-x  / 

2  b  c  2  b  c 

R«   X   i^a-^-b—c)  {a-^-c—b) 

2bc '^^' 

sine^    j.A  =  R^.X(-+*-0(--^+^)- 

4  be 

IfS  =  ^(^i+^  +  r),  then,  after  reduction, 

sineiA=Rv/IS-*^<^-'"). 
V  be 

In  the  same  manner  we  find 

sine  .V    B=Rt     (S-«)(S-r). 

>  ac 

.sinciC=Rv''<'S-'^HS-^).. 
>  ab 


172                                                ELLEN   OR  THE 
"But  why  IS  R2  —  R2  X        -    j- =R2  v  -       -     — r-      —  ? 

2  a  C  2  PC 

I  asked. 

"Ellen  will  prove  they  are,   she  answered,  which  perhaps  is 
easier  than  to  answer  more  directly. 

Thus: 

^  2  b  c  2bc 

2b c       2b c       2  be  ' 

(2).     alsoR«X^'^'±'^-rA^-'-'  = 
^    '  2bc 

R2  2  /^6-fR2  ,^2  -R2  ^2  _R2  ^2  _ 

2  /^  <'  "~ 

R22/^r       R2^2        R2/;2        K2^2 

2/^t"      '2^r         2/^r        2b  c  ^ 
R2     ,     R2^2^R2*-^_R2r2 

2  * <:        2  /^ r        2b c    ' 


Same  as  ( i  ). 


Wm:>PERINt;S   OK  AN   OLD    PINE 


173 


XITT- 


ii'T^HESE  formulas  are  obtained  and  demonstrated  by  the 
*  manipulation  of  s>Tnbols,  a  way  that  Ellen  does  not 
like  at  all  in  teaching  principles  although  it  may  be  very  useful 
tn  obtaining  certain  results.  For  though  conclusions  obtained 
arc  true,  as  for  instance  that  Dividing  one  formula  by  another 
and  considering  that 

sine  a     tan.  a         . 

:=:—,, —  we  have 

cos.  a         R 

ieA-fs'"eB_sme  ^(A  +  B)  cos  Jr  (  A  — H)_tang.  ^(A+B) 
doc  A—  sine  H^sine  J{A— B)  cos.  l  ( A-f  B)"'tang.  i(  A— B) 

it  does  not  tn  the  slightest  degree,  as  Ellen   has  said   before, 

Struct  the  scholar  in  the  fundamental  principles    which  are 

work,  the  tiling  by  far  of  most  importance,  and  also  the  most 
tJitc resting,  indeed  the  only  thing  of  interest  in  the  matter ;  and 
the  only  possible  way  of  intelligent  instruction,  or,  as  Ellen 
thinkSt  of  instruction  at  all.  The  other  way  begins  In  igno- 
rance and  ends  in  ignorance;  n(ft  is  it  possible  in  such  courses, 
to  get  any  intelligent  conception  of  the  order  of  creation;  the 
methods  by  which  the  universe  is  constructed, 

"Thus  the  formula  finally  arrived  at  from  the  above  expres* 
iton  ts^: 

•The  STiro  of  the  sines  of   two   arcs    is  to  their  difference,  as  the 
It  of  half  the   sum    of    these   arcs   is    to    the    tangent   of   half 
ifi^  difiference/*' 


Um^^ 


174  ELLEN   OR  THE 

"  And  how  would  Ellen  demonstrate  this?"  I  asked. 

"  She  would  demonstrate  it  from  the  principles  which  under- 
lie it/*  she  replied. 

**  In  taking  two  arcs  Ellen  will  select  a  quadrant  and  the  least 
little  bit  of  an  arc,  theoretically  the  shortest  possible.  Then, 
letting  the  longer  arc  remain  constant,  she  will  continuously 
increase  the  shorter  one  until  it  is  the  least  possible  shorter 
than  a  quadrant,  or  until  it  is  a  quadrant,  for  we  are  not  limited 
to  different  arcs. 

"  Of  the  first  two  arcs  taken  the  sum  of  the  sines  will  be  the 
least  possible  longer  than  a  radius,  and  the  difference,  the  least 
possible  shorter.  Half  the  sum  of  the  arcs  will  then  be  the  least 
possible  more  than  45^,  the  tangent  of  which  is  equal  to  the 
radius. 

"Hence  the  tangent  of  half  the  sum  of  these  arcs  is  the  least 
possible  longer  than  the  radius,  and  of  the  half  difference,  the 
least  possible  shorter.  And  we  will  have  I  plus  an  infinitesimal 
quantity  (the  sum  of  the  sines)  :  i  minus  an  infinitesimal  quan- 
tity (their  difference)  ::  i  plus  an  infinitesimal  quantity  (the 
tangent  of  half  the  sum  of.  the  arcs)  :  i  minus  an  infinitesimal 
quantity  (tangent  of  half  their  difference),  which  agrees  with 
the  proposition.  • 

**  If  the  smaller  arc  increases,  the  sum  of  the  sines  continu- 
ously increases,  and  their  difference  proportionally  decreases. 
The  same  is  true  with  the  tangents  of  the  half  sum  and  half  differ- 
ence, so  that,  the  proportion  when  the  variable  arc  is  the  least 
possible  shorter  than  the  quadrant,  is,  2  minus  an  infinitesimal 
quantity  (the  sum  of  the  sines  of  the  arcs)  :  an  infinitesimal 
quantity  (their  difference)  ::  longest  possible  quantity  less  than 


USTLRINC 


AN    OLD 


infifiity  (tangent  of  half  the  sum  of  the  arcs)  ;  the  shortest  pos- 
sible quantity  (tangent  of  half  their  difference),  which  again 
is  in  accord  with  the  proposition ;  or,  if  the  second  one  becomes 
a  quadrant,  2  :  o::  infinity  :  o,  which  is  a  demonstration  that 
any  quantity  multiplied  by  o  equals  o. 

"Again,  where  four  proportionals»  all  dependent  for  their 
variation  upon  the  same  variable,  varying  %vith  it  and  only  as  it 
varies,  pass  through  all  intermediate  values,  and  finish  together 
still  proportionals,  they  must  be,  as  Ellen  has  shown  in  the 
law  of  sines*  all  the  time  proportionals.  It  is  impossible  for 
them  to  be  otherwise, 

"For  these  functions  arc  so  connected  that  there  is  jtist  so 
much  length  in  each,  to  be  divided  up  for  the  separable 
movements,  it  makes  no  difference  how  many  of  them  there 
are;  Ellen  assumes  them  to  be  infinite.  The  space  passed  over 
consists  of  the  sum  of  these  movements,  and  as  in  each  case 
the  corresponding  movements  constitute  the  relationship  of 
these  functions,  this  relationship  is  equally  continuous  with  the 
movements." 

•*But,"  I  said,  *' Ellen  assumes  continuous  movements  and 
then  she  speaks  about  separate  movements." 

•'Continuous  movements/'  she  answered,  '*must  be  the  sum 
of  separate  movements,  and  so  the  particular  distance  which 
the  tangent,  or  any  function  of  an  arc,  makes,  when  the  arc  is 
leoglhencd ;  that  is,  the  corresponding  mov^cments  of  the  func- 
tions, where  such  movements  are  longer  than  the  movement  of 
the  arcs,  are  composed  of  an  indefinite  number  of  separate 
movements,  and  yet  it  makes  a  continuous  movement,  which 
corresponds  to  another  continuous  movement  made  by  the  arc. 


176  ELLES  OR  THE 

'*  And.  IS  ^^**^  has  ^d,  :n  order  that  each  condition  should 
exisc  eacii  f.incrii:a.  rh.ir  is  each  line,  must  be  di\nded  into  the 
same  number  :t  parts:  the  arst  part  of  each  being  used  at  the 
same  time,  the  second  part  next,  and  so  continuously  to  the 
lasr  pan 

"  It  may  be  rhat  the  space  passed  over  in  one  of  these  func- 
tions ar  the  same  inscmr  ot  time  is  double,  or  a  thousand  times, 
any  number  ot  times,  an  Innnite  number,  greater  than  that 
passed  over  by  the  arc.  or  another  function,  but  the  proportions 
wi!I  sell  remain,  for  proportions  do  not  consist  of  differences 
but  ot  reLiti\-e  cistances.     Thus. 

I  :  4  ::  4  :  i6:  or. 
rocoooo  :  4000000  ::  4000000  :  16000000. 
In  one  case  \\*e  have  differences  of  3  and  12,  and  in  the  other 
oi  jtooccoo  and  1 2-000000.  but  the  proportions  are  the  same, 
wh'ch  means  that  the  magnitudes  4  and  16  will  contain  the 
ma^r.  tuvics  I  a::  J.  4  the  same  number  of  times,  that  the  macrni- 
f.u:o>  4.XV000  and  1 0000000,  will  the  magnitudes  1 000000  and 
4^wooo. 

"  KIlea  will  now  demonstrate  this  formula  from  a  figure. 
She  will  take  two  arcs  AB  and  BD,  also  BE  equal  to 
BO.  rhen  will  AD  be  their  sum.  and  A E  their  difference. 
.-\nd  the  old  Pine  should  always  remember,  especially  when  he 
is  studying  Trigonometr\-,  that  half  the  sum  plus  half  the  differ- 
once  equals  the  greater  quantit>'  or  number,  and  half  the  sum 
minus  half  the  difference  the  less. 

'*  Ellen  will  draw  BH  and  DF.  sines  of  the  two  arcs,  and  also 
the  arc  AD',  equal  to  the  arc  DB,  and  D' F'  the  sine  of  AD' 
and  equal  to  D F.     She  will  also  divide  the  double  arc  AD  at 


WHISPERINGS   OF  AN   OLD   PINE 


177 


the  centre  J,  and  bisect  AE  by  CS,  draw  CBM,  BW 
equal  to  the  sine  F'D',  CJTP,  CE  and  CD,  also  CS'  making 
AS'  equal  to  AS,  and  MTS AS' T' perpendicular  to  CA  at 
point  A. 

"Then  is  the  angle  ACT  half  the  sum  of  the  arcs,  and 
SC  A  or  ACS'  half  their  difference.  And  therefore  TA  is  the 
tangent  of  half  the  sum  of  the  arcs,  and  S  A  or  S' A  the  tangent 
of  half  the  difference. 


"To  prove  that  BH  and  F'D'  the  sum  of  the  sines,  is  to 
HW  their  difference,  as  T  A  is  to  S  A. 

"Draw  BW  equal  to  B  W. 

"Through  S  draw  WZ,  to  the  diameter  extended  at  Z;  and 
through  T  the  line  W'TZ,.     Then,   because  of   the  uniform 


178  ELLEN   OR  THE 

divergence   of   the   sides   of   the  angles    at   Z,W'HandMA 
being  parallel  lines, 

W'H  :WH::TA  :  SA. 

"Which  was  to  be  proved.  For  W'H  is  the  sum  and  WH 
the  difference  of  the  sines,  and  TA  tangent  of  the  half  sum,  and 
SA  tangent  of  the  half  difference,  of  the  arcs  AB  and  BD. 

"  The  second  expression  is : 

'The  sum  of  the  cosines  of  two  angles  is  to  their  difference  as  the 
cotangent  of  half  the  sum  is  to  the  tangent  of  half  the  difference.' 

**  If  we  take  two  angles,  one  of  90^  the  other  the  least  possi- 
ble, we  will  have  i  minus  an  infinitesimal  :  i  minus  an  infini- 
tesimal::! minus  an  infinitesimal  :  i  minus  an  infinitesimal — 
which  is  a  true  proportion,  the  infinitesimals  in  each  ratio  being 
equal.  And  this  because  the  cosine  of  90^=0,  and  the  cotan- 
gent and  tangent  of  45^=1. 

"  Should  we  take  two  angles  of  90^  each,  we  will  have  o  : 
o::o  :  o. 

"If  we  take  one  angle  of  90°  and  the  other  of  45^,  we  will 
have  .707107  :  .707107 ::  .414214  :  .414214;  which  again  sus- 
tains the  proposition.  And,  as  these  proportions  are  con- 
tinuous, as  Ellen  has  proven,  they  must  always  exist. 

"The  third  formula  is; 

*  The  sum  of  the  sines  of  two  arcs  is  to  the  sine  of  their  sum,  as  the 
cosine  of  half  the  difference  of  these  arcs  is  to  the  cosine  of  half  their 
sum.' 

*'  Again  Ellen  will  take  a  quadrant  for  one  arc  and  the 
least  possible  for  the  other ;   and  we  will  have   I   plus  an  infini- 


WHISPERINGS   OF  AN   OLD   PINE  1 79 

tesimal  :  i  minus  an  infinitesimal ::  .707107  plus  an  infinitesi- 
mal :  .707107  minus  an  infinitesimal,  which  Ellen  considers  very 
correct  mathematics,  the  infinitesimals  in  each  ratio  being 
equal. 

"This  proportion  she  can  easily  prove  to  be  continuous, 
and  therefore,  to  always  take  place  between  these  functions. 

"  The  fourth  and  fifth  formulas  admit  of  the  same  proof, 
whether  we  take  arcs  whose  relations  are  self-evident,  or  get  the 
values  of  the  functions  referred  to 

**  Doubtless,  too.  figures  might  be  drawn  which  would  verify 
these  expressions,  but  the  winds  are  cold, 

*  Whilst  in  the  west  fast  fades  the  lingering  light.* 

"  So  Ellen  will  close  Trigonometry  with  a  brief  statement  of 
the  nature  and  origin  of  logarithms,  and  to  do  this  she  will 
take  the  geometrical  series  of  figures 

I,     2,     4,     8,     16,     32,     64,      128,     256,     512,     etc. 

placing  under  them  the  arithmetical  series 

o,     I,     2,     3,       4,       s,       6,         7,         8,         9,     etc. 

"The  multiplier  of  the  geometrical  series  is  2,  the  ratio  of 
the  arithmetical  i ,  and  any  number  in  the  arithmetical  series 
expresses  the  number  of  times  that  2  has  been  used  as  multi- 
plier— multiplying  each  time  the  product  of  the  previous  multi- 
plication,— to  produce  the  corresponding  figure  of  the  upper 
or  geometrical  series.  Thus  2  shows  that  the  product  of  the 
upper  series  has  been  taken  twice — 1x2=2,  2X2=4;  3  that 
it  has  been  taken  3  times — i  X2=2,  2x2=4,  4X2=8,  etc. 


l80  ELLEN   OR  THE 

"And  therefore  the  numbers  of  the  lower  line  represent  the 
power  to  which  this  second  figure  of  the  geometrical  series 
must  be  raised  to  correspond  to  the  number  of  this  power  in  the 
arithmetical  series;  and  hence  the  sum  of  two  logarithms — 
as  we  will  now  call  the  lower  figures,  from  the  Greek  words 
logon  arithmos,  number  of  ratios — is  equal  to  the  logarithm  of 
their  product. 

**Thus  9=3+6,  is  the  logarithm  of  512,  the  product  of  the 
corresponding  numbers  8  and  64.  That  is,  it  represents  the 
power  to  which  the  base  of  the  system  must  be  raised  to  equal 
512. 

"And  therefore,  too,  the  difference  of  any  two  logarithms  is 
the  logarithm  of  their  quotient  Thus  3,  the  difference  of  3  and 
6,  is  the  logarithm  of  the  quotient  of  their  corresponding 
numbers  8  and  64. 

"A  multiple  of  any  logarithm  is  the  logarithm  of  the  number 
corresponding  to  one  factor  raised  to  the  power  of  the  other 
factor.  Thus  12,  which  equals  3X4,  is  the  logarithm  of  4096, 
which  equals  the  4th  power  of  8,  or  the  3d  power  of  16. 

"  And  a  submultiple  of  a  logarithm  is  the  logarithm  of  the  cor- 
responding root  of  its  number.  Thus  3  the  submultiple  of  9  is 
the  logarithm  of  8,  the  third  root  of  512. 

"And  this  because  the  greatly  increased  advance  of  the  upper 
series  is  thus  represented.  It  is  entirely  regular,  as  is  also  that 
of  the  lower  series,  and  though  the  upper  series  gains  at  a  con- 
stant and  soon  at  a  terrific  pace,  the  expression  of  it  is  easily 
made  by  the  lower  series,  which  is  not  at  all  daunted  at  the 
speed  of  the  upper,  but  which  proceeding  in  its  moderate 
pace  defines  it. 


nSPERINGS  OF  AN  OLD  PINE 


I^I 


**That  is,  through  the  fixed  relationship  of  the  lower  figures 

the  upper,  with  complete  tables  of  numbers  and  their  cor- 

sponding  logarithms,  multiplication  may  be  accomplished  by 

.<idition,  division  by  substraction,  involution  by  multiplicationi 

Lod  evolution  by  division. 

**  It  is  evident  that  the  base  may  be  any  number,  integer  or 
vaction;  that  is,  the  same  relationship  will  exist  between  a 
^geometrical  and  arithmetical  series,  arranged  as  above,  whatever 
iDase  is  used  in  the  geometrical  series. 

The  most  common  system  for  general  use  is  that  of  Prof. 

^Kenry  Brrggs  of  London,  England,    in  which  the  base  is    lO, 

This  was  introduced  by  Mr.   Briggs   in  1615.     He  calculated 

^during  his  life  the  logarithms  of  30,000  numbers   to  the  new 

\)ase,  and  by  1628  the  logarithms  of  all  numbers  to  100,000  had 

been  computed. 

"In  the  Briggs  system  the  logarithm  of  10  is  i  ;  of  100,  2; 
of  1,000,  3,  etc.  The  logarithms  of  intermediate  numbers 
arc  fractional  which  may  be  calculated  by  the  principles  of 
mathematics,  the  most  convenient  method  being  by  the  alge- 
braic analysis  in  which  the  logarithms  are  considered  as  powers 
of  the  base.  Thus;  io°^l,  iq-soi  080-.2,  lo"*^^!^*— 3, 
10*  =  100,  etc. 

"As  the  logarithm  of  1  is  assumed  to  be  o,  the  logarithms  of 
numbers  less  than  Tare  considered  negative.  Thus  the  log- 
arithm of  i  would  be — ,30103,  but  for  convenience  in  working 
this  is  written  1.69897(=— .50103)  the  integral  figure  (or 
figures  when  used)  being  marked  with  a  minus  sign. 

•*For  more  complete  analysis  of  this  subject  Ellen  will  refer 
the  old  Pine  to  Chambers*  Encyclopedia. 


'■^■-^ 


1 82 


ELLEN   OR  THE 


"The  old  Pine  must  see  because  he  is  very  tall,  and  accus- 
tomed to  commanding  views,  that  a  system  of  logarithms  is  an 
ingenous  method  to  lessen  work  in  complicated  mathematical 
operations,  by  means  of  work  already  done,  and  properly 
arranged  in  tables. 


PART  II 

THE 
UNDULATORY  THEORIES 


THE  ItEW  YORK 
^OfeirC  LIBRA  KY 


WHISPERINGS   OF  AN    OLD   PINE 


[UNE  again  was  blossoming  above  our  hills.  The  great 
winter,  with  its  frozen  plains  of  snow  that  glisten  so  beau- 
i fully  in  the  calm  days  beneath  the  sunshine,  or  cold  and  for- 
bidding repel  the  embrace  of  wind  and  storm, — ^had  departed, 
I  ^nd  in  its  stead  the  soft,  fond  zephyrs  of  the  loving  sniiirner 
j  lingered  above  hill  and  dale. 

Hundreds  of  years  the  old  Pine  has  noticed  these  changes; 
^■Irbere  the  mountains  dwell  upon  the  western  sky;  where  they 
^HXtcnd  in  rising  column  at  the  north,  or  in  long  lines  melt  awav 
^Hn  the  south;  or  where  in  the  grandeur  of  beauty  and  like  the 
^fbiUowed  surface  of  a  great  sea  they  glide  to  the  extreme  east, 
Hrmnd  there  m  the  highest  forms  reflect  the  first  beams  of  the 
!       morning  light. 

Watching  the  beauty  of  this  scene,  viewing  not  only  the 

[millions  of  trees  that  dot  the  mountains  and  the  hillsides,  but 

the  landscape  as  a  whole,   comprising  a  number   of  com- 

mountain  ranges,  and  diversified  with  thousands  of  fields 

ad  homes,  with  rock,  plane  and  river, — a  soft,  familiar  step 

broke  on  my  ear. 

At  this  moment  the  golden  rim  of  the  sun  was  lifted  above 

tic  eaistern  horizon.     At  the  same  moment  the  pride  of  our 

stepped  from  the  bushes  upon  the  rocks;   and,  turning 


4  ELLEN   OR  THE 

gazed  at  all  the  glories  of  the  morning  now  so  rapidly  spread- 
ing from  sky  to  earth. 

*  Full  many  a  glorious  morning  have  I  seen, 

Flatter  the  mountain-tops  with  sovereign  eye ; 
Kissing  with  golden  face  the  meadows  green, 
.Gilding  pale  streams  with  heavenly  alchemy.* 

For  many  minutes  Ellen  watched  the  wondrous  scene,  then 
turning  again,  came  towards  me.  A  little  laugh  shook  the  new- 
born leaves. 

"It's  Ellen,"  she  said,  "come  so  early  in  the  morning  to  see 
her  favorite  tree." 

"  And  to  make  another  long  visit,"  I  said.  "  Surely  when 
Ellen  doesn't  come  but  once  a  year,  she  will  make  the  old  Pine 
a  good,  long  visit?" 

"Yes,"  she  answered,  "if  the  old  Pine  does  everything  to 
please  her." 

"  And  the  old  Pine  will  certainly  try,"  I  said.  "  He  always 
tries ;  for  he  loves  Ellen,  and  there  is  nothing  which  he  could, 
that  he  would  not  do  for  her." 

"Well,"  she  continued,  "here  is  Ellen,  come  to  redeem  her 
promises.  For  Ellen  told  the  old  Pine  that  at  some  time  she 
would  discuss  with  him  the  undulatory  theories." 

"Yes,"  I  said,  "and  the  old  Pine  will  be  very  much  inter- 
ested to  hear  what  Ellen  has  to  say  about  them ;  for  he  judges 
from  what  she  said  that  she  does  not  believe  in  them." 

"  No,  indeed,  she  does  not,"  she  replied ;  "  for  Ellen  can 
never  believe  in  anything  that  hasn't  the  sanction  of  common 
sense,  and  these  theories  arc  wholly  at  variance  with  it." 

She  threw  aside  the  light  shawl  that  she  carried  on  her  arm, 
and  again  seated  herself  upon  the  rocks  near  me. 


WHISPERINGS   OK  AK   OLD    PINE 


And  now,  Mr.  Pine/*  she  said,  **  Ellen  will  criticise  the 
"^iheory  of  sound  which  has  been  accepted  substantially  by  all 
^ttihe  scientists,  and  for  some  centuries  has  been  taught  and  is 
:anow  taught  in  nearly  if  not  every  school  and  college  on  earth. 
'Xn  doing  this  Ellen  wants  to  make  an  apology  for  herself.  For 
^she  is  really  ashamed  to  waste  time  on  a  theory  of  such  pre- 
^posterous  character  and  monstrous  inconsistencies. 

*' And  first  she  will  quote  what  Mr  Ganot  in  his  text  book 

^^n  Physics,  of  world-wide  circulation,  has  to  say  in  reference  to 

'^he  undulatory  theories,  showing  that  he  has  no  faith  in  them* 

IHe  could   not  make   the  admission  that  he  does  if   he    had, 

Tor  he  teaches  them  in  his  book,  and  certainly  if  a  man  really 

Relieved     a    thing   he    wouldn't    say    that    it    is     completely 

linknown.     The  book  is  prepared  for  the  market,  but  evidently 

he  perceives  the  intrinsic  falsity  of  these  theories,  and  realizes 

tliat  this,   in    time,  must  be   exposed.     He    says    (Chapter  I.. 

page  5,  Fourteenth  Edition) : 

•In  our  attempts  to  ascend  from  a  phenomenon  to  its  cause,  we 
assume  the  existence  of  physical  agents^  or  natural  forces  acting  upon 
matter ;  as  eitamples  of  such  we  have  gravitation^  heat^  lights  magnttism 
and  eifctricity, 

*  Since  these  physical  agents  are  disclosed  to  us  only  by  their  effects, 
their  intimate  nature  is  completely  unknown.  In  the  present  state  of 
idcDcei  we  cannot  say  whether  they  are  properties  inherent  in  matter, 
or  whether  they  result  from  movements  impressed  on  the  mass  of  sub- 
tile and  imponderable  forms  of  matter  diffused  through  the  universe.* 

**Hc  doesn't  mention  sound,  does  he,  Ellen?" 
**No/*    she   said,    '*but  he    mentions  light,  the   undulatory 
theory  of  which  arose  entirely  from  the  supposed  analogy  of 


13 

'^1 


6  ELLEN    OR   THE 

light  to  sound.     That  they  belong  in  the  same  category  is 
beyond  question ;   nor,  so  far  as  Ellen  knows,  does  any  one  dis 
pute  this.     MnTyndalU  in  his  book  on  Sound*  page  43,  says: 

'The  action  of  sound  thus  illustrated  is  exactly  the  same  as  that  of 
light  and  radiant  heat.  They,  like  sound,  are  wave-motions.  Like 
sound  they  diffuse  themselves  in  space,  diminishing  in  intensity 
according  to  the  same  law.  Like  sound  also,  light  and  radiant  heat, 
when  sent  through  a  tube  with  a  reflecting  interior  surface,  may  be  con- 
veyed to  great  distances  with  comparatively  little  loss.  In  fact,  every 
experiment  on  the  reflection  of  light  has  its  analogy  in  the  reflectioa^ 
of  sound.  On  yonder  gailer)'  stands  an  electric  lamp^  placed  close  tof 
the  clock  of  this  lecture-room.    An  assistant  in  the  gallery  ignites  the 


lamp,  and  directs  its  powerful  beam  upon  a  mirror  placed  here  behind 
the  lecture- table.  By  the  act  of  reflection  the  divergent  beam  is  con- 
verted into  this  splendid  luminous  cone  traced  out  upon  the  dust  of  the 
room.  The  point  of  convergence  being  marked  and  the  lamp  extin- 
guished,  I  place  my  ear  at  that  point.  Here  every  sound-wave  sent 
forth  by  the  clock  and  reflected  by  the  mirror  is  gathered  up,  and  the 
ticks  are  heard  as  if  they  came^  not  from  the  clock,  but  from  the  mirror* 
Let  us  stop  the  clock,  and  place  a  watch  u%  Fig.  1,  at  the  place 
occupied  a  moment  ago  by  the  electric  light     At  this  great  distance  the 


WHISPERINGS   OF   AN   OLD    PINE  7 

king  of  the  watch  is  distinctly  heard.  The  hearing  is  much  aided  by 
introducing  the  end  /  of  a  glass  funnel  into  the  ear,  the  funnel  here 
3U!ting  the  part  of  zn  ear- trumpet.  We  know,  moreover,  that  in  optics 
the  positions  of  a  body  and  of  its  image  are  reversible.  When  a  candle 
is  placed  at  this  lower  focus,  you  see  its  image  on  the  gallery  above,  and 
I  have  only  to  turn  the  mirror  on  its  stand  to  make  the  image  of  the 
Rawc  fall  upon  any  one  of  the  row  of  persons  who  occupy  the  front  seat 
in  the  gallery.  Removing  the  candle,  and  putting  the  watch  in  its 
place*  the  person  on  whom  the  light  fell  distintly  hears  the  sound. 
When  the  car  is  assisted  by  the  glass  funnel,  the  reflected  ticks  of  the 
clock  in  our  first  experiment  are  so  powerful  as  to  suggest  the  idea  of 
something  pounding  against  the  tympanum,  while  the  direct  ticks  are 
scarcely^  if  at  all,  heard.' 


'Sound,  like  light,  may  be  reflected  several  times  in  succession,  aiid, 
&$  the  reflected  light  under  these  circumstances  becomes  gradually 
feebler  to  the  eye,  so  the  successive  echoes  become  gradually  feebler  to 
the  ear/ 

•*  Again  Mr.  Tyndall  says,  after  giving  experiments  on 
sound  (*  Heat  a  Mode  of  Motion,*  pages  274-275)  : 

•UT\yare  these  experiments  on  sound  performed?  Simply  for  the 
purpose  of  giving  you  clear  conceptions  regarding  what  takes  place  in 
Ibc  c^se  of  heat ;  to  lead  you  from  the  tangible  to  the  intangible  ;  from 
the  region  of  sense  into  that  of  theory. 

'After  philosophers  had  become  aware  of  the  manner  in  which  sound 
wns  produced  and  transmitted,  analogy  led  some  of  them  to  suppose 
that  light  might  be  produced  and  transmitted  in  a  somewhat  similar 
manner.  And  perhaps,  in  the  whole  htstorj'  of  science,  there  was  never 
a  question  more  hotly  contested  than  this  one.  Sir  Isaac  Newton,  as 
indicated  in  our  second  lecture,  supposed  light  to  consist  of  minute 
pgirticles,  darted  out  from  luminous  bodies.     Huyghens,  the  contem- 


8  ELLEN  OR  THE 

porary  of  Newton,  found  great  difficulty  in  admitting  this  cannonade  of 
particles ;  or  in  realizing  that  they  could  shoot  with  inconceivable 
velocity  through  space,  and  yet  not  disturb  each  other.  This  celebrated 
man  entertained  the  view  that  light  was  produced  by  vibrations,  similar 

to  those  of  sound.' 

«  «  «  «  «  «     '       « 

^The  authority  of  Newton  bore  these  men  down,  and  not  until  a  man 
of  genius  within  these  walls  took  up  the  subject,  had  the  Theory  of 
Undulation  any  chance  of  coping  with  the  rival  Theory  of  Emission. 
To  Dr.  Thomas  Young,  formerly  Professor  of  Natural  Philosophy  in  the 
E.oyal  Institution,  belongs  the  honor  of  stemming  this  tide  of  authority, 
and  of  establishing,  on  a  safe  basis,  the  Undulatory  Theory  of  light. 
Great  things  have  been  done  in  this  edifice ;  but  scarcely  a  greater 
thing  than  this.  And  Young  was  led  to  his  conclusion  regarding  light, 
by  a  series  of  investigations  on  sound.  He,  like  ourselves  at  the  present 
moment,  rose  from  the  known  to  the  unknown,  from  the  tangible  to  the 
intangible.* 

**  And  so  the  old  Pine  will  see  that  if  either  one  of  the  undu- 
latory theories  is  proven  untrue,  they  are  all  proven  untrue." 

**  But  what  is  the  theory  which  you  condemn,  Ellen?" 
I  asked. 

"  It  is  too  silly  to  explain,"  she  continued.  *'  Let  those 
explain  it  who  believe  it,  if  any  such  there  are." 

**  But,"  I  said,  '*  Ellen,  it  will  be  impossible  for  us  to  discuss 
it  intelligently  without  a  statement  of  what  it  is." 

**It  is  impossible,"  she  replied,  "to  give  any  intelligent  state- 
ment of  it,  for  it  is  too  absurd  to  admit  of  one.  The  text 
books  say  that 

'Sound  is  the  peculiar  sensation  excited  in  the  organ  of  hearing  by 
the  vibratory  motion  of  bodies,  when  this  motion  is  transmitted  to  the 
ear  through  an  elastic  medium.' — Ganot 


WHISPERINGS   OF  AN    OLD    PINE 


'The  impression  which  the  mind  receives  through  the  organ  of  hear- 
ing is  called  sound.  But  the  same  word  is  constantly  used  to  signiiy 
^^at  progressive  vibratory  movement  in  a  medium  by  which  the  impres- 
9iOD  is  produced,  as  when  we  speak  of  the  velocity  of  sound/ — Oimsied, 

•*  From  these  definitions — and  all  text  books,  so  far  as  Ellen 
Vnows.  furnish  similar  ones — it  appears  that  the  undulatory 
theory  cannot  be  explained  with  one  definition,  which  alone 
suggests  its  falsity.  For  by  this  theory  it  is  necessary  to  con- 
sider sound  subjective  and  objective,  both  of  which  it  cannot 
possibly  be.  Subjectively,  sound  is  assumed  to  be  a  sensation 
produced  by  what  is  called  a  mode  of  motion;  that  is,  by  the 
mere  movement  of  something.  But  in  discussing  sound  the 
speed  of  this  movement  is  spoken  of  as  the  speed  of  sound. 
And  hence  by  this  theory  a  certain  kind  of  movement, 
of  a  thousand  different  things*  more  or  less,  is  sound. 
If  this  is  the  theory,  why  say  that  the  impression  which  the 
mind  receives  through  the  organ  of  hearing  is  sound? 
One  of  the  two  possibly  might  be  something  called  sound; 
both  of  them  certainly  cannot  be  the  same  thing.  One  may 
believe  in  realism  or  idealism,  but  it  is  impossible  that  he 
should  believe  in  both. 

**0n  another  page,  Mr.  Ganot  says:  *The  velocity  of  sound 
at  zero  may  be  taken  at  1093  feet  per  second/  Using  Mr. 
Ganot's  previously  given  definition  of  sound — that  is,  transpos- 
ing, under  the  axiom  that  things  which  are  equal  to  the  same 
things  are  equal  to  each  other — and  we  have:  *The  velocity  of 
the  peculiar  sensation  excited  in  the  organ  of  hearing  by  the 
vibratory  motion  at  zero,  may  be  taken  at  1093  feet  per  second.* 

**'rhc  old  Pine  will  see  that  there  is  no  possible  sense  to  this 


lO  ELLEN   OR  THE 

last,  except  under  supposition  that  the  peculiar  sensation,  etc., 
is  an  entity  with  the  power  of  traveling,  which  at  some  time 
must  exist  outside  of  the  organ  of  hearing  in  order  to  travel 
1093  feet  in  a  second.  But  this  is  manifestly  absurd,  and  so 
the  whole  theory,  however  taken,  is  absurd  and  impossible. 
Surely  the  old  Pine  must  see  that  the  theory  is  incredible,  and 
that  it  is  unnecessary  to  discuss  it  further." 

**Yes,"  I  said,  "the  old  Pine  does  see.  But  as  this  theory 
is  universally  accepted  in  science,  he  hopes  that  Ellen  will 
continue  to  expose  its  absurdities.  But  is  it  not  true,  Ellen, 
that  words  are  sometimes  used,  by  trope  or  metaphor,  with 
double  meaning?" 

"Yes,"  she  replied,  "that  is  sometimes  done,  but  always  there 
is  a  primitive  and  fixed  meaning  of  the  word  which  makes  the 
trope  possible.  Thus,  when  we  say  that  a  man  is  a  fox,  the 
word  fox  is  used  metaphorically  to  signify  that  the  man  has  the 
crafty  characteristics  of  that  animal.  But,  of  course,  the  term 
would  not  be  thus  used  except  as  its  usual  signification  is  per- 
fectly understood.  Besides,  such  use  would  be  entirely  out  of 
place  in  scientific  discussion.  In  any  proper  signification  of 
words,  the  peculiar  sensation  excited  in  the  organ  of  hearing, 
referred  to,  is  hearing  and  not  sound,  just  as  a  similar  sensation 
excited  in  the  organ  of  tasting  is  tasting  and  not  flavor,  or  in  the 
organ  of  smelling  is  smelling  and  not  odor.  Sound,  like  odor 
or  flavor,  is  the  exciting  substance.  Hearing,  like  tasting  or 
smelling,  is  the  subjective  action  or  result.  Any  theory  that 
does  not  make  this  distinction  is  crude  and  worthless.  It  is 
upon  its  face  a  humbug. 


TPE  NEW  YORK 
PUBLIC  LIBRARY 


WHISPERINGS   OF   AN    OLD    PINE 


13 


II. 


V 


NDER  'Copernicus*  the  British  Encyclopsedia  says: 


'  He  sought  by  a  comparative  study  of  the  various  astronomical  sys- 
tems of  the  ancients  to  evolve  from  them  a  single  system  at  once  simple 
md  consistent.' 

•'Thus  arose  the  Coper nica  11  system,  In  which  all  the  planets 
revolve  around  the  sun,  superseding  the  Ptolemaic,  in  which 
Mercury  and  Venus  revolved  around  the  siin»  whilst  itself^  with 
Mars,  Jupiter,  and  Saturn,  moved  round  the  earth.  In  this  case 
the  error  of  thousands  of  years'  standing,  which  supposed  the 
action  of  the  planets  to  be  controlled  by  different  laws,  was 
corrected ;  and  so  Ellen  would  correct  a  similar  error,  of 
equally  long  standing,  \vhich  makes  the  senses  governed  by 
different  laws;  or,  rather,  assumes  that  two  of  them  act  without 
cause,  which  places  them  outside  of  all  law. 

'•These  senses  are  touch,  taste,  smell,  hearing,  and  sight. 
We  know  that  in  order  to  experience  the  sense  of  touch  there 
is  and  must  be  contact  with  a  substance.  It  is  impossible  to 
obtain  the  result  without  this.  And  so  in  regard  to  taste; 
there  is  no  taste  possible  unless  there  is  something  to 
be  tasted. 

"Next  comes  odor.  And  this  is  so  pertinent  to  the  subject 
that  Ellen  is  discussing,  that  she  wilt  quote  at  length  from  an 


14  ELLEN   OR  THE 

article  on  Odors,  by  the  noted  French  scientist  and  writer,  Fer- 
dinand Papillon,  as  follows : 

'Descartes,  Leibnitz,  and  all  the  great  minds  of  the  seventeenth  cen- 
tury, believed  that  phenomena  are  such  interdependent  parts  of  one 
whole,  that  they  require  to  be  explained  by  each  other,  and  conse- 
quently, that  a  very  close  mutual  connection  should  be  maintained 
among  the  sciences.  In  their  view,  this  was  the  condition  of  rapid 
advance  and  intelligent  development.  The  experimental  method,  con- 
stant to  systematic  obstinacy  in  erecting  so  many  barriers  between  the 
different  sections  of  natural  philosophy,  has  greatly  hindered  the  com- 
pleteness of  whatever  knowledge  we  possess  as  the  result  of  mutual 
interaction  among  all  truths.  At  this  day,  such  barriers  are  tending  to 
vanish  of  their  own  accord,  and  the  science  of  man  in  his  relations  with 
external  media  begins  to  show  the  outlines  of  its  plan  and  harmonj. 
AVe  have  before  this  sketched  several  of  its  chapters,  and  we  will 
endeavor  now  to  write  another,  on  the  subject  of  odors. 


'The  seat  of  smell,  or  the  olfactory  sense,  is  the  pituitary  membrane 
lining  the  inner  wall  of  the  nostrils.  It  is  a  mucous  surface,  laid  in 
irregular  wrinkles,  and  receiving  the  spreading,  slender,  terminal  fila- 
ments of  a  certain  number  of  nerves.  This  membrane,  like  all  other 
mucous  ones,  constantly  secretes  a  fluid  designed  to  lubricate  it.  By 
the  aid  of  the  muscles  covering  the  lower  part  of  the  nostrils,  the 
apparatus  of  smelling  can  be  dilated  or  contracted,  precisely  like  that  of 
sight.  This  understood,  the  mechanism  of  olfaction  is  quite  simple. 
It  consists  in  the  contact  of  odorous  particles  with  the  olfactory  nerve. 
These  particles  are  conveyed  by  the  air  to  the  inside  of  the  nasal  cavi- 
ties, and  there  strike  upon  the  sensitive  fibres.  If  the  access  of  air  is 
prevented,  or  if  the  nerve  is  altered,  no  sensation  is  produced.  Experi- 
ments in  physiology,  in  fact,  have  settled  that  the  olfactory  nerves  (or 


WHISPERINGS   OF  AN   OLD   PINE  1 5 

those  of  the  first  pair)  are  assigned  exclusively  to  the  perception  of 
odors.  Loss  of  the  sense  of  smell  occurs  whenever  the  nerves  are 
destroyed  or  injured  by  any  process,  or  even  whenever  they  are  merely 
compressed.  On  the  other  hand,  it  is  a  matter  of  common  observation 
that  impeding  the  passage  of  air  into  the  nostrils  is  quite  as  effectual 
a  way  of  making  any  sort  of  olfactory  sensation  impossible.  Let  us 
add,  that  the  region  most  sensitive  to  odors  is  that  of  the  upper  part 
of  the  nasal  cavaties.  There  are,  as  we  shall  notice  in  proceeding, 
considerable  differences  as  regards  the  degree  of  sensitiveness  in  this 
sense  of  smell,  comparing  one  man  with  another.  But  it  is  a  still 
more  singular  fact  that  sometimes,  without  apparent  cause,  the  sense 
is  utterly  wanting.  In  other  cases  it  is  unaffected  by  the  action  of 
certain  odors  only,  an  analogous  infuinity  to  that  which  students  of 
the  eye  call  daltonism^  and  which  consists  in  the  perception  of  certain 
colors  only.  We  find  in  scientific  annals  the  case  of  a  priest  who  was 
insensible  to  all  odors  except  that  of  decayed  cabbage ;  and  another, 
of  a  person  to  whom  vanilla  was  entirely  without  scent.  Blumenbach 
speaks  too  of  an  Englishman,  with  all  his  senses  very  acute,  who 
jjerceived  no  perfume  in  mignonette. 

'  Olfaction  is  sometimes  voluntary,  sometimes  involuntary.  In  the 
former  case,  by  an  act  which  is  called  scenting  something,  and  is  re- 
sorted to  for  the  sake  of  a  keener  sensation,  we  first  close  the  mouth, 
and  then  sometimes  draw  in  a  full  breath,  sometimes  a  succession  of 
short,  quick  inspirations.  Then  the  muscular  apparatus  edging  the 
opening  of  the  nostrils  comes  into  play,  to  contract  that  orifice,  and 
point  it  downward,  so  as  to  increase  the  intensity  of  the  current  of 
inhaled  air.  When,  on  the  contrary,  we  wish  to  smell  as  little  as  pos- 
sible, the  organ  becomes  passive.  We  effect  strong  exspirations  by  the 
nose  to  drive  out  the  air  that  produces  scent,  and  inhalation,  instead 
of  being  performed  by  the  nostrils,  instinctively  takes  place  through 
the  mouth. 


1 6  ELLEN   OR  THE 

'  Scents  and  the  sense  of  smell  have  an  important  share  in  the  phe- 
nomena of  gustation,  that  is,  there  is  a  close  connection  between  the 
perception  of  odors  and  that  of  tastes.  Physiological  analysis  has 
clearly  brought  out  the  fact  that  most  of  the  tastes  we  perceive  proceed 
from  the  combination  of  olfactory  sensations  with  a  small  number  of 
gustatory  sensations.  In  reality,  there  are  but  four  primitive  and 
radical  tastes  —  sweet,  sour,  salt,  and  bitter.  A  very  simple  experi- 
ment will  convince  us  of  this  fact.  If  we  keep  the  nostrils  closed 
when  tasting  a  certain  number  of  sapid  substances,  so  as  to  neutralize 
the  sense  of  smell,  the  taste  perceived  is  invariably  reduced  to  one 
of  the  four  simple  savors  we  have  just  named.  Then,  whenever  the 
pituitary  membrane  is  out  of  order,  the  taste  of  food  is  no  longer  the 
same  ;  the  tongue  distinguishes  nothing  but  sweet,  sour,  salt,  or  bitter. 

'  It  is  time  now  to  begin  the  study  of  the  physiological  and  chemical 
conditions  of  smell,  and  for  this  we  must  first  inquire  how  odorous  sub- 
stances behave  with  regard  to  the  medium  which  separates  them  from 
our  organs.  Provost,  in  an  essay  published  in  1799  on  the  means  of 
making  emanations  from  odorous  bodies  perceptible  to  sight,  was  the 
first  to  bring  to  view  the  fact  that  certain  odorous  substances,  solid  or 
fluid,  placed  on  moistened  glass,  or  in  a  saucerful  of  water,  instantly 
act  on  those  molecules  of  the  liquid  which  they  touch,  and  repel  them 
more  or  less,  producing  a  vacuum.  He  judged  that  this  method  might 
serve  to  make  odors  sensible  to  sight,  and  enable  us  to  distinguish 
odorous  from  inodorous  bodies.  These  movements  of  odorous  bodies 
on  the  surfaces  of  liquids,  of  which  camphor  particularly  gives  so  curious 
an  instance,  have  lately  been  studied  with  the  greatest  care  by  a  French 
physiologist,  with  a  view  to  establishing  a  theory  of  odors.  With  this 
purpose  Li^geois  has  examined  most  of  the  odoriferous  substances,  and 
has  ascertained  that  almost  all  of  them  perform  various  motions  of  cir- 
culation and  displacement  on  the  surface  of  water,  resembling  those 
noted  with  camphor.     Some  act  precisely  as  camphor  does.     Among 


^*AN    OLD    riNE 

hcse  are  benzoic  acid,  succinic  acid,  the  rind  of  bitter  oranges,  etc. 
With  others,  motion  soon  stops,  for  they  are  quickly  surroonded  by  an 
oily  fiJm  which  keeps  them  confined.  Some  must  be  reduced  to 
powder  before  the  phenomenon  takes  place*  As  regards  odorous 
liquids,  it  occurred  to  Li^geois  to  saturate  very  light  and  spongy  seeds, 
themselves  odorless,  with  them,  and  he  then  found,  on  throwing  the 
aecdB  on  water,  that  circulatory  and  displacing  movements  took  place, 
OS  with  other  substances.  He  concluded,  from  a  series  of  experiments 
methodically  tried,  that  the  motions  in  question  must  be  attributed, 
not  to  a  release  of  gas,  acting  in  the  manner  of  a  reroil,  but  simply  to 
the  separation  and  rapid  diffusion,  within  the  water,  of  the  odorous 
particles.  The  volatility  of  substances  cannot  be  admitted  to  have  any 
part  in  explaining  the  phenomenon.  It  depends  wholly  on  the  affinity 
of  fluids  for  the  odorous  particles,  and  also  for  those  of  fatty  matter. 
Li^geois  found,  for  instance,  that  a  drop  of  oil  put  on  the  surface  of 
water,  without  sensibly  lessening  in  size,  emits  an  enormous  quantity  of 
microscopic  droplets,  which  are  diffused  through  the  mass  of  the  water. 
Aromatic  essences  produce  a  like  effect.  Though  insoluble  in  water, 
they  have  a  powerful  tendency  to  disperse  themselves  throughout  it, 
asDd  water  that  receiver  a  very  small  quantity  of  the  odoriferous  prin- 
ciptep  in  the  shape  of  extremely  fine  powder,  has  enough  to  gain  their 
perfume  completely.  Lidgeois's  experiments  give  proof  of  the  most 
diligent  labors  and  of  praiseworthy  sagacity.  Science  has  accepted 
them  with  satisfaction,  and,  after  employing  them  usefully,  will  preserve 
the  memory  of  their  author,  taken  away  in  the  flower  of  his  age,  at  the 
outset  of  a  noble  career  as  a  physiologist  and  surgeon. 

'  It  seemed,  to  quote  his  words,  as  though  in  these  experiments  we 
were  assisting  at  the  formation  of  the  odorous  molecules.  Those 
delicate  atoms  emitted  from  odorous  substances  and  diffused  through 
the  atmosphere  are,  in  fact,  the  very  same  that  impinge  on  ottr  pitui- 
tary membrane,  and  give  us  the  sensation  of  odors.     Moreover,  facts 


-»-  ■■^^ 


1 8  ELLEN   OR  THE 

long  ago  observed  display  this  revealing  action,  so  to  call  ft,  of  water 
upon  odors.  At  morning,  when  the  verdure  is  moist  and  the  flowers 
covered  with  sparkling  pearls  of  dew,  a  fresher  and  baknier  fragrance 
exhales  from  every  plant.  It  is  the  same  after  a  light  shower.  Vege- 
tation gains  heightened  tints,  at  the  same  time  that  it  diffuses  more 
fragrant  waves  of  perfume.  We  remark  an  effect  of  the  same  kind  in 
the  physiological  phenomenon  of  taste.  The  saliva  serves  as  an  excel- 
lent vehicle  for  diffusing  the  odorous  principles ;  then  the  movements 
of  the  tongue,  spreading  that  fluid  over  the  whole  extent  of  the  cavity 
of  the  mouth,  and  thus  enlarging  the  evaporating  surface,  are  clearly  of  a 
kind  to  aid  the  dispersion  of  the  odorous  principles,  which,  as  we  have 
seen,  take  a  considerable  part  in  the  perception  of  tastes. 

'  Now,  in  the  phenomenon  of  smell,  air  acts  in  the  place  of  water. 
It  seizes  the  odorous  particles  and  brings  them  into  contact  with  the 
pituitary  membrane.  It  is  the  vehicle,  the  solvent,  of  those  extremely 
subtile  atoms  which,  acting  on  the  delicate  fibres  of  the  nerve,  produce 
in  it  a  special  movement,  which  translates  itself  into  the  most  varied 
sensations.  Oxygen,  and  the  existence  m  that  gas  of  a  certain  pro 
portion  of  odorous  molecules,  are  the  two  essential  conditions  of  this 
phenomenon. 

*  Such  is,  at  least,  the  result  of  earlier  experiments,  and  of  those  per- 
formed of  late  years  by  Nickl^s.  A  curious  fact,  well  worthy  of  atten- 
tion, is  the  remarkable  diffusibility  and  degree  of  subdivision  exhibited 
by  some  odorous  substances.  Ambergris  just  thrown  up  on  the  shore 
spreads  a  fragrance  to  a  great  distance,  which  guides  the  seekers  after 
that  precious  substance.  Springs  of  petroleum-oil  are  scented  at  a  very 
considerable  distance.  Bartholin  affirms  that  the  odor  of  rosemary  at 
sea  renders  the  shores  of  Spain  distinguishable  long  before  they  are  in 
sight.  So,  too,  every  one  knows  that  a  single  grain  of  musk  perfiunes 
a  room  for  a  whole  year,  without  sensibly  losing  weight.  Haller 
relates  that  he  has  kept  papers  for  forty  years  perfumed  by  a  grain 


WHISPERINGS   OF  AN   OLD   PINE  19 

of  amber,  and  that  they  still  retained  the  fragrance  at  the  end  of 
that  time.  He  remarks  that  every  inch  of  their  surface  had  been 
impregnated  by  1-2,691,064,000  of  one  grain  of  amber,  and  that  they 
had  perfumed  for  1 1,600  days  a  film  of  air  at  least  a  foot  in  thickness. 
Evidently  the  material  quantity  of  the  odorous  principle  contained  in  a 
given  volume  of  such  air  is  so  minute  as  to  elude  imagination. 

*  Odors,  to  be  perceived,  must  be  taken  up  by  oxygen,  and  borne  by 
it  to  the  organ  of  smell. 

•  «•««««« 

*  The  learned  and  capable  author,  Piesse,  in  his  work  on  "  Odors,  Per- 
fumes, and  Cosmetics,"  says:  "Odors  seem  to  affect  the  olfactory 
nerves  in  certain  definite  degrees,  as  sounds  act  on  the  auditory  nerves. 
There  is,  so  to  speak,  an  octave  of  smells,  as  there  is  an  octave  of  tones ; 
some  perfimies  accord,  like  the  notes  of  an  instrument.  Thus  almond, 
vanilla,  heliotrope,  and  clematis,  harmonize  perfectly,  each  of  them 
producing  almost  the  same  impression  in  a  different  degree.  On  the 
other  hand,  we  have  citron,  lemon,  orange  peel,  and  verbena,  forming  a 
similarly  associated  octave  of  odors,  in  a  higher  key.  The  analogy  is 
completed  by  those  odors  which  we  call  half-scents,  such  as  the  rose, 
with  rose-geranium  for  its  semitone ;  '  petit-grain '  and  neroli,  followed 
by  orange-flower.  With  the  aid  of  flowers  already  known,  by  mixing 
them  in  fixed  proportions,  we  can  obtain  the  perfume  of  alnwst  all 
flowers." 

"Again  Mr.  Papillon  says: 

'To  complete  these  details,  it  remains  to  say  something  of  the  delu- 
sions of  the  sense  of  smell ;  for  this  sense,  like  the  others,  has  its  aber- 
rations and  hallucinations.  The  delusions  of  smell  are  hardly  ever 
isolated ;  they  accompany  those  of  hearing,  sight,  taste,  and  touch,  and 
are  also  less  frequent  than  the  latter. 


20  ELLEN   OR  THE 

"  And  again : 

'  The  intensity  and  delicacy  of  the  sense  of  smell  vary  in  mankind 
among  different  individuals,  and  particularly  among  different  races  of 
men.  While  some  persons  are  almost  devoid  of  the  sense  of  smell, 
others,  whose  history  is  related  in  the  annals  of  science,  have  displayed 
a  refinement  and  range  in  the  distinction  of  odors  truly  wonderfuL 
Woodward,  for  instance,  mentions  a  woman  who  foretold  storms  several 
hours  before  their  coming,  by  the  help  of  the  sulphurous  odor,  due 
probably  to  ozone,  which  she  perceived  m  the  atmosphere.  The 
scientific  journals  of  the  day  relate  the  account  of  a  young  American 
girl,  a  deaf-mute,  who,  by  their  odor  alone,  recognized  the  plants  of 
the  fields  which  she  collected.  Numerous  instances,  moreover,  prove 
that  in  savage  races  this  sense  is  very  greatly  more  developed  than 
among  civilized  men. 

'  But  it  is  among  the  other  mammals  that  we  find  the  sense  of  smell 
displayed  in  its  highest  degree  of  power  and  perfection.  Among  rumi- 
nants, some  pachyderms,  and  particularly  among  carnivorous  mammals, 
the  olfactory  membrane  attains  the  keenest  sensitiveness.  Buffon  has 
described  these  animals  with  extreme  exactness,  in  saying  that  they 
smell  farther  than  they  see,  and  that  they  possess  in  their  scent  an  eye 
which  sees  objects  not  only  where  they  are,  but  even  wherever  they 
have  been.  The  peculiarity  of  scent  in  the  dog  is  too  well  known  to 
need  more  than  an  allusion. 

•  ###«•#« 

'  Alexander  von  Humboldt  relates  that  in  Peru,  and  other  countries  of 
South  America,  when  it  is  intended  to  take  condors,  a  horse  or  cow  is 
killed,  and  that  in  a  short  time  the  smell  of  the  dead  animal  attracts 
a  great  number  of  these  birds,  though  none  had  before  that  been  seen 
in  the  country.     Other  more  extraordinary  facts  are  told  by  travelers. 


WHISPERINGS   OF  AN   OLD   PINE  21 

'  What,  now,  is  the  chemical  nature  of  the  odorous  principles  in 
plants  ?  The  chemistry  of  to-day  reduces  almost  all  of  them  to  three 
categories  of  well-ascertained  substances :  hydrocarburets,  aldehydes, 
and  ethers.  We  will  endeavor  to  give  a  clear  account  of  the  constitu- 
tion of  these  thr^e  kinds  of  substances,  and  to  mark  their  place  in  the 
register  of  sci'*nce.  The  hydrocarburets  are  simple  combinations  of 
carbon  and  hydr^/gen,  as,  for  instance,  the  petroleum-oils.  They  rep- 
resent the  simple  compounds  of  organic  chemistry.  As  to  aldehydes 
and  ethers,  their  composition  is  rather  more  complex ;  besides  carbon 
and  hydrogen,  they  contain  oxygen.  Every  one  knows  what  chemists 
mean  by  an  alcohol ;  it  is  a  definite  combination  of  hydrogen,  carbon, 
and  oxygen,  neither  acid  nor  alkaline,  which  may  be  regarded  as  the 
result  of  the  union  of  a  hydrocarburet  with  the  elements  of  water. 
Common  alcohol,  or  spirits  of  wine,  is  the  type  of  the  most  important 
series  of  alcohols,  that  of  the  mono-atomic  alcohols.  Chemists  repre- 
sent it  by  the  formula  C'H^O,  to  indicate  that  a  molecule  of  it  arises 
from  the  union  of  two  atoms  of  carbon  with  six  atoms  of  hydrogen  and 
one  of  oxygen.  Independently  of  the  alcohols,  which  are  of  great 
number  and  varying  complexity,  organic  chemistry  recognizes  another 
class  of  bodies,  of  which  vinegar  is  the  type,  and  which  receive  the 
name  of  organic  acids,  to  mark  their  resemblance  to  mineral  acids, 
siich  as  oil  of  vitriol  or  aqua-fortis.  Now,  every  alcohol,  on  losing  a 
certain  amount  of  hydrogen,  gives  rise  to  a  new  body,  which  is  called 
an  aldehyde ;  and  every  alcohol,  on  combining  with  an  acid,  produces 
what  is  called  an  ether.  These  rapid  details  allow  us  to  understand 
precisely  the  chemical  character  of  the  essences  or  essential  oils  which 
plants  elaborate  within  their  delicate  tissue.  Except  a  small  number 
among  them  which  contain  sulphur,  as  the  essences  of  the  family  of 
crucifers,  they  all  present  the  same  qualitative  composition  —  carbon  and 
hydrogen,  with  or  without  oxygen.  Between  one  and  another  of  them 
merely  the  proportion  of  these  three  composing  elements  varies,  by 


22  ELLEN   OR  THE 

regular  gradations,  but  so  as  always  to  correspond  either  to  a  hydrocar- 
buret,  or  to  an  aldehyde,  or  to  an  ether.  In  this  case,  as  in  almost  the 
whole  of  organic  chemistry,  every  thing  is  in  the  quantity  oi  the  com- 
posing elements.  The  quality  is  of  so  little  importance  to  Nature,  that^ 
w/iiU  following  always  the  same  laws,  and  constantly  using  the  same 
materials^  she  can,  by  merely  changing  the  ponderable  relations  of  the 
latter,  produce,  by  myriads  of  various  combinations,  myriads  of  sub- 
stances which  have  no  resemblance  to  each  other. 

•  ••••••• 

'Such  is  the  chemical  nature  of  most  of  the  odorous  principles  of 
vegetable  origin.  But  chemistry  has  not  stopped  short  with  ascertain- 
ing the  inmost  composition  of  these  substances;  it  has  succeeded  in 
reproducing  quite  a  number  of  them  artificially,  and  the  compounds 
thus  manufactured,  wholly  from  elements,  in  laboratories,  are  absolutely 
identical  with  the  products  extracted  from  plants.  ♦  •  *  An 
Italian  chemist,  who  was  then  employed  in  Paris,  Piria,  in  1838,  was 
the  first  who  imitated  by  art  a  natural  aromatic  principle.  By  means  of 
reactions  suggested  by  theory,  he  prepared  a  salicilic  aldehyde,  which 
turned  out  to  be  the  essence  of  meadow-sweet,  so  delicate  and  subtile 
in  its  odor.  A  few  years  later,  in  1843,  Cahours  discovered  methylsali- 
cilic  ether,  and  showed  that  it  is  identical  with  the  essence  of  winter- 
green.  A  year  after,  Wertheim  composed  essence  of  mustard,  while 
believing  himself  to  be  making  only  allylsulphocyanic  ether.  ♦  ♦  ♦ 
Nowadays  the  chemist  possesses  the  means  of  creating  many  other 
natural  essences.  Common  camphor,  essence  of  bitter-almonds,  that 
of  cummin  and  of  cinnamon,  which  are  aldehydes,  as  we  have  seen,  may 
be  prepared  without  camphor-leaves  or  almonds,  without  cummin  or 
cinnamon.  Besides  these  ethers  and  aldehydes  whose  identity  with 
essences  of  vegetable  origin  has  been  proved,  there  exist,  among  the 
new  bodies  known  to  organic  chemistry,  a  certain  number  of  products 
formed  by  the  union  of  cgmmon  alcohol  or  amylic  alcohol  with  differ- 


WHISPERINGS   OF  AN   OLD   PINE  23 

ent  acids,  that  is  to  say,  of  ethers,  which  have  aromatic  odors  more  or 
less  resembling  those  of  some  fruits,  but  as  to  which  it  cannot  yet  be 
affirmed  that  the  odors  are  due  to  the  same  principles  in  both  cases. 
However  this  may  be,  perfumers  and  confectioners,  more  industrious 
and  wide-awake  than  chemists,  have  immediately  made  good  use  of 
these  properties.  Artificial  aromatic  oils  made  their  first  appearance  at 
the  World's  Fair  of  London  in  1851.  There  was  there  exhibited 
a  pear-oil,  diffusing  a  pleasant  smell  like  that  of  a  jargonel,  and  employed 
to  give  an  aroma  to  bonbons.  This  product  is  nothing  else  than  a  solu- 
tion of  amylacetic  ether  in  alcohol.  Apple-oil  was  exhibited  beside  the 
pear-oil,  having  the  fragrance  of  the  best  rennets,  and  produced  by  dis- 
solving amylvaleric  ether  in  alcohol.  The  commonest  essence  was  that 
of  pineapple,  which  is  nothing  else  than  ordinary  butyric  ether. 
There  was  observed,  too,  an  essence  of  cognac,  or  grape-oil,  used  to 
impart  to  poor  brandies  the  highly-prized  aroma  of  cognac.  The 
product  which  was  then,  and  still  is,  the  most  important  article  of 
manufacture,  is  the  essence  of  "  mirbane,"  which  very  closely  resembles 
in  its  odor  that  of  bitter  almonds,  and  which  commerce  very  often  sub- 
stitutes for  the  latter.  Essence  of  mirbane  is  nothing  else  than  nitro- 
benzine,  which  results  from  the  action  of  nitric  acid  on  benzine. 
Benzine,  in  turn,  is  met  with  among  the  products  of  distillation  of  tar, 
which  also  yield  the  substances  used  in  preparing  those  beautiful  colors 
called  aniline.  Besides  the  essences  we  have  just  mentioned,  which  are 
gaining  an  increasing  importance  in  the  manufacturing  arts,  artificial 
essences  of  quinces  are  also  prepared,  and  essences  of  strawberries,  of 
rum,  etc.  All  these  preparations  serve,  it  must  be  admitted,  to  give  an 
aroma  to  the  cordials,  confectioneries,  and  sweetmeats,  which  are  so 
largely  sold  nowadays.  In  other  words,  the  products  of  industry  are 
constantly  taking  the  place  of  those  of  Nature  more  and  more.' " 


24  ELLEN   OR  THE 


III. 


ii 


THE  fact  that  all  odors  are  substantial  is  beyond  question. 
And  yet  it  was  at  this  point  that  the  scientists  made  their 
first  drift  from  the  canons  of  common  sense,  by  assuming  and 
asserting  that  odor  was  what  is  called  a  mode  of  motion. 
Thus  the  celebrated  English  philosopher  and  scientist,  Thomas 
Hobbes  (i 588-1679),  wrote: 

*  For  the  finding  out  the  cause  of  smells^  I  shall  make  use  of  the  evi- 
dence of  these  following  phenomena.  First,  that  smelling  is  hindered 
by  cold,  and  helped  by  heat.  Secondly,  that  when  the  wind  bloweth 
from  the  object,  the  smell  is  stronger ;  and,  contrarily,  when  it  bloweth 
from  the  sentient  toward  the  object,  the  weaker;  both  which  phe- 
nomena are,  by  experience,  manifestly  found  to  be  true  in  dogs,  which 
follow  the  track  of  beasts  by  the  scent.  Thirdly,  that  such  bodies,  as 
are  less  pervious  to  the  fluid  medium,  yield  less  smell  than  such  as  are 
more  pervious ;  as  may  be  seen  in  stones  and  metals,  which,  compared 
with  plants  and  living  creatures,  and  their  parts,  fruits  and  excretions, 
have  very  little  or  no  smell  at  all.  Fourthly,  that  such  bodies,  as  are  of 
their  own  nature  odorous,  become  yet  more  odorous  when  they  are 
bruised.  Fifthly,  that  when  the  breath  is  stopped,  at  least  in  men, 
nothing  can  be  smelt.  Sixthly,  that  the  sense  of  smelling  is  also  taken 
away  by  the  stopping  of  the  nostrils,  though  the  mouth  be  left  open. 

*  By  the  fifth  and  sixth  phenomenon  it  is  manifest,  that  the  first  and 
immediate  organ  of  smelling  is  the  innermost  cuticle  of  the  nostrils,  and 
that  part  of  it,  which  is  below  the  passage  conmion  to  the  nostrils  and 


THE  NEW  YORK 
PUBLIC  LIBRART 

ASiOr,,  LUNOX  AND 

TlLDitN  rC'.'NrJATlONJ 


WHISPERINGS   OF   AN   OLD   PINE  2/ 

the  palate.  For  when  we  draw  breath  by  the  nostrils  we  draw  it  into 
the  lungs.  That  breath,  therefore,  which  conveys  smell  is  in  the  way 
which  passeth  to  the  lungs,  that  is  to  say,  in  that  part  of  the  nostrils 
which  is  below  the  passage  through  which  the  breath  goeth.  For, 
nothing  is  srfielt,  neither  beyond  the  passage  of  the  breath  within,  nor 
at  all  without  the  nostrils. 

'  And  seeing  that  from  different  smells  there  must  necessarily  proceed 
some  mutation  in  the  organ,  and  all  mutation  is  motion ;  it  is  therefore 
also  necessary  that,  in  smelling,  the  parts  of  the  organ,  that  is  to  say  of 
that  internal  cuticle  and  the  nerves  that  are  mserted  into  it,  must  be 
diversely  moved  by  different  smells.  And  seeing  also,  that  it  hath  been 
demonstrated,  that  nothing  can  be  moved  but  by  a  body  that  is  already 
moved  and  contiguous ;  and  that  there  is  no  other  body  contiguous  to 
the  internal  membrane  of  the  nostrils  but  breath,  that  is  to  say  attracted 
air,  and  such  little  solid  invisible  bodies,  if  there  be  any  such,  as  are 
intermingled  with  the  air;  it  follows  necessarily,  that  the  cause  of 
smelling  is  either  the  motion  of  that  pure  air  or  ethereal  substance,  or 
the  motion  of  those  small  bodies.  But  this  motion  is  an  effect  pro- 
ceeding from  the  object  of  smell,  and,  therefore,  either  the  whole  object 
itself  or  its  several  parts  must  necessarily  be  moved.  Now,  we  know 
that  odorous  bodies  make  odor,  though  their  whole  bulk  be  not  moved. 
Wherefore  the  cause  of  odor  is  the  motion  of  the  invisible  parts  of  the 
odorous  body.  And  these  invisible  parts  do  either  go  out  of  the  object, 
or  else,  retaining  their  former  situation  with  the  rest  of  the  parts,  are 
moved  together  with  them,  that  is  to  say,  they  have  simple  and  invisible 
motion.  They  that  say,  there  goes  something  out  of  the  odorous  body, 
call  it  an  effluvium ;  which  effluvium  is  either  of  the  ethereal  substance, 
ot  of  the  small  bodies  that  are  intermingled  with  it.  But,  that  all 
variety  of  odors  should  proceed  from  the  effluvia  of  those  small  bodies 
that  are  intermingled  with  the  ethereal  substance,  is  altogether  incred- 
ible, for  these  considerations ;  first,  that  certain  unguents,  though  very 


28  ELLEN   OR  THE 

little  in  quantity,  do  nevertheless  send  forth  very  strong  odors,  not  only 
to  a  great  distance  of  place,  but  also  for  a  great  continuance  of  time, 
and  are  to  be  smelt  in  every  point  both  of  that  place  and  time ;  so  that 
the  parts  issued  out  are  sufficient  to  fill  ten  thousand  times  more  space, 
than  the  whole  odorous  body  is  able  to  fill ;  which  is  impossible.  Sec- 
ondly, that  whether  that  issuing  out  be  with  straight  or  with  crooked 
motion,  if  the  same  quantity  should  flow  from  any  other  odorous  body 
with  the  same  motion,  it  would  follow  that  all  odorous  bodies  would 
yield  the  same  smell.  Thirdly,  that  seeing  these  effluvia  have  great 
velocity  of  motion  (as  is  manifest  from  this,  that  noisome  odors  pro- 
ceeding from  caverns  are  presently  smelt  at  a  great  distance)  it  would 
follow,  that,  by  reason  there  is  nothing  to  hinder  the  passage  of  those 
effluvia  to  the  organ,  such  motion  alone  were  sufficient  to  cause 
smelling ;  which  is  not  so ;  for  we  cannot  smell  at  all,  unless  we  draw  in 
our  breath  through  our  nostrils.  Smelling,  therefore,  is  not  caused  by 
the  effluvium  of  atoms ;  nor,  for  the  same  reason,  is  it  caused  by  the 
effluvium  of  ethereal  substance  ;  for  so  also  we  should  smell  without  the 
drawing  in  of  our  breath.  Besides,  the  ethereal  substance  being  the 
same  in  all  odorous  bodies,  they  would  always  affect  the  organ  in  the 
same  manner ;  and,  consequently,  the  odors  of  all  things  would  be  alike. 

*  It  remains,  therefore,  that  the  cause  cf  smelling  must  consist  in  the 
simple  motion  cf  the  parts  of  odorous  bodies  without  any  efflux  or 
diminution  of  their  whole  substance.  And  by  this  motion  there  is 
propagated  to  the  organ,  by  the  intermediate  air,  the  like  motion,  but 
not  strong  enough  to  excite  sense  of  itself  without  the  attraction  of  air 
by  respiration.     And  this  is  a  possible  cause  of  smelling. 

*The  cause  why  smelling  is  hindered  by  cold  and  helped  by  heat  may 
be  this  j  that  heat,  as  hath  been  shown  in  Chapter  XXL,  generateth 
simple  motion ;  and  therefore  also,  wheresoever  it  is  already,  there  it 
will  increase  it ;  and  the  cause  of  smelling  being  increased,  the  smell 
itself  will  also  be  increased.     As  for  the  cause  why  the  wind  blowing 


WHISPERINGS   OF  AN   OLD   FINE 


29 


from  the  object  makes  the  smell  the  stronger,  it  k  all  one  with  that  for 
^«vhich  the  attraction  of  air  in  respiration  doth  the  same.  For,  he  that 
<:iniws  in  the  air  next  to  him,  draws  with  it  by  succession  that  air  in 
^^wrhich  is  the  objects  Nou*,  this  motion  of  the  air  is  wind,  and,  when 
smother  wind  bloweth  from  the  object,  will  be  increased  by  it. 

'That  bodies  which  contain  the  least  quantity  of  air,  as  stones  and 

xnetals,  yield  less  smell  than  plants  and  living  creatures ;  the  cause  may 

Ibe^  that  the  motion,  which  causeth  smelling,  is  a  motion  of  the  fluid 

^parts  only ;  which  parts,  if  they  have  any  motion  from  the  hard  j>arts 

in  which  they  are  contained,  they  communicated  the  same  to  the  open 

.sair,  by  which  it  is  propagated  to  the  organ.     Where,  therefore,  there 

src  no  fluid  parts  as  in  metals,  or  where  the  fluid  parts  receive  no 

^aation  from   the  hard  parts,  as  in  stones,  which  are  made  hard  by 

.accretion,  there  can  be  no  smell.     And  therefore  also  the  water,  whose 

parts  have  little  or  no  motion,  yieldeth  no  smell.     But,  if  the  same 

-water,  by  seeds  and  the  heat  of  the  sun,  be  together  with  particles  of 

earth  raised  into  a  plant,  and  be  aften^^ards  pressed  out  again,  it  will  be 

odorous,  as  wine  from  the  vine.     And  as  water  passing  through  plants 

is  by  the  motion  of  the  parts  of  those  plants  made  an  odorous  liquor; 

so  also  of  air,  passing  through  the  same  plants  whilst  they  are  growing, 

are  made  odorous  airs.     And  thus  also  it  is  with  the  juices  and  spirits, 

which  are  bred  in  living  creatures. 

•'riiat  o<lorous  bodies  may  be  made  more  odorous  by  contrition 
piocceds  from  this,  that  being  broken  into  many  parts,  which  are  all 
odorous,  the  air,  which  by  respiration  is  drawn  from  the  object  towards 
the  organ,  dolh  in  its  passage  touch  upon  all  those  parts,  and  receive 
their  motion.  Now,  the  air  toucheth  the  superficies  only;  and  a  body 
having  less  superficies  whilst  it  is  whole,  than  all  its  parts  together  have 
after  it  is  reduced  to  powder,  it  follows  that  the  same  odorous  body 
yieldeth  less  smell  whilst  it  is  whole,  than  it  will  do  after  it  is  broken 
mto  small  parts.    And  thus  much  of  smells/ 


30  ELLEN   OR  THE 

"Of  course  we  understand  that  all  of  this  is  unmitigated  non- 
sense, but  no  more  so  than  it  was  when  written,  and  no  more 
so  than  the  same  sort  of  statement  is  concerning  sound.  It  will 
be  noticed,  too,  that  the  last  paragraph  suggests  a  similar 
senseless  explanation  for  the  increase  of  smell,  as  scientists  of 
to-day  give  for  increase  of  sound  by  sounding  boards. 

**And  thus  in  the  definition  of  smell,  the  Encyclopaedic 
Dictionary  of  recent  date,  a  very  excellent  work,  says : 

'  Smell  is  the  perception  of  odorous  emanations,  the  nature  of  which  is 
not  certainly  known.  They  may  consist  of  aerial  waves,  or  may  be 
aerial  particles  of  the  odorous  substance.  In  either  case,  they  are  ex- 
tremely delicate ;  air  containing  only  a  millionth  part  of  hydrogen  sul- 
phide, having  a  distinct  odor,  and  a  minute  portion  of  musk  will  con- 
tinue, without  appreciable  loss  of  weight,  to  render  its  presence  percep- 
tible in  a  large  room  for  years.  These  particles  must  be  conducted  to 
the  nostrils  by  the  air,  or  no  impressions  will  be  perceived.  Smell 
exists  in  all  the  higher  animals.  Danvin  (Descent  of  Man,  Part  I, 
Ch.  I.)  says  that  it  is  of  supreme  importance  to  the  ruminants  in  warn- 
ing them  of  danger,  to  the  carnivora  for  finding  their  prey,  and  to  others 
again,  as  the  wild  boar,  for  both  purposes  combined.  Mr.  S.  P.  Wood- 
ward finds  it  present  in  the  cephalopods  and  gasteropods.* 

**And  thus,  too,  in  Appleton's  Popular  Science  Monthly, 
May,  1882,  a  writer,  discussing  this  question,  says: 

*The  following  paragraph  is  similar  to  others  I  have  occasionally 
seen  going  the  rounds  of  the  papers  for  the  last  twenty-five  or  thirty 
years  : 

*"It  is  said  that  a  grain  of  musk  is  capable  of  perfuming  for  several 
years  a  ( hamber  twelve  feet  square  without  sustaining  any  sensible 
diminution  of  its  volume  or  its  weight.     But  such  a  chamber  contains 


WHISPERINGS    OF   AN    OLD    liNE 


31 


9^^^5,984  cubic  inches,  and  each  cubic  inch  contains  1,000  cubic 
tenths  of  inches,  making  in  all  nearly  three  billions  of  tenths  of  an  inch* 
Now,  it  is  probable,  indeed  almost  certain,  that  each  such  cubic  tenth 
of  an  inch  of  the  air  of  the  room  contains  one  or  more  of  the  particles 
of  the  musk,  and  that  this  air  has  been  changed  many  thousands  of 
times.  Imagination  recoils  before  computation  of  the  number  of  the 
particles  thus  diffused  and  expended.  Yet  h:ive  they  altogether  no 
appreciable  weight  and  magnitude.— i/e^i-^Zryi"  H/ustrafions  i*/  Saen^eJ* 

*  .\fore  than  thirty^six  years  ago  I  announced,  in  some  lectures  I  was 
then  engaged  in  delivering,  that  there  were  some  facts  in  the  phenom- 
cna  of  odors  and  the  sense  of  smell  that  were  incompatible  with  the 
efHuvia  or  diffusioa-of-particles  theory ;  and  I  suggested  an  explanation 
based  on  the  idea  of  a  vibration  or  wave-motion,  and  an  "odoriferous 
ether*'  analogous  to,  if  not  identical  with,  that  of  the  luminiferous  ether. 

•In  the  year  1863,  in  a  letter  to  Professor  Tyndall,  I  submitted  the 
thought  to  him.  Mter  quoting  some  passages  from  his  book,  **  lieat  a 
Mode  of  Motion,"  upon  the  subject  of  odors,  1  wrote  as  follows :  *'  I 
wouKI  respectfully  ask  if,  In  the  consideration  of,  or  in  the  course 
of,  c\periments  u|)oii  this  subject,  it  has  ever  occurred  to  you  that  i?rt'<;r 
might  be  as  essentially  a  'mode  of  moiion  '  as  heat,  light,  or  sound? 
•  •  •  The  seemingly  unlimited  generation  of  odoriferous  par- 
ticles (?)  by  certain  substances,  withotit  sensible  diminution  of  bulk  or 
weight,  first  led  to  the  conception  that,  however  copiously  odoriferous 
particles  of  matter  were  disseminated  through  the  atmosphere,  the 
odorous  property  itself  w^as  as  purely  a  specific  variety  of  motion  as  the 
tmdulations  of  the  luminiferous  ether.  That  this  muif  be  the  explana- 
tion of  the  action  of  the  odor-generating  force  for  a  part  of  its  route  to 
the  human  sensoriura  seems  to  be  incontrovertible,  for  it  is  hardly  con- 
ceivable that  the  material  particles  should  actually  penetrate  the  mem- 
brane and  force  their  way,  as  moving  bodies,  through  the  pulpy  tissue 

'.  the  nen-cs  to  the  seat  of  sensation ;  but  that  through  that  portion  of 


32  ELLEN   OR  THE 

their  career,  at  least,  their  power  is  propagated  by  wave-like  motions 
analogous  to  those  of  heat  and  sound." 

'  Professor  Tyndall  did  me  the  honor  to  answer  my  letter,  but  not  to 
indorse  my  view,  except  in  a  very  faint  and  qualified  manner.  Never- 
theless, reflection  and  added  experience  have  only  gone  to  confirm  me 
in  the  correctness  of  it,  and  I  venture  to  predict  that  before  many  years 
it  will  be  as  much  an  accepted  fact  of  science  as  the  undulatory, 
luminiferous-ether  theory  now  is. 

'  In  the  case  given  above  the  entire  space  of  the  chamber  is  thoroughly 
impregnated  with  the  perfume  as  mnrh  as  if  it  was  an  absolute  solid  of 
odor.  And  yet  these  "particles,"  so  profusely  diffused  through  the 
room,  are  wafted  away,  and  their  places  supplied  by  new  emissions  from 
the  undiminished  "  grain,"  "many  thousands  of  times  "  every  year  with- 
out appreciable  "  sensible  diminution  of  its  volume  or  weight,"  or  pun- 
gency. This  is  an  obvious  impossibility  upon  any  theory  of  molecular 
or  atomic  diffusion.  The  assumption  of  immense  diffusibility  and 
vastness  of  inter- particular  spaces  would  only  enhance  the  difficulty,  for 
the  odor  spans  the  spaces  —  is  as  absolutely  continuous  as  if  the  par- 
ticles were  in  actual  contact.  That  is,  in  the  given  space,  the  chamber, 
anywhere  within  the  limits  of  the  odor,  there  is  no  place  where  it  is  not. 
This  actio  in  distans  implies  ethereal  motion  —  vibration  —  between  the 
particles. 

'According  to  this  view  the  odoriferous  bodies,  or  their  molecules, 
have  no  more  to  do  (in  the  sense  of  physical  impact)  in  producing  the 
sensation  of  smell  than  a  luminous  body  —  a  candle  or  the  sun  —  has  to 
do  (by  impact)  with  the  sensation  of  light.  There  is  corporeal  impact 
or  touch  in  neither  case.  Of  course,  with  each  molecule  as  a  center  of 
activity,  the  effect  will  be  more  pronounced  at  the  immediate  surface 
(as  with  all  radiant  energies)  than  at  any  distance.  And,  undoubtedly, 
particles  of  disintegrating,  odorous  matter  are  often  brought  in  contact 
with  the  Schneiderian  membrane ;  but  the  sensation  of  that  impact,  if 


WHISPERINGS   OF   AN   OLD   TINE 


35 


t^iere  be  any,  would  be  of  touch,  not  of  smell,  as  surely  as  that,  from 
tHat  point  of  contact  to  the  sensorium,  the  effect  or  influence  is  con- 
ireye*!  by  a  vibration  —  a  wave*motion  in  the  *' fluid "  of  the  Bcrve- 
dtict  —  as  the  undulations  of  the  luminiferous  ether  are  propagated 
St  long  the  course  of  the  optic  nerve  to  the  seat  of  sensation,  where  they 
4Ue  translated  into  light  and  color.  But,  if,  for  any  portion  of  the  dis- 
t^ince  between  the  internal  sense  and  the  fragrant  body,  the  odor,  like 
M^ht,  is  but  a  motion,  it  is  safe  to  assume  it  for  all.  Tht  analogy  of 
tJiis  mode  of  odors  to  that  of  light  and  sound  is  something  in  its  favor/ 


*•  In   this  article  we  have  another  illustration  of  the  folly  of 

I     ignorance,  very  similar  and  perhaps  equal  to  that  of  Huyghens 
^^nd  Dr.  V'oung  in  their  theory  of  light. 
I  •*  Of    the    senses,    there     remain    only    hearing    and    sight. 

I  XJnable  to  weigh  the  substances,  sound  and  light,  with  cither  a 
I  liay-scale  or  a  balance,  the  scientist  denies  their  existence. 
I  lie  might  as  well  deny  the  existence  of  the  spheres  and  the 
^^H-vnountains  because  he  cannot  weigh  them  with  his  scales/' 
^"  "  But/*  I  said,  **  such  things  as  these  last  he  estimates  the 
^^  "Weight  of  with  the  aid  of  mathematics,  does  he  not?" 
^B  *'Yes/*  she  replied,  **he  invents  a  scale  of  the  mind  for  such 
I  emergency;  and  Ellen  thinks  he  would  better  invent  such  for 
■  this  other  emergency,  where  things  are  too  small  and  too  light 
to  be  weighed  by  the  contrivances  of  man,  which ^  at  the  best,  as 
EUcn  thinks,  can  weigh  but  few  things  of  those  which  exist  in 
the  universe.  But  now  again  the  scientist  prates  about  what 
he  calls  modes  of  motion." 

"And  what  are  these,  Ellen?''  I  asked. 

•*  Infinite  folly,  as  announced  by  science,  the  serious  concep- 
tion of  which  would  be  possible  only  after  one  has  surrendered 


34  ELLEN    OR   THE 

all  his  wits.  For  the  assumption  is  not  only  that  nature  in  this 
wonderful  work  of  creation  follows  no  system ;  but  also  that 
something  is  got  out  of  nothing.  For  no  one,  so  far  as  Ellen 
knows,  claims  that  sound  exists  in  particles  of  air  when  they 
lie  quiescent,  if  ever  they  do  so  He,  any  more  than  that  odor  so 
exists.  Although  the  scientist  claims  that,  when  moved  in  a 
certain  manner,  this  result  is  obtained  through  them.  And  so 
these  same  scientists  claim  that  a  similar  result  is  obtained  from 
the  movement  of  the  particles  of  a  thousand  different  materials, 
such  as  iron,  steel,  brass,  etc.,  —  indeed,  the  particles  of  all 
elastic  bodies.  The  old  Pine  must  beware  of  the  scientists,  for 
they  arc  very  foolish  people." 

"Yes,"  I  said,  *'the  old  Pine  sees  how  readily  they  follow 
the  paths  of  folly." 

*'Ycs,  indeed,"  she  said.  ''For  although  the  theory  as  to 
the  sense  of  smell  has  been  abandoned,  because  demonstrated 
to  be  untenable,  they  hasten  to  assume  a  similar  one  for  the 
two  remaining  senses,  —  hearing  and  sight 


i^iilbrERlNGS 


35 


IV. 


*•  QOUND  Is  produced  by  contact,  or  shock.     And  Ellen 
^     thinks  the  contact  of  any  two  particles   will  produce 
it  the  microphone  is  an   instrument  which    magnifies 

Sound  to  the  car,  as  a  microscope  magnifies  size  to  the  eye, 
and  with  it  can  be  heard  the  step  of  a  fly.     Thus  Ganot  says 

In  his  Ph\sics : 


'  Ihc  \v.Ukiag  of  a  fly  on  the  base  suggests  the  stamping  of  a  horse; 
the  scratching  of  a  quill,  the  rustling  of  silk,  the  beating  of  the  pulse 
are  perceived  in  the  telephone  at  a  distance  of  a  hundred  miles  from 
the  source  of  sound  ;  while  a  drop  of  water  falling  upon  the  base  has  a 
lotul,  cracking  sound/ 

*'From  which  it  would  seem  to  follow  that  any  motion  may 
produce  a  sound;  that  is,  that  any  contact  of  two  things 
makes  sound.  For,  if  the  step  of  a  fly  makes  sound,  wc  may 
believe  that  the  contact  of  any  two  particles,  however  infini- 
tesimal and  light,  makes  sound.  It  follows  that  sound,  as  inter- 
preted to  us,  IS  dependent  more  upon  our  capacity  of  hearing 
than  upon  the  thing  itself;  for  the  thing  itself  would  seem  to 
exist  everywhere  and  always,  being  the  result  of  motion,  which 
exists  everj'where  and  always.  So  that  Ellen  can  see  that  the 
music  of  the  spheres  need  not  be  a  myth  to  all  beings,  but 
might  be  and  probably  is  to  some — whose  sense  of  hearing  is 
fitted  for  it — a  beautiful  harmony. 

"And   it  follows,  too,  as   Ellen   thinks,   that  the  mediums 


36  ELLEN   OR  THE 

which  carry  sound  to  us  are  not  the  only  mediums  which 
carry  sound,  but  simply  the  only  ones  which  carry  it 
to  us,  and  that  sound  equally  with  light  extends  over  the 
universe." 

"But  Ellen  wouldn't  always  want  sound,  would  she?" 
I  asked. 

"And  why  not?" 

"Why,"  I  said,  "it  would  become  monotonous,  would  it 
not?  and  disagreeable?" 

"  Ellen  thinks  not,"  she  replied  ;  "certainly  not  any  more  than 
light.  Variety  has  been  called  the  spice  of  life,  and  in  variety 
doubtless  there  is  much  pleasure,  as  in  the  variety  of  light  and 
darkness,  or  of  sound  and  silence.  But  Ellen  thinks  that  the 
roar  of  the  ocean  is  always  agreeable,  and  so  the  murmurings 
of  a  mountain  stream,  or  the  whisperings  of  the  old  Pine. 
Sound  especially  appeals  to  the  intelligent,  and  the  greater  the 
intelligence  the  more  docs  it  appeal.  For  those  things  which  we 
see  are  not  the  more  pervaded  with  beauty  than  those  things 
which  we  hear.  And  Ellen  can  well  conceive  of  a  world  of 
harmony,  as  constant,  beautiful,  and  glorious  as  a  world 
of  light. 

''Motion  then  causes  collision,  from  which  results  vibration 
and  sound.  Docs  sound  make  vibration,  or  vibration  sound? 
They  are  certainly  intimately  connected ;  for  the  character  of 
sound  is  indicated  by  vibration.  Thus  the  sound  is  high  or 
low,  according  to  the  number  of  vibrations  each  second,  the 
high  sounds  being  accompanied  with  increased  frequency  of 
vibrations,  and  always  the  same  vibration  is  connected  with  the 
same  sound." 


WHISPERINiiS    OF  AN   OLD    PINE 


J9 


"And  what  is  vibration?"  I  asked. 

"  It  is   the  movement  of  a  body  to  and  fro,"  she  answered. 

"And  its  cause?*' 

*•  Must  be  the  movement  of  particles  within  the  body.     The 

text-books  say  it  is  a  motion  to  and  fro,  or  to  or  fro,  and  do 

>t  attempt  to  explain  its  ultimate  cause.     Its  immediate  causc» 

Ellen  has  said,   is  coHision,  and   any  collision  in   an  elastic 

body  causes  it." 

'*But  why  should  collision  cause  it?" 

**Thc  only  possible  explanation  that  Ellen  can  see  is  that 
collision  produces  or  arouses  into  action  a  substance  which 
makes  the  vibration.  And  apparently  this  substance  is  sound. 
The  collision  oi  inelastic  bodies,  as  cotton  or  wool,  docs  not 
produce  much  sound  or  vibration.  Mr.  Newton  ascribed  the 
action  of  electric  bodies  to  an  elastic  fluid. 

**  Ellen  thinks  that  all  motion,  caused  by  material  things 
comes  from  pressure.  That  all  pressure  oi  elastic  bodies 
cT^MCs  or  brings  into  action  motion ;  and  as  all  bodies  are 
somewhat  elastic,  all  pressure  either  makes  or  arouses  some 
motion. 

"Any  pressure  makes  motion  by  mnking  or  releasing, 
as  Ellen  thinks,  a  substance  having  unbalanced  motion. 
This    substance  enters  any  body  with  which  it  is  in   contact, 

bor  perhaps  is  created  in  the  body  pressed,  causing  it  to  move, 
or  carrying  it,  provided  there  is  carrying  power  enough 
created  to  do  this.  So  Ellen  thinks  that  all  motion  is  progres- 
sive; that  it  enters  into  a  thing,  into  each  part  or  par- 
ticle Of  molecule  of  a  body,  until  it  has  entered  into  all  the 
molecules,  when    the    body   moves.     But  the   body  docs   not 


'^^   -^^     -■ 


40  ELLEN   OR  THE 

move  until  motion  has  so  entered  into  all  the  molecules.  Thus, 
if  we  push  a  train  of  cars,  the  train  does  not  move  at  once,  but 
only  by  degrees,  as  the  motion  has  time  to  enter  it.  And  so 
when  a  bullet  is  fired  through  a  pane  of  glass,  it  cuts  a  round 
hole,  without  otherwise  breaking  the  glass,  because  it  goes 
through  too  quickly  to  allow  the  motion  to  spread  into  the 
glass.  So  Ellen  thinks  when  you  pull  a  wagon  or  anything  else, 
it  will  not  move  until  motion  has  had  time  to  enter  into  it, 
and  that  always,  however  caused,  the  principle  of  motion 
has  to  take  possession  of  a  body,  before  a  body  will  move. 
And  as  a  body  will  not  float  until  there  is  water  enough  to  float 
it,  so  Ellen  thinks  a  body  will  not  move  until  the  necessary 
amount  of  motion  to  move  it  has  entered  it;  and  that  the 
motion  is  just  as  much  material  as  the  water,  only  that  as  we 
approach  that  domain  where  matter  appears  as  force,  we  more 
nearly  approach  matter  in  its  essence,  where  motion  is  active 
because  unbalanced.  Thus,  as  Ellen  has  said  before,  dynamite 
or  any  explosive  is  composed  of  matter.  A  blow  disunites  it, 
and  a  great  amount  of  motion,  in  the  form  of  expanding  gas, 
is  released.  How  many  kinds  of  such  motion  there  may  be 
Ellen  does  not  know,  but  always,  as  Ellen  thinks,  motion  is 
moving  matter.  Gravitation  is  another  kind ;  and  Ellen  can 
well  see  that  there  may  be  many  different  kinds,  with  many 
rates  of  speed.  Indeed,  again  before  her,  as  everywhere  in 
nature,  she  beholds  another  road  leading  to  the  infinite." 

"But  what  does  Ellen  mean,"  I  asked,  "by  the  necessary 
amount  of  motion  to  move  a  body?  Would  not  the  slightest 
amount  of  unbalanced  motion,  added  to  a  body  at  rest, 
move  it?" 


WHISPERINGS   OF  AN  OLD   FINE 


41 


*' Ellen  meatit  enough  to  overcome  friction,  or  any  other 
ipposing  force  which  might  exist.  Could  v\e  imagine  a  body 
^t  rest,  where  no  such  opposing  force  could  act,  the  slightest 
unbalanced  force  added  would  cause  it  to  move/* 

"And  Ellen  thinks  all  unbalanced  forces  are  moving  matter?" 
••She  ha?  no  doubt  of  it;  and  therefore  if  a  body  does  not 
THove.  it  roust  be  because  the  motions  in  the  material  of  which 
it  is  composed  are  in  equilibrium.  Then  will  it  move  as  soon 
sks  enough  unbalanced  motion  enters  into  it,  and  in  the  direc- 
tion that  this  motion  tends/' 

"Hasn*t  Ellen  very  original  Ideas  about  motion?'* 
"  How  else  can  it  be  explained?"  she  asked, 
"The    old    Pine    supposed/'    I    said,    "that    motion    was    a 
"wnystery/' 

•*And  so  it  is  a  mystery/*  she  said;  '*all  things  arc  a  mys* 
tcry.  But  Ellen  doesn't  want  to  have  to  entertain  too  many 
mysteries;  nor  ts  there  necessity.  One  material  is  enough  for 
the  creation  of  things,  including  the  motion* 

••  For  motion  separated  from  matter  is  inconceivable.  But, 
if  not  separable,  it  is  a  part  of  matter,  and  hence  of  necessity 
enters  into  the  combinations  of  matter  Certainly  the  old  Pine 
supposes  that  matter  combines  with  other  matter  to  make 
things,  doesn't  he  ?  ** 

"WTiy,  yes/*  I  said;  *' the  old  Pine  doesn't  know  of  any 
other  way  in  which  things  are  made/* 

*•  And  there  is  no  other/'  she  said.  **And  thus  motion,  itself 
matter,  passes  through  matter,  as  a  stream  passes  through  the 
meadows,  or  a  ball  through  the  air,  or  an  elephant,  or  a  bird, 
or  a  cloud,  or  one  of  the  innumerable   things  which  we  call 


42  ELLEN   OR  THE 

small,  because  it  may  take  a  microscope  which  magnifies  one 
hundred  thousand  times  to  see  it.  This  thing  matter  in 
its  existence  is  infinite,  sustained  in  some  way,  as  Ellen  thinks^ 
and  has  said  before,  by  nature's  circulatory  methods,  in  which 
there  is  neither  beginning  nor  end.  Surely  the  old  Pine  doesn't 
think  there  is  any  end  to  a  circle?" 

"No,"  I  said,  "though  he  thinks  perhaps  there  may  have 
been,  at  some  time,  an  end  to  it,  just  as  there  are  ends  to  a 
hoop  before  it  is  welded." 

"  But  Ellen  doesn't  think  there  is  any  end  in  nature's  circu- 
latory methods.  Nor  does  she  see  how  it  would  be  possible 
for  the  creation  to  exist  without  such  methods.  But  these 
introduce  no  change  in  the  way  of  making  things.  Constantly 
matter  changes,  as  a  fluid  differs  from  a  solid,  and  such 
differences  continue  to  take  place  indefinitely,  as  Ellen 
thinks,  and  by  a  circulatory  method,  but  always  it  is 
the  same  matter,  and  always  the  law  of  its  use  is  combination 
in  different  proportions.  And  it  is  because  of  the  great  variety 
in  the  material  that  such  a  great  variety  of  things  can  be  made. 
And  so  we  have  solid  matter  and  fluid  matter,  gaseous  matter 
and  radiant  matter,  and  Ellen  knows  not  what  form  of 
matter  may  lie  beyond  these  in  either  direction.  This, 
then,  only,  we  see,  that  the  changes  of  matter  are  many,  but 
that  all  things  made  from  it  are  equally  substantial.  In  this 
respect  all  things  are  alike,  and  must  be.  Otherwise  some- 
thing would  have  to  become  nothing.  That  is,  matter  in  its 
changes  would  have  to  become  nothing.  Does  the  old  Pine 
think  that  a  snowflake  is  less  material,  and  in  that  sense  less 
substantial,  than  a  mountain?" 


WinsrERlNGS   OF  AN    OLD    I'lNt: 


43 


"No/*  I  said,  *'it  is  also  composed  of  matter.  But  it 
doesn't  weigh  as  much,  or  last  as  long." 

**But  It  can  float  through  the  air,"  she  replied,  "or  lodge 
on  Ellcn*3  hat,  to  much  better  advantage.  Mountains  wouldn't 
be  at  all  good  for  those  purposes.  Then  the  old  Pine 
mustn't  forget  that  everything  in  the  material  imiversc  is 
made  by  the  same  law.  And  there  are  lots  of  different  things. 
And  then  nature  has  such  a  tremendous  system  of  differences, 
that  no  two  things,  as  Ellen  thinks,  arc  ever  exactly  alike.  No 
two  persons,  no  two  snowflakcs,  no  two  sounds.  But  Ellen 
knows  that  all  things  come  from  nature's  great  laboratory,  and 
are  formed  by  the  changes  in  matter*  quality  and  quantity. 
We  will  suppose,  then,  that  that  kind  of  matter  which 
w*c  know  as  radiant  matter,  succeeds  gaseous  matter,  as  the 
latter  succeeds  liquid.  And  so  by  these  changes  of  matter,  in 
a  manner  purely  logical,  we  can  account  for  those  most 
remarkable  phenomena  of  nature.  —  sound,  light,  heat,  color, 
magnetism,  and  electricity. 

•'This  thing  motion,  then,  as  Ellen  thinks,  is  a  property 
or  phase  of  matter  And,  therefore,  whenever  motion  passes, 
a  substance  passes;  or,  wherever  there  is  motion,  there  is 
matter, 

**  Upon  this  subject  of  the  homogeneity  of  motion  and  matter, 
Ellen  has  recently  met  with  the  following  quotations : 


'  Force   is  inseparable  from  matter,  is  one  of  its  eternal  indwelling 
properties/ — MqUscHoIL 

*  Fundamentally,  as  is  readily  seen,  there  exists  neither  force  nor 
nuUtcr*     Both  are  abstractions  of  things,  such  as  they  are,  looked  at 


44  ELLEN  OR  THE 

from  different  standpoints.  They  complete  and  presuppose  each  other. 
Isolated,  they  are  meaningless/ — Dubois  Raymond. 

'  As  we  can  think  of  no  force  without  a  material  substratum,  so  we 
know  of  no  matter  which  is  not  connected  with  a  number  of  forces.' — 
F.  Mohr. 

*  Force  without  matter  is  not  a  reality,  and  both  by  their  union  have 
made  the  world  and  all  its  phenomena.* — P/i,  SpiUer. 

'  We  know  of  no  matter  which  does  not  possess  force,  and  on  the 
other  hand  we  know  of  no  forces  which  are  not  joined  to  matter.* — 
HaeckeL 

'To  regard  matter  as  passive,  and  to  suppose  a  force  working  on  it 
from  without,  is  so  grave  an  error  that  it  would  not  be  possible  to  fall 
into  it,  if  inborn  and  mystical  fancies  did  not  cloud  the  mind.  Matter 
and  force,  like  force  and  matter,  are  no  separable  entities,  but  different 
conditions  of  one  and  the  same  thing.* — F.  Vignoii, 

'  Matter  and  force  are  separable  only  in  thought ;  in  reality  they  arc 
one.* — A,  Mayer. 

'  We  must  hold  firmly  to  the  principle  that  matter  and  force  arc 
indivisibly  joined  together,  so  that  force  without  matter  has  no 
independent  existence.* — S.  Cornelius, 

'  It  is  apparent  that  all  attempts  to  isolate  forces  from  matter,  and 
vice  versa^  are  only  one-sided  abstractions,  depending  on  the  notion 
that  force  and  matter  may  be  found  in  Nature  as  distinct  entities^ 
because  in  speech  they  are  distinct  words.* — Weis. 

*The  first  and  last  word  of  Science  will  always  be  the  indivisible 
union  between  or  the  identity  of  force  and  matter.* — A.  Lefevre. 

"Dr.  Guyot,  the  eminent  scientist  and  philosopher,  is  thus 
quoted  in  the  London,  Edinburgh  and  Dublin  Philosophical 
Magazine,  Vol.  41 ; 


WHISPERINGS    UV 


.* Matter  has  only  one  property — namely,  movement.     Movement  can 

ftly  exhibit  itself  to  our  senses  and  to  our  spirit  of  induction  through 

matter  and  in  nutter.     .\nd,  reciprocally,  matter  iis  only  perceptible  to 

om  senses  and  comprehensible  to  our  minds  by  its  movements.     Move- 

Imcnt  is  inherent  in  and  essential  to  the  smallest  atoms,  as  well  as  to  the 
greatest  material  systems.  In  the  whole  universe  we  cannot  discover  a 
Rpgle  particle  of  matter  which  is  in  absolute  rest.  Matter  and  move- 
pBic  arc  two  creations  of  the  same  principle ;  they  are  consubstantial, 
lad  accordingly  proportional  tu  one  another. 

*The  first  notion  which  we  can  have  of  moliun  cannot  arise  from  the 
iDfinitely  small  molecules  of  bodies,  because  they  escape  the  impression- 
aiiy  of  our  senses.  They  reach  tis^  therefore,  from  the  change  of 
place  effected  under  our  eyes  by  bodies  themselves.  Hence  motion 
has  been  defined  as  the  motion  of  a  ifoJy  from  one  point  of  space  to 
another.  In  order  that  this  definition  might  be  exact,  it  would  t>c  nee- 
fjtaaxy  to  say  "  motion  is  the  passage  of  hodia  and  atoms  from  one 
point  of  space  to  another,"  because  a  particle,  a  molecule  which  we  can 
neither  see  nor  touch»  may  also  change  place  in  the  body  of  which  it 
forms  j>art,  an<l  such  is  clearly  a  motion  identical  in  principle  with  the 
tuotion  of  bodies.  The  difiference  oi  the  two  motions  is  only  relative; 
the  one  is  exterior  to>  the  other  is  interioj  in,  the  body.  Hut,  wonilei- 
fiil  to  relate,  observation  of  all  the  phenomena  of  nature  shove's  that  they 
lmnsfi)rm  themselves  the  one  into  the  other,  and  are  thus  mutually 
connected  and  complementary.  The  more  of  exterior  motion  a  body 
accomplishes^  the  leas  is  there  of  internal  motion,  and  inversely.  In 
ether  wordS|  the  same  quantity  of  matter  always  possesses  the  same 
imoitnt  of  motion. 

*Ttic   inertia  of  matter  is  therefore  an   error.     "What  does  it  sig- 

[ftify?"  say  the  learned  who  are  teore  mechanicians  than  philosophers; 

*if  the  hypothesis  of  inertia  permits  us  to  calculate  all  the  facts  of 

iibrium  of  motion  and  of  force  which  occur  on  the  surface  of  the 


46  ELLEN    OR   THE 

earth,  or  rather  in  our  physical  and  mechanical  operations,  that  is  all 
we  want.  Whether  an  hypothesis  be  true  or  false,  if  it  be  in  accord 
with  facts,  if  it  be  a  sure  guide  for  practical  questions,  we  call  it  true." 
*  I  grant  that  a  mechanic  or  practical  man  may  hold  such  language ; 
but  they  who  feel  the  importance  of  truth,  they  who  understand  that  its 
quest  is  the  most  beautiful  mission  of  the  human  mind,  and  that  its  dis- 
covery and  enunciation  infallibly  guide  humanity  in  the  path  of  moral 
and  material  progress,  such,  I  say,  will  never  admit  that  a  false  hypoth- 
esis can  have  the  same  value  as  a  true  one,  they  will  never  allow  that 
the  atmospheric  vacuum  is  as  well  explained  by  the  horror  of  nature  as 
by  the  weight  of  the  atmospheric  column ;  and  yet  these  two  explana- 
tions express  equally  well  the  same  fact.  Inertia  is  an  hypothesis  as 
little  refined  as  that  of  the  horror  of  a  vacuum ;  it  explains  nothing,  and 
stereotypes  error  in  face  of  the  most  brilliant  truths.  Does  inertia  ex- 
plain the  motion  of  the  heavenly  bodies?  Does  it  explain  the  motions 
of  animals?  No.  But  the  sidereal  systems  comprehend  all  known 
matter ;  and  animal  organizations  form  the  last  term  of  material  com- 
binations. Inertia  therefore  remains  impotent  in  regard  to  the  sponta- 
neous phenomena  of  the  one  or  the  other  kind ;  between  the  alpha  and 
omega  of  the  world  it  only  claims  a  puny  territory,  namely  the  relative 
movement  and  rest  of  bodies  in  equilibrium  amongst  themselves  in  a 
system  full  of  life.* 

**  Ellen  might  add  many  more  such  quotations,  but  these 
would  appear  to  show  that  Mind  naturally  recognizes  the  fact 
that  motion  and  matter  are  inseparably  united,  and  together 
form  force. 

"Motion  may  emanate  from  mind  or  matter.  But  as  Ellen 
has  before  said,  in  the  material  world  motion  is  only  continued, 
so  far  as  we  know,  through  contact.  That  is,  it  is  only  by 
being  pushed  or  pulled  that  one  material  thing  is  moved  by 


WHISPERINGS    OK   AX    OLD    TINE 

ainother.  Any  idea  of  attraction  must  resolve  itself  into  this. 
Thus  Mr.  Newton  held.*  And  among  recent  writers  it  is  well 
explained  by  Mr.  Lodge,  one  of  the  most  eminent  of  living 
physicists,  and  considered  to  be  perhaps  the  highest  authority 
in  electricity,  who  says : 

^  Now  if  there  is  one  thing  with  which  the   human  race   has   been 

Dre  conversant  from  time  immemorial  than  another,  and  ctjiicerning 
which  more  experience  has  been  unconsciously  accumulated  than 
about  almost  anything  else  that  can  be  mentioned,  it  is  the  action  of 
pnt  hoify  im  another ;  the  exertion  of  force  by  one  body  upon  another, 
the  transfer  of  motion  and  energy  from  one  body  to  another ;  any  kind 
of  effect,  DO  matter  what,  which  can  be  produced  in  one  body  by  means 
of  another,  whether  the  bodies  be  animate  or  inanimate.  The  action 
of  a  man  in  felling  a  tree,  in  thrusting  a  spear,  in  drawing  a  bow;  the 
action  of  the  baw  again  on  the  arrow,  of  powder  on  a  bullet,  of  a  horse 
cm  a  cart ;  and  again,  the  action  of  the  earth  on  the  moon,  or  of  a 
magnet  on  iron.  Every  activity  of  every  kind  that  we  are  conscious  of 
may  be  taken  as  an  illustration  of  the  action  of  one  body  on  another. 

*Now  I  wish  to  appeal  to  this  mass  of  experience,  and  to  ask,  is  not 
the  direct  action  of  one  body  on  another  across  empty  space,  and  with 
no  means  of  communication  whatever,  is  not  this  absolutely  unthink- 
&ble?  We  must  not  answer  the  question  off-hand,  but  must  give  it  due 
consideTation«  and  we  shall  find,  I  think,  that  wherever  one  body  acts 
on  another  by  obvious  contact,  we  are  satisfied  and  have  a  feeling  that 
the  phenomenon  is  simple  and  intelligible;  but  that  whenever  one 
body  apparently  acts  on  another  at  a  distance,  we  are  irresisliljly  im- 
paled to  lo;ik  for  the  connecting  medium. 

'If  a  marionette  dancea  in  obedience  to  a  prompting  hand  above  it^ 
lay  intelligent  child  would  feel  for  the  wire,  and  if  no  wire  or  anything 

Sec  iJAgt  90,  Vol.  L.  2il  etiiiiuri. 


48  ELLEN   OR  THE 

corresponding  to  it  was  discovered,  would  feel  that  there  was  some- 
thing uncanny  and  magical  about  the  whole  thing.  Ancient  attempts 
at  magic  were  indeed  attempts  to  obtain  results  without  the 
trouble  of  properly  causing  them,  to  build  palaces  by  rubbing  rings  or 
lanterns,  to  remove  mountains  by  a  wish  instead  of  with  the  spade  and 
pickaxe,  and  generally  to  act  on  bodies  without  any  real  means  of 
communication ;  and  modern  disbelief  in  magic  is  simply  a  statement 
of  the  conviction  of  mankind  that  all  attempts  in  this  direction  have 
turned  out  failures,  and  that  action  at  a  distance  is  impossible. 

*  If  a  man  explained  the  action  of  a  horse  or  a  cart  by  saying  that 
there  was  an  attraction  between  them  varying  as  some  high  direct 
power  of  the  distance,  he  would  not  be  saying  other  than  the  truth — 
the  facts  may  be  so  expressed — but  he  would  be  felt  to  be  giving  a 
wretchedly  lame  explanation,  and  any  one  who  simply  pointed  out  the 
traces  would  be  going  much  more  to  the  root  of  the  matter.  Similarly 
with  the  attraction  of  the  magnet  for  a  distant  magnetic  pole.  To 
say  that  there  is  an  attraction  as  the  inverse  cube  of  the  distance 
between  them  is  true,  but  it  is  not  the  whole  truth;  and  we  should  be 
obliged  to  any  one  who  will  point  out  the  traces,  for  traces  we  feel 
sure  there  are. 

'  If  any  one  tries  to  picture  clearly  to  himself  the  action  of  one  body 
on  another  without  any  medium  of  communication  whatever,  he  must 
fail.  A  medium  is  instinctively  looked  for  in  most  cases ;  and  if  not 
in  all,  as  in  falling  weights  or  magnetic  attraction,  it  is  only  because 
custom  has  made  us  stupidly  callous  to  the  real  nature  of  these  forces. 

'  Remember,  then,  that  whenever  we  see  a  thing  being  moved  we 
must  look  for  the  rope  :  it  may  be  visible  or  it  may  be  invisible, 
but  unless  a  thing  is  either  pushed  or  pulled  there  can  be  no  action. 
And  if  you  further  consider  a  pull  it  resolves  itself  into  a  push  ;  to  pull 
a  thing  toward  you,  you  have  to  put  your  finger  behind  it  and  push ; 


/ 


WHISPERINGS   OF  AN    OLD    PINE  49 

horse  is  said  to  pull  a  cart,  but  he  is  really  pushing  at  the  collar ; 
engine  pushes  a  truck  by  means  of  a  hook  and  eye ;  and  so  on. 

•There  is  still  the  further  very  important  and  difficult  question  as  to 
ymrlxy  the  parts  hang  together,  and  why  when  you  push  one  part  the  rest 
follows.  Cohesion  is  a  very  striking  fact^  and  an  explanation  of  it  is 
snuch  to  be  desired.    »    ♦     ♦ 

•  There  must  be  contact  between  bodies  before  they  can  directly  act 
oxi  each  other ;  and  if  they  are  not  in  contact  with  each  other  and 
yet  act,  they  must  both  be  in  contact  with  some  third  body  which  ii 
^He  medium  of  communication,  the  rope/ 


f 

/ 


so  ELLEN   OR   THE 


V. 


^^  A  ND  what  is  elasticity,  Ellen  ?  "  I  asked. 

-'^  **  The  word  is  used  technically,"  she  replied,  "  to  denote 
a  property  of  bodies;  that  of  resuming  their  original  form  or 
volume  when  the  force  altering  it  ceases  to  act." 

*'  And  does  it  not  mean  the  force  that  does  this?" 

*'It  is  often  used  to  mean  such  force,  and  Ellen  hardly  sees 
the  necessity  of  the  other  use,  but  as  the  former  use  has  long 
obtained,  and  as  the  words  clastic  force  are  frequently  used  for 
the  force  operating,  it  would  seem  to  be  best  to  make  the  dis- 
tinction general.  And  in  talking  with  the  old  Pine,  Ellen  will 
do  this." 

*'  And  do  not  the  scientists  always  use  the  word  with  the 
same  signification?" 

**Not  at  all,"  she  answered;  '*thcy  use  it  with  several 
significations." 

*' And  why  do  they  do  this?" 

**  Presumably  because  they  do  not  know  any  better.  As 
Ellen  thinks,  they  don't  know  half  of  the  time  what  they  are 
talking  about.  She  doesn't  think  the  ordinar>'  scientist  has 
any  exact  idea  about  this  thing  elasticity.  Nor  docs  she  think 
that  a  single  one  of  the  whole  of  them  has  any  intelligent  idea 
of  what  they  profess  to  believe  in  undulator>'  theories.  The 
trouble  with  them  is  that  there  are  so  many  of  them,  and  they 
are  so  ignorant." 

"And  are  they  all  ignorant?"  I  asked. 


"All  that  Ellen  has  yet  heard  from/*  she  replied,  ** though  of 
course  there  is  a  difference  in  degree. 

''Lord  Kelvin*  in  his  article  on  Elasticity  in  the  British  Ency- 
dopardta,  says : 

•  Elasticity  of  matter  is  that  property  in  virtue  of  which  a  l>ody  requires 
force  to  change  its  bulk  or  shape,  and  requires  a  continued  applica- 
tion of  the  force  to  maintain  the  change,  and  springs  bac^  when  the 
iotte  is  removed,  and,  if  left  at  rest  without  the  force,  does  not  remain 
at  rest  except  in  its  previous  bulk  and  shape.  The  elastli  ity  is  said  to 
be  perfect  when  the  body  always  requires  the  same  force  to  keep  it  at 
rest  in  the  same  bulk  and  shape  and  at  the  same  temperature  through 
whatever  variations  of  bulk,  shape,  and  temperature  it  be  brought.  A 
bcxly  is  said  to  possess  some  degree  of  elasticity  if  it  requires  any  force 
to  keep  it  in  any  particular  bulk  or  shape/ 

•*  Chambers*  Encyclopedia  says : 

'When  an  external  force  acts  wpon  a  solid  body,  it  produces  at  first 
i%ht  altentions  in  the  relative  positions  of  the  particles ;  and  if  before 
these  alterations  exceed  a  certain  limit,  the  force  ceases  to  act,  the  par- 
tic!e«  relwrn  to  their  former  position,  and  the  disfigurement  disap- 
ftears.  This  power  or  property  of  recovering  their  previous  form  after 
alteration,  is  called  elasticity,  and  we  are  justified  in  ascribing  it  to  all 
IxxlieSi  though  in  %*ery  different  degrees.  It  was  once  helieved  that 
there  were  definite  limits  within  which  changes  of  form  produced  by 
pressure  or  other  forces  disappeared  completely.  It  was  thought,  for 
instance,  that  when  a  weight  of  no  great  magnitude  is  suspended  from 
a  metallic  wire,  the  slight  increase  of  length  which  the  wire  is  observed 
to  undergo,  is  completely  lost  when  the  weight  is  removed  :  and  the 
limit  to  which  the  wire  might  thus  be  stretched,  and  still  suffer  no  per- 
manent increase  of  length,  was  called  the  limit  uf  its  elasticity.  But 
tecent  more  accurate  experiments  have  shown  that  no  such  limits  exist, 


54  ELLEN   OR  THE 

at  least  in  the  case  of  metals ;  or,  which  is  the  same  thing,  that  perma- 
nent lengthening  results,  however  slightly  the  wire  be  loaded — it  never 
contracts  again  quite  so  far  as  it  was  stretched.  It  is  necessary,  there- 
fore, to  fix  the  limit  arbitrarily ;  and  this  is  done  by  agreeing  that  it 
shall  be  heM  to  begin  when  the  metal  in  question  suffers  a  permanent 
elongation  of  0*00005  of  its  length.  To  get  the  elastic  extensibility  of 
a  wire,  then,  we  must  compare  its  length  with  a  weight  suspended,  with 
its  length  when  the  weight  is  removed.  In  this  way  it  is  found  that 
the  extensions  produced  are  proportional  to  the  extending  forces  or 
weights.  From  this  law,  then,  we  can  calculate  what  weight  it  would 
require  to  stretch  a  wire  or  rod  of  a  square  inch  in  section  to  double  its 
own  length ;  supposing  it  possible  to  proceed  so  far  without  breaking 
it,  and  that  the  law  of  elasticity  continued  up  to  this  point  unaltered. 
This  weight,  which  is  different  for  every  metal  or  kind  of  wood,  is  called 
the  coefficient  or  modulus  of  elasticity  of  the  particular  substance ;  and 
is  used  in  mechanics  in  calculating  how  far  a  given  weight  will  extend 
a  wire  or  rod  of  given  diameter.  This  coefficient  is  not  constant  for 
the  same  metal ;  for  all  circumstances  that  increase  the  density  of  the 
metal,  increase  the  modulus  of  elasticity.  Bodies  manifest  elasticity 
not  only  when  extended  in  length,  but  also  when  compressed,  when 
bent,  or  when  twisted.  If  an  ivory  ball  be  dropped  from  a  height  upon 
a  marble  slab  smeared  with  fat  and  lampblack,  when  caught  after  the 
rebound,  it  is  seen  to  have  touched  the  marble,  not  in  a  point,  but  in 
a  circle  of  several  lines  in  diameter ;  and  must  therefore  have  lost  for 
a  time  its  spherical  shape  over  that  extent.  In  the  same  way  the  mark 
of  a  well  hit  golf-ball  is  pretty  broadly  shown  upon  the  face  of  a  club 
after  the  stroke.  The  elasticity  shown  by  wires  and  threads  of  glass 
when  twisted,  has  been  turned  to  account  in  the  Torsion-balance, 
for  measuring  other  weak  forces.  Steel,  ivory,  caoutchouc,  etc.,  are 
well  known  for  their  elastic  properties,  to  which  they  owe  much  of 
their  utility.' 


<GS    UF   Af 


D  n.NE 


55 


"Ganot  says: 


Elasticity  is  the  property  owing  to  which  bodies  resume  their  original 
form  Of  volume,  when  the  force  which  altered  that  form  or  volume 
ceases  to  act.  Elasticity  may  be  developed  in  bodies  by  pressure,  by 
Iraction  or  /uJ/ift^,  flexion  or  hfuiiti*^^  and  by  torsion  or  twistif^g.  In 
lr«ktlug  of  the  general  properties  of  bodies,  the  elasticity  developed  by 
pressure  alone  re<]uires  consideration ;  the  other  kinds  of  elasticity, 
\K\ng  peculiar  to  solid  bodiesi  will  be  considered  amongst  their  specific 
properties. 

*  Gases  and  liquids  are  perfectly  elastic  ;  in  other  words,  after  under- 
ling a  change  in  volume  they  regain  exactly  their  original  volume 
when  the  pressure  becomes  what  it  originally  w^as.  Solid  bodies  present 
different  degrees  of  elasticity,  though  none  present  the  property  in  the 
same  perfection  as  liquids  and  gases,  and  in  all  it  varies  according  to 
Ihc  lime  during  which  the  body  has  been  exposed  to  pressure. 
Caoutchouc,  ivory,  glass,  and  marble  possess  considerable  elasticity  i 
had,  clay*  and  fats  scarcely  any. 

*  There  is  a  hmit  to  the  elasticity  of  solids,  beyond  w^hich  they  either 
break  or  are  incapable  of  regaining  their  original  form  and  volume. 
This  is  called  the  limit  of  elasticity ;  within  this  limit  all  substances  are 
perfectly  clastic.  In  sprains,  for  instai^ce,  the  elasticity  of  the  tendons 
has  been  exceeded.  In  gases  and  liquids,  on  the  contrary,  no  such 
Umtt  can  be  reached ;  they  always  regain  their  original  volume  when 
|}ie  original  pressure  is  restored.     •     *     • 

*  ElLAinicm'  OF  Traction'* — Elasticit)%  as  a  general  property  of  matter, 
has  been  already  mentioned,  but  simply  in  reference  to  the  elasticity 
devdbped  by  pressure  i  in  solids  it  may  also  be  called  into  play  by 
traction,  by  torsion,  and  by  flexure.  The  definitions  there  given 
ifquiie  some  extension.  In  ordinary  life  w^e  consider  those  bodies  as 
highly  clastic  which,  like  caoutchouc,  undergo  considerable  change  on 
the  application  of  only  a  small  force.     Yet  the  force  of  elasticity  is 


$6  ELLEN    OR  THE 

greatest  in  many  bodies,  such  as  iron,  which  do  not  seem  to  be  very 
clastic.  For  by  /orc^  of  elasticity  is  understood  the  force  with  which 
the  displaced  particles  tend  to  revert  to  their  original  position,  and 
which  force  is  equivalent  to  that  which  has  brought  about  the  change. 
Considered  from  this  point  of  view,  gases  have  the  least  force  of 
elasticity;  that  of  liquids  is  considerably  greater,  and  is,  indeed, 
greater  than  that  of  many  solids.  Thus  the  force  of  elasticity  of  mercury 
is  greater  than  that  of  caoutchouc,  glass,  wood,  and  stone.  It  is,  how- 
ever, less  than  that  of  the  other  metals,  with  the  exception  of  lead. 

'This  seems  discordant  with  ordinary  ideas  about  elasticity;  but  it 
must  be  remembered  that  those  bodies  which,  by  the  exertion  of  a 
small  force,  undergo  a  considerable  change,  generally  have  also  the 
property  of  undergoing  this  change  without  losing  the  property  of 
reverting  completely  to  their  original  state.  They  have  a  wide  limit 
of  elasticity.  Those  bodies  which  require  great  force  to  effect  a 
change  are  also,  for  the  most  part,  those  on  which  the  exertion  of  a 
force  produces  a  permanent  alteration ;  when  the  force  is  no  longer 
exerted,  they  do  not  completely  revert  to  their  original  state.  ♦     »     • 

*  By  experiments  it  has  been  ascertained  that  for  elasticity  of  traction 
or  pressure — 

^The  alteration  in  length  within  the  limits  of  elasticity  is  in  proportion 
to  the  length  and  to  the  load  acting  on  the  body^  and  is  inversely  as  the 
cross  section, 

*It  depends,  moreover,  on  the  specific  elasticity;  that  is,  on  a  special 
property  of  the  material  of  the  body.  If  this  coefficient  be  denoted 
by  E,  and  if  the  length,  cross  section,  and  load  be  respectively  desig- 
nated by  /,  s,  and  P,  then  for  the  alteration  in  length  e^  we  have 

IV 
s 

*  If  in  the  above  expression  the  sectional  area  be  a  square  millimetre, 

and  P  be  one  kilogramme,  then 

e 
e=Elf  from  which  E=™7~  * 


WHISPERINGS    OF  AN   OLD    PINE 


57 


which  expresses  by  what  fraction  the  length  of  a  bar  a  square  milli- 
metre in  section  is  altered  by  a  load  of  a  kilogramme.  This  is  called 
the  coefficient  of  elasticity ;  it  is  a  very  small  fraction,  and  it  is  therefore 

very  desirable  to  use  its  reciprocal,  that  is     —     or  ft,  as  the  modulus 

of  elasticity ;  or  the  weight  in  kilogrammes  which  applied  to  a  bar 
would  elongate  it  by  its  own  length,  assuming  it  to  be  perfectly  elastic. 
This  coefficient  is  known  as  Young's  modulus.  This  cannot  be 
observed,  for  no  body  is  perfectly  elastic,  but  it  may  be  calculated 
from  any  accurate  observations  by  means  of  the  above  formula. 

*  The  following  are  the  best  values  for  some  of  the  principal  sub- 
stances : 


\^ 

e 

Wrought-iron 

20,869 

0-000048 

Steel- iron 

18,809 

0*000053 

Platinum 

17,044 

0-000058 

Copper     . 

12,500 

0*000080 

Slate 

",035 

0-000090 

Zinc 

8,734 

0*000114 

Brass 

8,543 

o-ooo  I  I  7 

Crown  Glass 

7,917 

0-000126 

Plate  Glass 

7,015 

0-000142 

Rock  Salt 

4,230 

0-000236 

Marble      . 

2,309 

0-000382 

Lead 

1,803 

0*000555 

Bone 

1,635 

0-0006 1 2 

Acacia 

1,262 

0000792 

Pine 

1,113 

0-000890 

Oak 

921 

0*001085 

Whalebone 

700 

0-001428 

Ice 

650 

o-oi  1667 

Sandstone 

631 

0001521 

Fir 

564 

0-00  T  768 

Gypsum    . 

400 

0*002500 

58  V  ELLEN    OR   THE 

'Thus,  to  double  the  length  of  a  wrought-iron  wire  a  square  milli- 
metre in  section  would  (if  this  was  ix)ssible)  require  a  weight  of  about 
19,000  kilogrammes;  but  a  weight  of  fifteen  kilogrammes  produces  a 
permanent  alteration  in  length  of  13^ 4  th,  and  this  is  the  limit  of 
elasticity.  The  weight,  which  when  applied  to  a  body  of  unit  section 
just  brings  about  an  appreciable  permanent  change,  is  a  measure  of 
the  ///////  of  elasticity.  Whalebone  has  only  a  modulus  of  700,  and 
experiences  a  permanent  elongation  by  a  weight  of  five  kilogrammes ; 
its  limit  is,  therefore,  relatively  greater  than  that  of  iron.  Steel  has  a 
high  modulus,  along  with  a  wide  limit. 

'Longitudinal  stretching  is  accompanied  by  a  lateral  contraction,  and 
the  ratio  of  the  contraction  to  the  proportional  stretching  is  known  as 
PoissorCs  coefficient.  It  was  taken  by  him  to  be  one-fourth,  but  later 
experiments  have  found  the  ratio  to  be  about  one-third.  When  a  wire 
is  stretched  by  a  load  to  within  the  limit  of  elasticity,  some  time  often 
elapses  before  the  full  effect  is  produced,  and  conversely  when  the 
load  is  removed  the  wire  does  not  at  once  wholly  resume  its  original 
condition,  but  a  small  portion  of  the  deformation  remains,  and  it  only 
reverts  to  its  initial  state  after  the  lapse  of  some  time.  This  phenom- 
enon, which  is  met  with  in  most  elastic  changes  of  form,  is  called  the 
clastic  after-action  or  effect^  or  the  elastic  fatigue. 


*  Both  calculation  and  experiment  show  that  when  bodies  are  length- 
ened by  traction  their  volume  increases. 

'When  weights  are  i)Iaced  on  a  bar,  the  amount  by  which  it  is  short- 
ened, or  the  coefficient  of  contraction,  is  equal  to  the  elongation  which 
it  would  experience  if  the  same  weights  were  suspended  to  it,  and  is 
represented  by  the  above  numbers. 

*  The  influence  of  temperature  on  the  elasticity  of  iron,  copper,  and 
brass  was  investigated  by  Kohlrausch  and  Loomis.  They  found  that 
the  alteration  in   the  coefficient  of  elasticity  by  heat  is  the  same  as 


WHISPERINGS   OF   AN   OLD    PINE 


59 


^ich  heat  produces  in  the  coefficient  of  expansion  and  in  the 
s^ractlve  power ;  it  is  a]so  much  the  same  as  the  change  in  the  per- 
xnanent  magnetism^  and  in  the  speciiic  heat,  while  it  is  less  than  the 
^lt«ration  in  the  conductivity  for  electricity. 


'EiAsncnY  or  Torsiox, — The  laws  of  the  torsion  of  wires  were 
determined  by  Coulomb,  by  means  of  an  apparatus  called  the  torsion 
halan^r.  It  consists  essentially  of  a  vertical  metal  wire,  clamped  at 
the  upper  end  in  a  support,  and  holding  at  the  other  a  metal  sphere, 
to  which  is  atlixed  an  index.  I  mmediaiely  below  this  there  is  a  hori- 
xontal  graduated  circle.  If  the  needle  Is  turned  from  its  position  of 
equilibrium  through  a  certain  angle,  which  is  the  ang/t  of  torsion^  the 
force  necessary  to  produce  this  effect  is  the  force  if  /orston.  When, 
after  this  deflection,  the  sphere  is  left  to  itself,  the  reaction  of  torsion 
produces  its  effect,  the  wire  untwists  itself,  and  the  sphere  rotates 
about  its  vertical  axis  with  increasing  rapidity  until  it  reache:^  its 
position  of  et|uihbrium.  It  does  not,  however,  rest  there  ;  in  virtue  of 
ils  inertia  (force  of  action)  it  passes  this  position,  and  the  wire  under- 
goes $L  torsion  in  the  opposite  direction.  The  equilibrium  being  again 
destroyed,  the  wite  again  tends  to  untwist  itself,  the  same  alterations 
are  again  produced,  and  the  needle  does  not  rest  at  zero  of  the  scale 
until  after  a  certain  number  of  oscillations  about  this  point  have  been 
completed* 

•  By  means  of  this  apparatus  Coulomb  found  that  when  the  amplitude 
of  the  oscillations  is  within  certain  limits,  the  oscillations  are  subject  to 
the  following  laws ; 

•  L  The  osdilationt  are  very  nearly  isochronous. 

•  n.  For  the  same  wire^  the  angle  of  torsion  is  proportional  to  the 
moment  of  the  force  of  torsion, 

*UI.  With  the  same  forte  of  torsion^  ami  with  un res  of  the  same 
Mamiter^  the  angles  of  torsion  are  proportional  to  the  length  of  the 
mnes. 


6o 


EIXEX    OR   THE 


*  IV.  The  same /one  of  torsion  heing  applied  to  wires  of  the  same 
length,  the  angles  of  torsion  are  inversely  proportional  to  the  Jourtk 
powers  of  the  diameters. 

'Werlheim  examined  the  elasticity  of  torsion  in  the  case  of  sioui 
rods  by  means  of  a  diHerent  apparatus,  and  found  that  it  is  also  subject 
to  these  laws.  He  further  found  that,  all  dimensions  being  the  same, 
different  substances  undergo  diiTerent  degrees  of  torsion  for  the  same 
force^  and  each  substance  has  its  own  coefficient  of  torsion,  which  is 

usually  denoted  by   ---  or  by  r.    The  value  of  this  coefficient  is  about 

one- fifth  that  of  the  modulus  of  elasticity. 

1   F  / 
'  The  laws  of  torsion  mav  be  enunciated  in  the  formula  it'= — -        ;   in 

which  w  is  the  angle  of  torsion,  F  the  moment  of  the  force  of  torsion, 

/  the  length  of  the  wire,  r  its  radius,  and  ^—  the  specific  torsion-coeffi' 

cient. 

'  As  the  angle  of  torsion  is  inversely  proportional  to  the  fourth  power 
of  the  radius,  rods  of  some  thickness  require  very  great  force  to  pro- 
duce  even  small  twists.  With  very  small  iliameters,  such  as  those  of  a 
cocoon  or  glass  thread,  the  proportionality  l>etween  the  angle  of  torsion 
and  the  twisting  force  holds  even  for  several  complete  turns. 

*  EiASTicnT  OF  Flexure. — A  rod  or  thin  plate»  fixed  at  one  end,  after 
having  been  more  or  less  bent,  when  left  to  itself,  strives  to  return  to 
its  original  position.  This  property  is  known  as  the  elasticity  of 
tlexure,  and   is  very  distinct  in  steel,  caoutchouc,  wood,  and  paper. 

*  If  a  rectangular  bar  be  clamped  at  one  end  in  a  horirontal  position 
and  loaded  at  the  other  end  by  a  weight,  a  flexure  will  be  produced  which 
may  be  observed  by  the  cathetometer.     The  amount  of  this  Aexure,  A, 

is  represented  by  the  formula  A^  *^   — -  where  P  is  the  laad»  /  the 

bh  ^ 

length  of  the  bar,  d  its  breadth,  h  its  depth  or  thickness,  /a  the  modulus 


diii^ 


1 

■ 

THE  FEW.  YORK 
POBLIC  LIBRARY 

T]X.OIIH  fOU»4  0ATlOMi 
It                                k 

^H 

WHISPERINGS   OF  AN   OLD    PINE 


63 


rettstlcltV;  and  k  a  constant  which  depends  on  the  manner  in  which 
^c  rod  is  supported,  the  three  principal  cases  being  represented  in 
Sg.  2 ;  a  is  that  in  which  the  rod  is  supported  at  one  end ;  in  b  the 
wfl  rests  on  knife  edges,  with  both  ends  free ;  while  in  c  both  ends  are 
gill ;  if  one  and  the  same  bar  be  fastened  in  these  different  ways  the 
ilaes  of  \  are  respectively  as  64  :4  :i. 


*  If  the  section  of  the  bar  is  a  circle  with  radius  r,  then 


A-- 


4    Vf-^k 
3   ^O^' 


*  It  will  thus  be  seen  that  if  fur  a  given  load  the  depression  is  not  to 
greater  with  a  long  beam  than  with  a  short  one,  the  height  must 

bcrease  in  the  same  ratio  as  the  length. 

'  It  is  clear  that  an  accurate  measurement  ol  the  flexure  of  a  bar 
imishes  a  means  of  determining  its  modulus  of  elasticity » 

•The  elasticity  of  flexure  is  applied  in  a  vast  variety  of  instances — 
ejcample,  in  bows,  watch-springs,  carriage- springs ;  in  spring  bal- 
Dces  it  is  used  to  determine  weights,  in  dynamometers  to  determine 
be  force  of  agents  in  prime  movers ;  and,  as  a  property  of  wool,  hair, 
nd  feathers,  it  is  applied  to  domestic  uses  in  cushions  and  mattresses. 

*  Whatever  be  the  kind  of  elasticity,  there  is,  as  has  been  already 
lid,  a  limit  to  it  —  that  is,  there  is  a  molecular  displacement  beyond 
bbich  bodies  are  broken,  or  at  any  rate  do  not  regain  their  primitive 
&mL     This  limit  is  affected  by  various  causes*    The  elasticity  of  many 

metals  is  increased  by  hardening,  whether  by  cold,  by  means  of  the 
dr^w-plate,  by  rolling,  or  by  hammering.     Some  substances,  such  as 


64  ELLEN   OR  THE 

Steel,  cast  iron,  and  glass,  become  both  harder  and  more  elastic  bf 
tempering. 

'Elasticity,  on  the  other  hand,  is  diminished  by  annealings  which 
consists  in  rabing  the  body  to  a  temperature  lower  than  that  necessary 
for  tempering,  and  allowing  it  to  cool  slowly.  By  this  means  the 
elasticity  of  springs  may  be  regulated  at  pleasure.  Glass,  when  it  b 
heated,  undergoes  a  true  tempering  in  being  rapidly  cooled,  and  hence, 
in  order  to  lessen  the  fragility  of  glass  objects,  they  are  reheated  in  a 
furnace,  and  are  carefully  allowed  to  cool  slowly,  so  that  the  particles 
have  time  to  assume  their  most  stable  position.* " 

"And  what  is  the  reciprocal  of  a  number,  Ellen?"  I  asked. 
"It  IS  one  dfvidcd  by  the  number,  so  that  the  reciprocal 
of  a  fraction  expresses  the  number  of  times  that  the  frac- 
tion is  contained  in  unity.  The  modulus,  then,  of  elasticity 
represents  the  number  of  times  that  the  coefficient  of  elasticity 
is  contained  in  unity.  And  this  represents  the  number  of  kilo- 
grams of  weight  or  pressure  that  it  would  take  to  stretch  a 
body  of  uniform  cross  section  its  own  length.  The  old  Pine 
should  be  very  particular  to  remember  this,  as  it  enters  into  the 
present  explanation  of  Mr.  Newton's  formula  for  the  speed  of 
sound." 

"And  what  is  the  moment  of  the  force  of  torsion,  Ellen?" 
"It  is  the  power  producing  rotation  about  an  axis,  and  is 
measured  by  the  product  of  the  acting  force  into  the  lever  on 
which  it  acts.  Thus  the  weight  that  a  man  can  raise  with  a 
windlass  depends  upon  the  length  of  the  crank  or  lever  and  the 
power  which  is  applied. 

"We  have  a  force,  BP  (Fig.  3)." 

"  Yes,"  I  said,  "it  looks  like  a  very  nice  force." 


WlllSPERmOS  OF  AN    OLD    PINE  65 

''And  it  is  a  very*  nice  force,  an  awfiilK-  nice  force,     And  we 
iiavc  a  point,  A." 
*^V^es/*  I  said,  "it  luuks  pretty  lonesome^ — as  if  it  was  up 
tree/' 

•'But  it  isn't  up  a  tree;    it's  in  the  air.     Draw  AN  perpen- 

fltcttlar    to    B  P,     Connect    AB,AC\     The    product  of    the 

number  of  units  of  force  in  P  and  the  number  of         a 

units  o(  length  in  AN  is  called  the  moment  of  P 

i^th  respect  to  A.     Since  the  force  P  can  be 

represented  by  a  straight-hne,  the  moment  of  P 

Oan  be  represented  by  an  area.     If  B  C  represents  ^'S*  3- 

^he  force,  the  moment  will  be  represented  by  twice  the  area  of 

^die  triangle  ABC;    for  BCxAN  is  equal  to  twice  the  area  of 

Clic  triangle.     The  perpendicular  AN  is  sometimes  called  the 

<^rfn  of  the  force. 

••In  considering  the  speed  of  sound,  Ganot  says: 

*From  Uieoretical  considerations  Newton  gave  a  rule  for  calculating 
^lie  velocity  of  sound  in  gases,  which  may  be  represented  by  the 
formula 

in  which  v  represents  the  velocity  of  the  sound,  or  the   distance  it 
travels  in  a  second^  ^  the  elasticity  of  the  gas,  and  if  its  density. 

•*rhis  formula  expresses  that  the  velocity  of  the  propagation  of  sound 
in  leases  is  directly  as  the  square  roof  of  the  elasticity  0/  the  gas,  ami 
iaversefy  as  the  square  root  of  its  density,^ 


**The  words  Mr,  Newton  uses  in  above  formula  are  'elastic 
lorce/  and  that  is  the  meaning  of  Mr.  Ganot,  or  his  translator, 


66  ELLEN   OR  THE 

"And  so  the  article  on  Acoustics  by  Professor  Dav 
Thompson,  of  the  University  of  Aberdeen,  in  the  Encycl 
paedia  Britannica,  says: 

*  Hence,  denoting  the  ratio  which  any  increase  of  pressure  bears 
the  diminution  of  the  unit  of  volume  of  the  substance,  and  which 
termed  the   elasticity  of  the  substance,  by  ^,  we  shall  obtain  for  t 
velocity  of  a  wave  of  longitudinal  displacements,  supposed  small,  t 
equation : 

v^=yj£s  orz^=*/ — .* 

"In  this  use  of  the  word  'elasticity'  by  this  eminent  physici! 
the  modulus  of  elasticity  is  intended.     The  symbol  s  represen 
the  volume  of  the  unit  of  mass,  and  p  represents  the  mass 
the  unit  volume. 


WHISPERINGS    OF   AN    ULD    il.NL 


67 


VI, 


^^CLLEN    has    quoted    enough,    intelligently    studied,    to 
^*-'    tell  what  these  principles   are  which   connect  with  that 
j>ropcrty    of    bodies    called    elasticity.     And     she    has    also 
quoted    enough    to    show    that    the    scientists    in    their    text 
l^ooks    and   discourses    on    this    subject,    use   the    word    elas- 
^city     indiscriminately    to    denote    a     property,    force,    and 
ratio.     And,  so  far  as  Ellen  knows,  they  all  do  this.     This, 
-ml  course,  they  wouldn't  do  if  they  were  well  grounded  tn  the 
IcQOwledge  of  their  art,  and  good  nnechanics  in  the  use  of  lan- 
guage.    And  the   result   is   that  they  force  disbelief  in    their 
theories  and  throw  themselves  into   ridicule,  by  asserting  in 
one    place   that   the   same   bodies    are    highly  elastic,   and    in 
another  that  they  are  not.     Such  misstatements,  too,  provoke 
the  indignation  of  those  who  are  really  anxious  to  arrive  at 
truth.     And  it  becomes  most  evident  that  those  who  undertake 
to  teach  are  themselves  the  most  in  need  of  instruction, 

"  In  air  and  all  gases  there  is  a  principle  of  expansion,  the 
limits  of  which  we  do  not  know.  Its  force  is  increased  by 
compression,  and,  in  unconfined  air,  is  therefore  in  part,  at 
least,  the  result  of  gravitation.  Elastic  force  in  gases  is  a 
cause  of  expansion.  But  the  most  familiar  cause  of  expansion 
is  heat 

**Thc  old   Pine   will   see    that    Ellen    is   trying  to    explain 


68  ELLEN   OR  THE 

elastic  force,  something  that  the  text-books,  as  far  as  she 
knows,  have  never  attempted.  But  for  some  reason  a  thing  is 
elastic.  Certainly  it  is  not  so  because  of  no  reason.  That  is, 
there  is  some — and  a  well-defined — distinction  between  a  so- 
called  elastic  and  an  inelastic  body.  The  one  contains  a 
force  that  causes  its  molecules  to  return  to  their  original 
position  when  disturbed,  and  the  other  does  not,  although 
it  may  be  true  that  all  bodies  are  to  some  extent  elastic. 
The  difference,  then,  between  the  two  is  in  a  force.  And 
a  force  must  be  something,  for  it  is  incredible  to  suppose 
a  result — in  this  case,  the  re-adjustment  of  the  particles — 
obtained  from  nothing.  But  if  something,  then,  so  far  as  wc 
have  any  knowledge,  it  must  be  composed  of  matter,  for  there 
is  nothing  else  to  compose  it  of  in  the  material  universe.  And 
Ellen  thinks  we  would  have  knowledge  if  there  was;  that,  as 
she  has  said  before,  the  little  bit  of  the  universe  which 
we  see  is  an  epitome  of  the  whole,  and  that  in  this  epitome 
all  the  laws  are  at  work  which  govern  the  whole.  Hence, 
elastic  force  is  matter  in  motion.  There  is  no  other  possible 
explanation." 

*'  And  is  such  elastic  force  sound?"  I  asked. 

"Ellen  thinks  that  it  may  be,"  she  replied.  ** Certainly 
sound  makes  elastic  bodies  vibrate;  and  certainly,  too,  as 
Ellen  thinks,  elastic  force  like  sound  is  electrical.  Both,  too, 
are  matter  in  motion,  and  to  that  extent  similar.  But  sound, 
as  Ellen  will  show,  is  an  active  form  of  disturbance  as  long  sls 
it  remains  in  a  body,  the  body  returning  to  rest  only  when 
sound  has  left  it. 

"Sound    is    caused    by   shock,   and    the    least    shock    will 


WHISPERINGS    OF  AN   OLD    PINE  69 

cause  it.  That  is,  it  is  caused  by  contact,  and  contact  is 
always  the  result  of  motion.  But  Ellen  has  told  the  old 
Pine  that  motion  is  inherent  in  matter  and  therefore  eternal, 
eternal  as  matter;  from  which  it  follows  that  sound  is  con- 
stant as  matter,  always  existing,  though,  like  every  other  sub- 
stance made  of  matter,  always  perishing.  And  it  perishes  as 
an  apple  perishes,  or  a  pumpkin,  or  a  house.  For  it  is  made 
by  a  law  of  all  matter — combination ;  so  it  perishes  from  that 
other  great  law  governing  all  matter — disintegration,  when  it  is 
changed  into  something  else. 

**  And  so  the  old  Pine  can  see,  unless  he  is  awfully  blind,  that 
sounJ,  like  odor,  is  a  substance,  endowed  with  a  power  of 
motion,  and  dispersing  as  it  moves.  It  is  created  in  showers, 
flows  naturally  in  straight  lines,  and  spreads  in  all  directions 
where  there  are  channels  for  it  or  things  capable  of  conducting 
it.  Unlike  a  stream,  it  is  not  controlled  by  gravitation,  but 
ascends  as  well  as  descends.  Many  substances  will  transmit  it 
as  water,  metals,  wood,  or  any  elastic  substance ;  but  air  is  the 
most  common  medium  through  which  sound  is  made  manifest 
to  us.  By  it  sound  is  conducted  to  that  open  gate  of  the  ear, 
and  through  this  to  that  house  not  made  by  hands,  in  whose 
recesses  dwells  something  far  more  wonderful  than  sound — a 
soul  or  spirit. 

"And  this  spirit  learns  to  use  sounds  for  the  communication 
of  ideas.  Each  entity  of  sound  then  becomes  a  vessel  loaded 
with  ideas  or  parts  of  ideas.  And  when  all  the  parts  have  arrived 
they  are  put  together  as  a  house ;  and  so  ideas  are  introduced 
to  the  soul  and  where  there  are  many  of  them  they  are  like  a 
town  or  city.     And  they  are  all  brought  to  the  souK  or  the 


^0  ELLEN   OR  THE 

many  souls  which  live  in  these  houses  of  the  body,  by  the 
myriads  of  the  boats  of  sound,  which  are  always  plying  in  the 
ocean  of  the  air.  Surely  the  old  Pine  sees  with  the  mind's  eye 
the  millions  of  things  which  are  constantly  occurring  which  we 
cannot  see  with  the  physical  eye." 

"  Yes,"  I  said,  **the  old  Pine  sees.  But  the  air  is  not  the 
only  medium  that  transmits  sound?" 

**  Oh,  no,"  she  replied,  **  nor  can  the  vessels  of  sound  sail  as  fast 
over  or  through — for  Ellen  knows  not  which  it  is — the  particles 
of  air,  as  they  can  over  or  through  the  particles  of  many  other 
substances.  Thus  a  car  may  travel  on  a  road  six  to  ten  miles 
an  hour  and  on  a  rail  twenty  to  thirty  or  more.  And  sound 
passes  through  water  nearly  four  times  as  fast  as  through  air 
and  through  some  metals  much  faster;  and  so,  depend- 
in;^  on  the  nature  of  its  track,  its  speed  is  regulated.  And 
thus,  too,  if  the  car  comes  in  contact  with  these  media, 
sound  will  enter  it  more  readily  than  from  the  air,  reach 
the  auditory  nerve,  and  travel  along  it  until  it  comes  to 
the  soul.  For  the  nerves  of  sensation,  as  Ellen. thinks,  are 
very  similar  to  those  channels  or  rivers  which  pass  from  an 
ocean  up  into  a  country.  Nor  is  it  possible  that  they  can  be 
otherwise.  For  they  are  not  the  soul  or  spirit,  and  hence  of 
necessity  must  lead  to  the  soul  or  spirit." 

'*  And  Ellen  thinks  that  certain  of  them  are  channels  to  carry 
the  ships  loaded  with  sound,  odor,  flavor,  and  light?" 

"Yes,"  she  said;    "she  knows  that  they  are." 

"But  the  scientists  say  that  it  is  through  the  motion 
of  these  nerves,  or  matter  connected  with  them,  that  all  of 
these  things  are  communicated  to  the  soul." 


WHISPERINGS   OF  AN   OLD   PINE  7 1 

**  As  well  might  the  goods  of  a  ship  be  conveyed  inland  by 
leaving  them  at  the  mouth  of  a  river,  and  then  disturbing  its 
waters,"  she  replied.  **  The  old  Pine  knows  that  any  such  thing 
is  incredible.  Nor  is  it  possible  for  sound,  or  odor,  or  flavor, 
or  light,  to  reach  the  soul,  only  as  they  ascend  the  channels 
of  the  nerves  to  their  destination,  the  soul." 

"But,"  I  said,  "Ellen,  how  could  shock  make  sound?" 
"Surely  the  old  Pine  cannot  think  of  anything  better  to 
make  it,"  she  answered.  "And,  with  vibration  to  shape  and 
distribute  it,  it's  a  wonderfully  good  mill,  as  Ellen  thinks. 
And  so  is  a  cloud  for  making  and  distributing  rain.  Now  this 
thing  sound  must  come  to  the  intelligence  that  recognizes  it,  as 
everything  must  which  intelligence  recognizes.  Perhaps  the 
most  wonderful  of  all  things  is  light,  by  which  the  images  of 
things  are  brought  from  a  distance  to  the  observer  through 
the  eye,  and  he  is  thus  made  familiar  with  or  aware  of  their 
-existence.  The  moving  of  blocks  of  wood,  or  of  air,  or  any 
other  substance,  between  the  centre  of  sound  and  the  brain, 
would  not  and  could  not  produce  any  thing  but  change  of  posi- 
tion, which  is  not  sound.  A  stove  moved  is  still  a  stove.  And 
so  anything  moved  may  be,  and,  if  uninjured,  is  the  same  thing 
as  before.  Motion  alone  will  not  change  its  identity  nor  add 
to  its  capacities.  It  is  impossible,  then,  that  the  mere 
movement  of  anything  should  produce  in  that  thing  any 
phenomena  which  were  not  inherent  in  it.  Nor  could  it 
make  any  difference  how  far  it  was  moved,  or  how  fast. 
So  if  the  thing  sound  was  not  in  the  substances  moved. 
or  in  the  brain  whence  the  movement  went,  it  would  not  and 
could  not  take  place.     In  the  undulatory  theory  it  is  not  sup- 


^2  ELLEN   OR   THE 

posed  to  be  in  the  substances  moved ;   nor  does  any  one  sup- 
pose it  to  be  in  the  brain." 

"Except,  Ellen,  under  the  supposition  of  the  idealists, 
as  Kant  or  Bishop  Berkeley,  that  there  is  no  material  exist- 
ence, but  that  all  things  are  sensations,  and  exist  only  in 
the  mind." 

**But,"  she  said,  "the  professed  believers  in  undulatory 
theories  are  not  idealists,  but  realists  of  a  pronounced  type  in 
everything  which  they  can  see.  Here  they  are  neither  realists 
nor  idealists,  but  profess  a  mongrel  belief  in  a  cause  not  only 
insufficient,  but  demonstrated  by  the  attending  phenomena  to 
be  impossible."  ^ 

**But  the  old  Pine  supposed  this  theory  held  that  the  drum 
skin  of  the  ear  was  made  to  vibrate  by  aerial  waves  dashing 
upon  it.  That  this  vibration  was  carried  along  to  the  Corti 
fibres,  whose  vibration  set  going  a  nerve  stimulus,  which  went 
to  the  centre  of  hearing  in  the  brain  and  gave  rise  to  the  sensa- 
tion of  sound." 

"And  what  is  a  nerve  stimulus?"  she  asked. 

"The  old  Pine  doesn't  know." 

"  Nor  does  any  one  else,"  she  answered.  "  For  it  is  but 
'•Sound — signifying  nothing.' 
It  is  a  word  coined  by  scientists  to  cover  their  ignorance. 
The  old  Pine  is  both  too  honest  and  too  sensible  to  be  deceived 
by  it.  Instead  of  accepting  nature's  laws  as  we  know  them, 
scientists  think  they  can  improve  them  and  so  offer  others. 
And  this  they  do  whilst  teaching  that  nature's  laws  are 
fundamental  and  universal.  But  they  are  so  utterly  incom- 
petent, that,  without  the  slightest  hesitation,  they  will  proclaim 


THE  NFw  YOFfK 
j  ^l^Bi.lC  LIBRART 
i 

t 

--•-iN  i'Cu.NLAUCN> 


WrnsPERINGS   Ol'*  AX    Ulji    1*1NE 


/D 


principles  in  one  brcaili.  and  |^n  back  on  them  in  another. 
Thus  the  inost  important  of  nature's  laws» — that  by  which  she 
forms  each  separate  thing,  which  is  perfectly  understood,  and 
which  In  Rcientific  principles  must  be  fundamental  and  uni- 
versal,—scientists  ignore  at  the  ver>^  first  opportunity,  and 
substitute  therefor  their  own  vagaries.  From  this  utterly 
,,w.   -I.-,.,   jj.jjp   jj^i^,  ^^^  ^^j.]^   j^^g  g|g^  arisen  very  largely  the 

'Ti  -m  and   atheism  of  science;    or    rather,  perhaps,  the 

two  arise  from  tJie  same  cause, —  ignorance, 

**Thc  following  extracts  (rom  Biichner's  'Force  and  Matter/ 
tipon  Ihe  Universality  of  Naturc*s  Laws,  illustrate  the  present 
posttiofi  of  science  in  this  matter: 


*Thc  tinivcrsality  of  terrestrial  laws  is  above   all  doubt,  as  far  as 
icoce  is  concerned*'^/?!/  /V<f/, 

*  In  the  present  condition  of  our  knowledge  with  respect  to  the  worlds 

s^uiTotuidtng  our  earth,  we  can  declare  with  perfect  assurance  that  the 

^same  materials,  the  same  forces,  the  same  physical  laws,  with  which  we 

^jo  this  earth  find  ourselves  moulded  and  surfoundeil^  are  found  in  the 

.AU  which  is  visible  to  us,  and  that  they  are  at  work  in  all  places  in  the 

aame  fashion  and  with  the  same  inherent  necessity  as  in  our  immediate 

proximity.     Natural  philosophy  and  astronomy  have  furnished  us  with 

complete   proofs   of   this  in   sufficient  number ;   astronomical   science 

Indeed  could  not  exist  as  such,  if  the  universality  of  terrestrial  laws  were 

iKit  recognized 

*l^t  m  fir^i  tuiiijiucr  Gravitation,  that  universal  primal  and  funda- 
mental force  of  Nature,  by  which  are  regulated  the  movements  and  the 
gcfieral  mutual  effects  produced  by  all  bodies  in  the  imiverse  upon  each 
cither.  The  laws  by  which  these  movements  and  effects  take  place, 
wt  ioTarfable  in  all  the  realms  of  space  into  which  the  telescope  peers 


76 


ELLEN   Ok   THE 


and  which  are  reached  by  calculation.  The  movements  of  all,  even  ihe 
most  distant,  bodies  take  place  according  to  the  same  laws  by  which 
bodies  thrown  on  our  earth  move,  by  which  a  stone  falls,  a  cannon-ball 
flies,  or  a  pendulum  oscillates.  When  we  see  the  countless  atoms  of 
dust  dancing  in  our  room  in  the  light  of  the  sun  their  movement  is  gov- 
erned (as  Dii  Prel  remarks)  by  the  same  law  which  guides  the  move- 
ments of  the  stars  in  the  furthest  realms  of  space  to  which  our  eyes  can 
reach  by  aid  of  the  most  powerful  instrument  —  that  is,  by  the  law  ot 
gravity.  All  astronomical  calculations  respecting  the  most  distant 
planets  and  their  movements  have  been  ba^ed  on  this  known  law,  and 
they  have  proved  correct.  Everybody  knows  that  by  the  aid  of  this 
calculation,  astronomers  foretell  eclipses  of  the  sun  and  of  the  moon, 
transits  of  planets,  etc,  with  unfailing  certainty  as  to  the  day,  hour  and 
minute,  and  calculate  hundreds  of  years  in  advance  the  appearances 
and  re*appearances  of  comets,  those  well  known  knights- errant  of  space, 
having  for  their  orbits  now  an  ellipse,  now  a  parabola,  now  a  hyperbola ; 
and  they  do  so  despite  the  many  disturbances  anrl  irregularities  to  which 
the  movements  of  these  bodies  are  liable. 

'Astronomers  have  even  succeeded  by  calculations  based  wholly  on 
the  law  of  gravitation  or  rotation  in  determining  the  presence  of  stars 
which  were  only  discovered  by  the  telescope  when  it  was  known  in 
which  direction  they  were  to  be  looked  for.  Thus,  in  the  year  1S46, 
the  French  astronomer  Leverrier  came  on  the  track  of  Neptune,  until 
then  unseen  by  any  telescope,  in  directing  his  attention  to  the  disturb- 
ance shown  by  the  neighboring  planet  Uranus  in  its  orbit.  When,  in 
consequence  of  this,  Galle,  at  Berlinj  turned  his  telescope  towards  the 
specified  place,  he  found  the  planet  of  which  both  the  spot  and  the  mass 
had  been  already  determined.  Just  the  same  thing  has  happened  within 
the  last  few  years  in  the  case  of  the  intraraercurial  planet  Vulcan,  which 
has  not  yet  been  seen  with  complete  certainty,  but  tlie  existence  of 
which  is  scientifically  proved.     But  that  which,  more  than  everything 


WHISPERINGS   OF  AN   OLD    PINE  // 

else,  proves  that  the  laws  of  gravitation  or  attraction  exist  in  the  remot- 
est regions  of  fixed  stars,  which  are  separated  from  us  by  many  billions 
of  miles,  just  the  same  as  these  laws  are  in  force  in  our  solar  system  or 
on  our  earth,  is  the  study  of  the  remarkable  double  stars,  which  have 
become  better  known  only  of  late  years.  These  are  situated  so  close 
together  that  they  can  only  be  distinguished  from  each  other  by  means 
of  the  most  powerful  instruments,  and  revolving  around  each  other. 
In  their  singular  movements  they  obey  the  law  of  gravity,  as  do  the 
planets  of  our  solar  system.  Thus,  the  presence  of  a  second  body  near 
the  splendid  fixed  star  Sirius  (a  in  Cam's  Ma/or)  now  known  to  be  a 
double  star,  was  deduced  from  its  peculiar  movements  on  the  basis  of 
the  law  of  gravitation,  twenty  years  before  Clark  discovered  the  star 
itself  at  Boston,  on  Jan.  31,  1862.  It  had  revealed  its  existence,  thanks 
to  our  conviction  of  the  universal  force  of  gravitation,  before  ever  a 
human  eye  had  gazed  upon  it.  "  If  any>vhere,"  said  the  astronomer 
M.  W.  Mayer,  "  we  have  in  this  discovery  the  most  conclusive  argument 
in  favor  of  the  universality  of  attraction  between  masses  in  the  universe.'* 
Indeed,  the  existence  of  these  remarkable  double  stars  shows  that  while 
in  the  fathomless  depths  of  space  the  creative  force  of  Nature  seems  to 
love  to  reveal  itself  in  very  much  the  same  variety  as  here  on  our  earth, 
yet  it  never,  nor  in  any  place,  follows  any  laws  unknown  to  us,  or  others 
than  those  to  which  it  would  have  entrusted  the  building-up  and  the 
governance  of  the  world.  On  the  contrary,  all  these  mar\ellous  worlds 
have  been  evolved  according  to  the  same  simple  laws  as  those  which 
built  and  rule  our  little  earth. 

'  Astronomers,  confidently  relying  on  the  laws  of  gravitation,  do  not 
hesitate  to  authoritatively  lay  down  the  existence  of  dark  or  to  our  eyes 
imperceptible  satellites  of  some  of  the  fixed  stars,  e.  g.  Procyon,  as  the 
consequence  of  their  peculiar  movements. 

.  'It  may  also  be  remarked  that  the  physical  condition  of  all  the 
planets  whose  proximity  to  our  globe  renders  possible  a  sufiicientljr 


78  ELLEN   OR  THE 

exact  determination  of  their  surfaces,  is  similar  or  analogous  to  that  of 
our  earth.  Venus  has  high  mountains ;  Mars  has  continents  and  seas, 
summer  and  winter.  The  moon  has  mountains,  plains,  valleys  and  vol- 
canoes like  the  earth.  All  the  planets  of  our  system  have  seasons, 
days  and  nights  as  we  have,  although  their  relative  lengths  vary. 
Besides,  they  are  all  spherical  in  shape,  like  the  earth ;  i.  €,  they  bulge 
out  at  the  equator  and  are  flattened  at  the  poles ;  like  the  earth,  they 
are  more  or  less  inclined  on  their  axes  and  have  the  double  motion  of 
rotation  and  translation ;  all  these  are  signs  of  a  similar  origin.  Hence 
the  genesis  of  our  globe  yields  us  a  sure  analogy  for  the  history  of  the 
origin  and  evolution  of  the  other  planets. 

'The  laws  of  light,  no  less  than  those  of  gravitation,  are  the  same 
throughout  the  universe  and  the  same  as  on  our  earth.  Light,  whether 
solar  or  artificial,  has  throughout  the  same  composition  and  the  same 
velocity,  and  its  refraction  takes  place  everywhere  in  the  same  way. 
The  light  sent  to  us  by  the  most  distant  fixed  stars  through  a  space  of 
many  billions  of  miles,  is  distinguishable  in  nothing  from  the  light  of  our 
sim ;  it  follows  the  same  laws  and  is  of  the  same  composition.  So  little 
doubt  is  there  among  learned  men  on  this  head  that  the  different  color- 
ing of  the  light  proceeding  from  fixed  stars  enables  them  to  decide  with 
absolute  certainty,  on  the  one  hand  as  to  the  temperature,  condition 
and  stage  of  development  of  these  stars,  on  the  other  as  to  their  indi- 
vidual and  relative  movements  in  space.  Thus  we  are  likewise  in  a 
position  to  determine  according  to  terrestrial  processes  the  areas  of  the 
umbrae  and  penumbrae  arising  from  solar  and  lunar  eclipses.  Even  the 
ring  of  the  planet  Saturn  throws  a  shadow  on  it  and  receives  in  its  turn 
a  shadow  from  the  planet.  Lastly,  the  photographs  taken  of  individual 
fixed  stars  prove  that  the  light  emitted  by  them  contains,  like  sunlight, 
chemically  active  as  well  as  luminous  rays.  The  same  remark  applies 
to  the  heating  rays,  as  has  been  shown  by  very  delicate  instru- 
ments. 


WHISPERINGS    0¥   AN    OLD    PINE  79 

•  Like  the  laws  of  light,  the  laws  of  heat  are  the  same  throughout  the 
universe,  heat  being  the  commonest  and  most  widely  distributed  form  of 
energy  known  to  us,  and  being  at  this  day  universally  regarded  as  merely 
another  form  of  light.  The  heat  coming  to  us  from  the  sun  or  from 
the  other  fixed  stars  works  exactly  according  to  the  same  principles  as 
the  rays  of  heat  do  which  are  emitted  by  our  earth  or  by  the  hot-springs 
found  therein.  On  caloric  circumstances  depend  the  solidity,  the 
fluidity,  the  gaseous  condition  of  bodies;  therefore  these  conditions 
must  exist  everywhere  upon  similar  terms,  so  to  speak.  It  has  been 
shown  in  a  preceding  chapter  that  the  other  forces  of  nature,  such  as 
electricity,  magnetism,  mechanical  power,  chemical  affinity,  etc.,  are  so 
closely  bound  up  with  caloric  circumstances  and  stand  to  these  in  such 
intimate  relationship,  based  upon  reciprocal  interchange,  that  they  can- 
not be  separated  from  one  another;  therefore  must  all  these  forces 
exist  where  warmth  exists,  that  is  to  say,  everywhere.  This  is  espe- 
cially true  of  the  relation  of  heat  to  the  form  and  manner  of  chemical 
combination  and  dissociation,  which  must  necessarily  proceed  through- 
out the  universe  in  a  uniform  manner,  since  the  experiments  carried  on 
by  the  help  of  spectral  analysis  have  proved  to  demonstration  the  uni- 
versal distribution  of  chemical  elements  identical  with  those  existing  on 
our  earth.  But  long  before  this  most  recent  and  interesting  method  of 
investigation  had  become  known,  the  same  conclusion  had  been  arrived 
at  by  the  study  of  those  visible  and  tangible  messengers  from  another, 
non-terrestrial  world,  which  we  designate  as  meteorites  or  meteoric 
stones.  Chemistry  has  not  been  able  to  discover  a  single  element  not 
present  in  our  world  in  these  remarkable  bodies,  the  cosmic  origin  of 
which  was  for  centuries  regarded  as  a  preposterous  myth,  while  people 
on  the  other  hand  believed  firmly  and  steadfastly  in  downright  impos- 
sible things  and  events.  These  bodies  are  hurled  to  us  from  other 
worlds  or  from  the  primal  ether,  in  all  probability  from  the  very  depths 
of  the  space  pertaining  to  the  fixed  stars,  possibly  as  pieces  or  remnants 


So  ELLEN    OR  THE 

of  shattered  planets  or  dissolved  comets.  Among  the  twenty-one  ele- 
ments or  chemical  groups  found  in  these  bodies  up  to  the  present  time, 
there  is  not  a  single  one  alien  to  those  of  our  own  globe,  and  the  sub- 
stances predominant  in  them,  such  as  iron,  silicon,  oxygen,  are  the 
very  ones  which  also  predominate  on  the  surface  of  the  earth.  Daubr^e 
has  also  discovered  that  the  similarity  that  exists  between  these  meteor- 
ites and  the  terrestrial  minerals  increases  in  proportion  as  we  penetrate 
more  deeply  into  the  crust  of  the  earth,  and  that  several  of  the  minerals 
found  at  the  greatest  depths  (such  as  olivine,  herzolite,  serpentine,) 
are  in  composition  and  condition  almost  identical  with  the  meteorites ; 
and  lastly,  that  in  closer  proximity  to  the  surface  of  the  earth  minerals 
are  found  which  are  formed  of  constituents  similar  to  those  of  the 
meteorites,  but  oxidized  (united  with  oxygen,)  and  thereby  having  their 
mineral  character  changed.  Daubr^e  further  succeeded  in  artificially 
obtaining  from  terrestrial  stones  substances  closely  resembling  meteor- 
ites. The  investigation  of  meteorites  has  shown  moreover  that  the 
crystals  distributed  throughout  their  internal  structure  are  formed 
according  to  the  very  laws  of  crystallization  which  we  recognize  in  ter- 
restrial crystals,  and  that  their  forms  in  no  wise  differ  from  those  known 
to  us.  Even  the  microscope,  as  Moldenhauer  remarks,  (Das  Weltall 
und  seine  Entwicklung,  I,  p.  7),  has  not  failed  to  render  aid  in  this 
direction.  "It  appears  in  the  structure  of  the  meteorites,  those  little 
bodies  that  fall  upon  us  from  far-off  unknown  regions,  that  the  internal 
construction  of  alien  inorganic  masses  is  essentially  identical  with  that 
of  our  own." 

'These  facts  alone  would  be  sufficient  to  prove  that  —  in  the  words 
of  Professor  Spiller  —  "the  unity  of  the  forces  of  Nature  extends  to  the 
very  atoms  of  matter,'*  and  that  "  the  formative  force  for  each  material 
and  for  each  atom  of  matter  is  the  same  in  the  whole  universe."  But 
that  which  was  only  raised  to  high  probability  by  the  investigation  of 
meteorites,  has  been  made  almost  into  a  certainty  by  spectral  analysis^ 


WHISPERINGS   OF  AN   OLD    PINE  gj 

that  ''language  of  light''  as  it  has  been  rightly  termed,  the  glance  of 
which  pierces  through  the  chemical  constitution  of  the  most  distant 
stars.  Above  all  things  it  has  taught  us  that  the  mass  of  the  sun  — and 
indeed  nothing  else  could  be  expected  from  the  fact  of  all  the  members 
of  the  solar  system  deriving  their  origin  from  the  same  primal  mist  — 
contains  no  other  chemical  elements  in  its  ardent  or  incandescent 
integument  than  those  which  exist  in  our  earth.  These  elements,  as 
everyone  knows,  are  sodium,  iron,  calcium,  magnesium,  chromium, 
nickel,  barium,  zinc,  cobalt,  manganese,  titanium,  aluminium,  stron- 
tium, lead,  copper,  cadmium,  cerium,  uranium,  potassium,  vanadium, 
palladium,  molybdenum,  hydrogen,  oxygen,  nitrogen.  There  is  still 
some  doubt  about  the  presence  of  a  number  of  other  known  elements, 
such  as  indium,  lithium,  rubidium,  caesium,  bismuth,  tin,  silver,  beryl- 
lium, lanthanum,  yttrium,  iridium,  silicon,  sulphur,  carbon,  etc.  Prob- 
ably all  the  metalloids  (non-metals)  are  to  be  found  in  them ;  other 
heavy  metals,  such  as  gold,  silver  and  mercury,  may  be  present  in  the 
deeper  parts  of  the  sun  or  of  its  envelope,  inaccessible  to  spectral 
analysis.  The  chemical  composition  of  the  solar  envelope  offers  gen- 
erally the  greatest  resemblance  to,  or  analogy  with,  the  chemical  con- 
stitution of  meteoric  stones.* 

*  Of  course,  astronomers  have  not  contented  themselves  with  merely 
using  the  spectroscope  —  which  is  able  to  yield  such  positive  data  on 

*  It  must  not  be  forgotten  that  one  material,  or  one  substance,  has  been  discovered 
in  the  solar  spectrum  that  corresponds  with  no  terrestrial  one,  and  which  has  there- 
fore been  named  helium.  But  according  to  the  distmguished  spectroscopist  Norman 
Lockyer,  helium  is  apparently  nothing  more  than  a  modified  form  of  hydrogen ;  and 
besides,  Professor  Palmieri  of  Naples  states  that  he  has  lately  discovered  the  helium 
line  in  the  spectrum  of  the  lava  of  Vesuvius.  In  point  of  fact  it  is  very  possible  that 
an  element,  the  presence  of  which  has  not  yet  been  discovered  on  the  earth,  may 
play  an  important  part  elsewhere,  and  on  the  other  hand  an  element  predominant 
with  us  may  only  be  present  to  a  slight  extent  in  the  composition  of  other  stars.  The 
general  identity  or  unity  of  materials  is  therefore  open  to  no  doubt  whatever. 


:$2  :  '  ELUSN  OR  THE 

]the  chemical  composition  of  the  most  distant  bodies -«- to  investigate 
•the  sun,  but,  despite  the  great  difficulties  involved,  it  has  been  turned 
alsalo  account  in  the  study  of  the  planets,  comets,  fixed  stars,  nebulae, 
falling  stars,  etc.  The  result  has  been  materially  the  same  throughout. 
These  enquiries  have  proved  the  truth  of  the  theory  propagated  by 
earlier  astronomers,  viz.,  that  the  so-called  fixed  stars  are  nothing  but 
actual  suns,  in  the  atmospheres  or  luminous  envelopes  of  which  are 
found  again  in  an  incandescent  condition  those  known  bodies,  some  of 
which  have  already  been  mentioned,  like  iron,  calcium,  sodium,  mag- 
nesium, tellurium,  antimony,  bismuth,  mercury,  hydrogen,  nitrogen,  etc. 
Hydrogen  appears  to  play  the  chief  part  in  most  of  the  fixed  stars,  and 
to  cause  the  same  violent  eruptions  and  whirlwinds  in  them  as  it  does 
in  the  sun.  If  all  the  substances  found  in  the  sun  have  not  yet  been 
shown  to  exist  in  the  fixed  stars,  this  probably  results  from  the  faintness 
of  the  spectra,  arising  from  the  immensity  of  the  distances.  The  same 
remark  applies  to  the  yet  more  distant  nebulae  or  to  those  glowing 
masses  of  gas  which  astronomers  regard  as  systems  of  worlds  in 
course  of  evolution,  and  the  spectra  of  which  denote  principally  hydro- 
gen and  nitrogen.  The  comets  have  also  been  analyzed  by  means  of 
the  spectroscope,  notwithstanding  the  dimness  of  their  light  which  ren- 
ders accurate  observation  very  difficult,  and  carbon  and  hydrogen  have 
been  discovered  in  them.  Kven  falling  stars  have  been  submitted  to 
the  same  analysis,  and  it  is  claimed  that  carbon,  as  well  as  glowing 
vapors  of  sodium  and  magnesium,  have  been  discovered  in  them.  It 
need  hardly  be  mentioned  that  the  light  of  the  planet,  being  borrowed 
from  the  sun,  must  show  the  same  composition  as  that  of  the  sun  itself. 
'These  discoveries  form  landmarks  in  the  history  of  science  and  are 
worthy  of  being  placed  side  by  side  with  the  greatest  discoveries  of  all 
ages.  They  prove  that  matter  is  essentially  identical  not  only  within 
our  solar  system,  but  in  the  whole  universe,  down  to  the  regions  of  fixed 
stars  and  nebulae.     Now  seeing  that  identity  of  substances  must  neces- 


VVIIISPERINGS   OF  AN   OLD    PINE 


8J 


Msmly  imply  identity  of  forces,  and  that  **  the  sperial  form  in  which  a 

s^ubstaoce  ptoUuces  its  regular  effect  is  the  direct  outcome  of  its  chem- 

LJkral  condition''  (Dti  Prel,)  no  doubt  can  remain  as  to  the  similarity  of 

L  msiaterials  and  forces  throughout  the  universe  and  as  to  the  similarity  of 

I -development  in  our  solar  system  and  in  the  most  distant  heaven  of  the 

:Axed  stars  —  a  view  which  is  now  thoroughly  accepted  by  all  scientists 

.^wfho  have  conccntiated  their  attention  on  the  study  of  this  question. 

1  I*rofcsiSor  Kirchoff  himself,  the  famous  discoverer  of  spectral  analysis, 

1-vas  stated  his  conviction  "  that  the  substances  and  forces  in  the  whole 

mxniverse  are  essentially  the  same.** 

•AU  these  facts  and  observations — with  those  already  given  at  the 

l>cgmiung  of  the  chapter — prove  to  demonstration  the  universality  of 

^r^atural   laws,  a  phrase  which  is  indeed  but  another  expression  for  the 

xcgular  working  of  matter  and  of  its  forces,  arising  from  its  chemical 

mjiil  phy&ical  nature,  and  these  laws  cannot  therefore  be  confined  to  our 

^obe,  but  most  act  in  a  similar  fashion  throughout  the  entire  universe. 

•       •      •      The  visible  universe  surrounding  us  is  an  infinite  whole» 

composed  of  the  same  substances,  borne  by  the  same  energies,  swayed 

\yy  the  same  immutable  natural  laws. 

'Oerstedl  rightly  maintained,  in  treating  of  the  identity  of  mental  and 

phvsjral  laws,  that  this  universal  application  of  the  law^s  of  Nature  which 

are  conceived  by  reason,  presupposes  also  a  fundamental  equality  of  the 

conceptive  faculty  of  the  intellect  throughout  the  universe.     Should 

reasoning  beings  exist  otjtside  of   our  planet — and   this  is  probable 

enough,  since  it  is  difficult  to  see  why  the  same  or  similar  causes  should 

not,  under  the  same  or  similar  conditions,  produce  the  same  or  similar 

results  everywhere  —  their  thinking  power  must  necessarily  be  the  same 

aSy  or  similar  to,  ours,  although  in  degree  or  development  it  may  vary 

to  almost  any  extent.    The  principles  of  the  physical  development  of 

maD  are  also  likely  to  be  on  the  whole  identical.     So  great,  however,  is 

tbe  diversity  of  the  individual  worlds  in   point  of  mass,  temperature, 


■*^>^    -"^ 


84  ELLEN    OR  THE 

density,  illumination,  physical  condition  of  the  surface,  etc.,  and  so  far 
do  the  phases  of  development  diverge  from  each  other  in  the  individual 
stars,  that  we  have  a  perfect  right  to  assume  also  the  possibility  of  an 
endless  diversity  in  the  respective  organization  of  the  inhabitants  of 
each  individual  world.  *  *  *  One  thing  only,  as  we  have  said 
Ulready,  can  be  stated  with  comparative  certainty,  and  it  is  that  the 
identity  of  cosmical  substances  and  laws  admits  of  the  inference  that 
the  fundamental  principles  of  physical  and  mental  phenomena,  of 
organic  and  inorganic  life,  must  be  the  same  ever3rwhere. 

*"In  the  life  of  the  mind,"  says  Ph.  Spiller  (Die  Urkraft  des  Welt- 
alls,  1876,)  "there  must  eventually  be  some  features  of  absolute  unity, 
despite  the  diversity  that  may  exist  in  its  organization.  The  laws  of 
thinking  are  no  doubt  the  same  throughout  the  universe."  ' 


THE  NEW  YCRK 
PUBLIC  LIBRAHY 


'-  N  f :  ^  .s ..  s , . .  > 


WmsPERlNUS    OF   AN    OLD    TINE 


87 


VIL 


r^'T'HIS    undulatory    theory    of     sound    is    wrong,   because, 
*       first,   it  IS   unscientific,  being    based   on   wrong    pria- 
second,   the  system   of  waves    w^hich   it  contemplates 
Id   not  possibly  exist;     third,  such   a  system,   if  existing, 
Duld  not  bend  tlie  ear  drum  in  and  out;   and  fourth,  a  mere 
lechanical  pressure  on  the  tympanum  of  the  ear  could  not  pro- 
luce  the  phenomena  of  sound. 
•^For,  as  Ellen  has  pointed  out,  the  universal  law  of  nature 
creation   is   by  the  combination  of   elements  or  substances. 
There  is  no  other,  and  any  suggestion  of  it  comes  only  from 
ery  incompetent  thinkers,  and  is  upon  its  face  incorrect. 
'*  Ellen  will  show  that  its  system  of  waves  cannot  exist. 
•*  It  would  be  impossible  for  such  a  system  of  waves,  if  exist- 
ig,  to  exert  the  mechanical  force  which  they  arc  supposed  to 
jlcrform,  anil  must  perform  if  the  theory  is  true*     For,  omitting 
Jie  other  mechanical  operations  that  enter  into  the  problemp 
car-drums  are  a  substantial  quantity  and   require    a  definite 
amount  of  energy  to  bend  them  once  in  and  once  out.     Nor  is 
Htiits  any  negligible  amount  even  lor  a   single  ear-drum.     But 
^BLlfae  same  sound,  and  that  not  a  loud  one,  is  heard   by  many 
^HBlssands  through  this  movement  of   ear-drums,  it   is  evident 
|biat  it  will  require  a  very  large  amount  of  mechanical  energy 
to  fulfil  the  necessities  of  this  theory — an  amount  that  many 
^■inimals  such  as  insects  or  birds  could  no  more  exert  than  they 
could  remove  mountains.     Thus  the  Katy-did  or  Whip-poor- 


88  ELLEN   OR  THE 

will  can  be  heard  over  a  space  where  many  thousands  of  people 
could  be  placed,  who  would  all  hear  the  sound  if  present,  the 
aggregate  weight  of  whose  ear-drums  might  reach  the  sum  of 
hundreds  or  thousands  of  pounds,  for  every  ear-drum  weighs 
half  a  grain,  more  or  less.  So  that  our  pretty  Whip-poor-will, 
while  he  is  singing,  must  exert  a  force  to  move  such  an  amount 
hundreds  of  times  each  second,  if  this  theory  was  true.  But 
the  old  Pine  and  Ellen  both  know  that,  though  a  fine  musician, 
the  Whip-poor-will  cannot  exert  any  such  amount  of  physical 
energy.  And  therefore  it  is  certain  that  ear-drums  are  not 
thus  bent  in  and  out  by  a  mechanical  energ>''  exerted  by  the 
Whip-poor-will,  as  would  have  to  be  the  case  if  this  theory  was 
true.  The  whole  conception  is  that  of  one  utterly  ignorant  of 
the  laws  of  mechanics,  and  equally  without  a  vestige  of  com- 
mon sense. 

**  And  fourth,  there  are  no  phenomena  of  sensation  which  do 
not  first  exist  materially.  They  may,  then,  or  may  not,  be  per- 
ceived by  any  particular  intelligence;  but  this  much  is  certain, 
that  they  cannot  be  perceived  as  sensations  until  so  existing. 
And  this  is  true  to  the  minutest  detail.  Thus  we  have  a 
tree,  with  its  trunk,  bark,  limbs,  flowers,  and  leaves,  including 
every  indentation  of  the  bark,  the  form  and  order  of  every 
branch  and  every  twig,  and  the  shape  and  position  of  every 
flower  and  every  leaf.  Because  of  this  absolutely  complete 
image  of  the  tree,  is  the  absolutely  complete  sensation  of  a 
tr(x\  So,  too,  if  the  material  tree  is  deficient,  the  sensation 
will  be  deficient,  and  to  exactly  the  same  extent.  Thus,  were 
the  ribs,  veins,  and  notches  of  the  leaves,  or  of  a  single 
leaf,  or  a  single  vein  of  a  single  leaf  wanting  in  the  physical 


WHIi^PERINCS  or  AN   OLD   HNE 


8y 


Ifce,  It  would  be  wanting  in  the  sensation.  Docs  any  one 
suppose  that  it  is  any  different  with  sound,  or  that  there 
h  any  exception  in  this  law  of  sensations?  Does  any  onr* 
doubt  that  all  the  marvellous  differences  of  sound*  which 
arc  as  many  and  as  manifest  as  any  that  exist  in  any 
of  the  phenomena  of  nature,  are  first  formed  materially? 
There  is  no  more  possible  question  about  this  than  that 
they  exist  at  all.  This  is  one  of  nature's  many  universal 
laws.  The  heavens  and  earth  will  pass  away  before  this  law- 
will  pass  away.  As  a  rainbow  is  builded,  or  a  raindrop  ;  as  an 
icicle  is  formed,  or  a  snowflake  with  its  crystals  of  such  exquisite 
beauty;  so  arc  sounds  formed  perfect  in  every  part,  and  repre- 
senting an  infinite  number  of  differences,  because  built  up 
in  nature  so  as  to  represent  them.  For,  though  we  cannot  sec 
this  phenomenon,  sound,  we  recognize  it  in  our  sensations,  and 
know  that  nothing  is  perceived  by  them  except  as  it  exists  first 
materially.  Sound,  then,  must  be  created  before  it  can  be 
beard." 

'•  It  is  made  by  vibration,  is  it  not,  Ellen?'*  I  asked. 

"Us  immediate  cause  is  pressure  or  shock/'  she  answered, 
*'lrom  which  results  vibration,  between  which  and  sound  there 
always  exists  an  exact  relationship.  But  vibration,  as  Ellen 
thinks,  must  be  the  result  of  moving  matter  by  whatever  name 
called.  And  it  has  generally  been  attributed  to  the  elastic  prop- 
erty of  bodies,  which,  to  a  certain  extent  at  least,  is  occasioned  by 
^o'lt ;   but  as  Ellen  will  abundanti}'  show^  it  is  caused  by  sound. 

* '  licrruil  said : 

'(i)  Everybody  in  nature  is  porous,  and  these  pores  arc  propor- 
lional  to  the  dcosity  of  the  substance.     (2)  These  pores  arc  filled  with 


90  ELLEN   OR  THE 

different  fluids,  and  principally  with  caloric.  But  caloric  possesses  a 
strong  repulsive  force ;  from  which  it  follows  that  when  an  elastic  body 
is  compressed  the  caloric  in  its  pores  drives  back  by  its  repulsive  power 
the  displaced  parts  and  brings  them  to  their  former  state.' 

"And  Mr.  J.  C.  Maxwell  says: 

'  The  laws  of  elasticity  express  the  relation  between  the  changes  of 
the  dimensions  of  a  body  and  the  forces  which  produce  them.  These 
forces  are  called  pressures  and  their  effects  compressions.  Pressures 
are  estimated  in  pounds  on  the  square  inch,  and  compressions  in  frac- 
tions of  the  dimensions  compressed.* 

"  Sound  is  a  product  of  such  conditions,  and  is,  as  Ellen 
thinks,  in  its  nature  as  well  as  in  its  surroundings,  of  electrical 
character.  Let  any  one  place  the  stem  of  a  vibrating  tuning 
fork  anywhere  on  the  head.  Here  is  no  possibility  of  air 
waves,  but  the  sound  is  complete  and  is  heard  the  most  dis- 
tinctly possible,  for  the  force  that  makes  it,  or  the  sound, 
passes  from  the  fork  into  the  head." 

"But,  Ellen,"  I  said,  **do  not  all  the  scientists  agree  that  the 
thing  which  takes  place  in  the  production  of  sensations,  as 
sound,  smell,  taste,  when  the  substance  comes  in  contact  with 
the  nerves  of  sensation,  is  a  motion?     Thus  Mr.  Tyndall  writes: 

'The  various  nerves  of  the  human  body  have  their  origin  in  the 
brain,  which  is  the  seat  of  sensation.  When  the  finger  is  wounded, 
the  sensor  nerves  convey  to  the  brain  intelligence  of  the  injury,  and  if 
these  nerves  be  severed,  however  serious  the  hurt  may  be,  no  pain  is 
experienced.  We  have  the  strongest  reason  for  believing  that  what 
the  ner\'es  convey  to  the  brain  is  in  all  cases  motion.  The  motion 
here  meant  is  not,  however,  that  of  the  nerve  as  a  whole,  but  of  its 
molecules  or  smallest  particles. 


VVmSPERINGS   OF   AN   OLD    PINE 


91 


'Different  nenxs  are  appropriated  to  the  transmission  of  different 
tinds  oi  molecular  motion.  The  nerves  of  taste,  for  example,  are  not 
^::onipetent  to  transmit  the  tremors  of  light,  nor  is  the  optic  nerve  com- 
^)etent  to  transmit  sonorous  vibrations.  For  these  a  special  nerve  is 
-■lecessary,  which  passes  from  the  brain  into  one  of  the  cavities  of  the 
^ar»  and  there  divides  into  a  multitude  of  lilaments.  It  is  the  motion 
imparted  to  this,  the  auditory  nerve,  which,  in  the  brain,  is  translated 
into  sound,' 


^ 


And  Ellen  knows  that  there  are  such  nerves  connected  with 

the  brain;  and  does  not  Ellen  think  the  scientists  know,  when 

ey  affirm   so   positively  that   it  is   motion,  and   nothing  else, 

hich  passes  along  these  nerves?'* 

**  Ellen    knows,    old    Pine,    that  they    don't  know    anything 

I  about  it." 
'*And  does  not  Ellen  think  that  their  claim  is  true?'* 
"Ellen  does  not  think  so/* 
"And  what  does  she  think?" 
**She   thinks   that   in   each   case   the  substance  causing  the 
sensation   is  introduced   into  the  system  of  the  body,  just  as 
food  and  drink  are;    that   the   motion    of    the  nerves  answers 
the   same    purpose  as  those   of   the    muscles    in    swallowing, 
and  no  other;   that  the  whole  proceeding  is  a  substantial  one, 
and  that  in  this  way  and  no  other  is  every  phenomenon   of 
nature  accomplished;   that  nowhere  does  something  come  from 
nothing,  or  the  motion  of  one  thing  give  the  effect  of  another; 
M^  that  there  is   no  confusion   in    the   order  of   nature,  but  that 
^Kcver>ni^'here  and  ahvays  things  are  created  in  the  same  manner* 
^       and  produce  their  effects  in  the  same  manner,  and  that  manner 
it  by  their  presence.     Nor  does  Ellen  think  that  anything  is 


92  ELLEN   OR  THE^ 

6r  cart  be  effective  where  it  is  not,  or  cSinnot  reach.  WSen 
camphor  or  any  other  remedy  is  snuffed  into  the  hose  to' 
relieve  some  trouble  in  the  head,  does  the  old  Pine  think 
that  what  takes  place  is  an  appropriate  motion  in  some  muscle 
or  nerve?  That  takes  place,  for  it  is  the  manner  provided 
by  nature  for  the  introduction  of  such  remedy  to  the  part 
where  it  is  needed,  and  the  motion  accomplishes  this^  its  part. 
But  the  healing  power  is  in  the  remedy,  to  be  accomplished 
by  contact,  cither  of  its  whole  substance  or  of  an  effettive 
part  put  out  from  it.  It  is  the  soul  and  not  the  nerves 
that  tastes  or  smells  or  hears;  nor  does  it  taste  or  smeU 
or  hear  a  motion,  but  that  particular  substance  formed  by 
nature,  through  her  always  sufficient  law  of  combinations;' to 
produce  the  effect  intended.  As  Mr.  Tyndall  does  not  stafe 
what  this  strongest  reason  that  he  refers  to  is,  it  is  i'm^ossible 
to  discuss  it.  Ellen's  reply  is  that  no  such  reason  exists;  but 
that  on  the  contrary  wc  have  the  strongest  possible  reasons  to 
believe  that  whenever  the  finger  is  wounded,  a  new  substance*  is 
created,  which,  through  the  medium  of  the  nerve,  conveys  the 
sense  of  injury  to  the  brain.  If  the  nerve  is  cut,  it  of  course 
cannot  convey  this  sense  of  injury." 

*' And  what  arc  these  strongest  reasons  that  Ellen  refers  to?" 
I  asked. 

**Thc  strongest  of  all  possible  reasons,"  she  said,  ^*  the  uni- 
versality of  nature's  laws.  For  everything  that  happens  in  the 
material  universe  takes  place  in  this  way,  by  a  combinatidni  of 
this  most  wonderful  thing  we  call  matter.  So  far  as  we  have 
knowledge,  there  is  no  exception.  Nor  does  Ellen  think  that 
any  exception  is  possible;   else   must  something  come  frbm 


WHISPERINGS   OF  AN   OLD   PINE  93' 

nothing.  Thus  we  have  all  sensations — those  that  give  pleas-' 
are  and  those  that  give  pain ;  sensations  of  beauty,  whatever 
they  are;  sensations  of  odor;  sensations  of  taste,  both  those 
that  are  agreeable  and  those  that  are  disagreeable,  those  that 
are  healthful  and  those  that  are  noxious ;  the  pleasant  sensa-' 
tions  from  an  orange  and  the  fatal  ones  from  poison.  Nor  is 
it  possible  for  Ellen  to  think  that  the  sense  of  injury  is  con- 
veyed or  can  be  in  any  different  manner.  Does  the  old  Pine 
think  that  he  could  devise  a  better  way  of  creation?" 

"The  old  Pine  certainly  does  not,  but  thinks  just  as  Ellen 
does,  that  nature's  method  of  accomplishment  in  the  material 
universe  is  by  appropriate  substances,  endowed  with  their 
proper  motions;  for  he  knows  of  no  instance  where  this  is 
otherwise,  nor  can  well  imagine  that  it  could  be  otherwise." 

"  Sensible  old  Pine,"  she  answered.  "  It  is  only  the  scientists 
who  operate  by  modes  of  motion  in  the  books,  where  alone 
this  method  of  performance  has  any  existence.'* 

"And  yet,  Ellen,  is  it  not  possible  to  communicate  by  modes 
of  motion,  as  in  telegraphing?  The  old  Pine  thinks  that  with 
pre-arrangement  between  parties  much  if  not  all  information 
might  be  so  communicated." 

"  Ellen  will  admit,"  she  said,  '*  that  information  may  be 
communicated  by  symbols  through  the  aid  of  intelligence ;  but 
this  is  not  at  all  what  Mr.  Tyndall  is  considering,  but«instead  the 
laws  of  sensation,  which  have  to  do  entirely  with  matter,  and 
its  effect  upon  mind. 

**  Why  mind  should  recognize  a  picture  or  a  fragrance,  or 
why  certain  combinations  should  make  such,  Ellen  does  not 
know.     Nor  can  she  see  any  good  reason  why  she  should.     If 


94  ELLEN   OR  THE 

she  did  know,  she  might  busy  herself  in  making  creations.  But 
she  knows  they  do,  even  to  the  trembling  of  a  leaf.  And  she 
realizes  that  the  power  which  made  them  knew  how  and  why. 
To  that  power  the  causes  and  effects  are  as  plain  as  the  making 
of  a  dress  is  to  Ellen,  or  the  manufacturing  of  a  pitcher  to  him 
who  can  make  it. 

"  Locke  thus  describes  sensation : 

'  Our  senses,  conversant  about  particular  sensible  objects,  do  convey 
into  the  mind  several  distinct  perceptions  of  things,  according  to  those 
various  ways  wherein  those  objects  do  aflfect  them  :  and  thus  we  come 
by  those  ideas  we  have  of  Yellow,  White,  Heat,  Cold,  Sofl,  Hard,  Bit- 
ter, Sweet,  and  all  those  which  we  call  sensible  qualities,  which,  when 
I  say  the  senses  convey  into  the  mind,  I  mean  they  from  external 
objects  convey  into  the  mind  what  produces  there  those  perceptions. 
This  great  source  of  most  of  the  ideas  we  have,  depending  wholly  upon 
our  Senses,  and  derived  by  them  to  the  Understanding,  I  call  Stn- 
sation:  " 


THli  ixii^'  'if^^^^^ 
PUBLIC  LlbHAKY 


9.  .,Jl^ 


WHISPERINGS    OF   AN   OLD    PINE 


97 


VIIL 


ii 


BUT,"  I  said,  **  Ellen,  the  speed  of  sound  is  governed  by 
the  elasticity  and  density  of  the  media  through  which 
It  pas!ies,  U  it  not?" 

**  Nut  with  Fallen's  definition  of  elasticity.  And  she  thinks, 
^o,  this  definition  is  the  most  common ;    and   therefore  such 

atemcnt  is  misleading  if  not  untrue.  Sound  is  propagated 
in  rubber,  which  is  very  elastic,  very  poorly;  and  lead,  which 
is  very  dense  and  inelastic,  is  a  good  conductor  Putty,  both 
inelastic  and  dense,  is  a  much  better  conductor  of  sound  than 
india  rubber/* 

"  Yet  all  the  text  books  teach  this,  and  would  appear  to 
show  it  in  their  tables.*' 

**  Ellen  has  but  very  little  confidence  in  any  of  their  state- 
ments/' she  answered. 

**  But  w^hy,"  I  asked,  "  shoufd  scientists  mi  state  ?  *' 

"  Because  of  their  ignorance,  Ellen  might  say,  but  she  thinks 
the  difficulty  lies  deeper  than  that,  because  of  their  indifference 
to  Truth.  The  name  of  those  who  do  not  know  is  legion*  but 
want  of  rehgion  far  more  than  want  of  knowledge,  is  responsi- 
ble for  error.    And  by  religion  Ellen  means  the  love  of  Truth/* 

"  And  what  is  Truth/'  Ellen?  " 

"Everything  that  is/*  she  answered.  "The  sunshine  that 
falls  upon  the  mountain,  or  lingers  upon  the  meadow.  God 
and  His  Laws  are  Truth :  and  the<e  laws,  as  Ellen  thinks,  may 
be  plainly  read,  whether  goveminoj  the  spiritual  or  material/' 


98  ELLEN   OR  THE 

"  Then  Ellen  does  not  think  that  those  who  sought  truth 
would  lie  ?" 

**  She  knows  that  they  would  not.  For  those  who  seek  will 
find,  and  find  that  for  which  they  seek,  not  its  opposite.  And 
to  Ellen  an  hypothesis  taught  as  a  known  principle  is  a  lie. 
But  Mr.  Ganot  says  that  the  intimate  nature  of  all  those  things 
that  we  are  talking  about  is  completely  unknown,  and  ever>' 
intelligent  scientist  that  Ellen  has  ever  talked  with  about  undul- 
atory  theories  admits  that  they  are  but  hypotheses  and  may  be 
wrong.  Let  them  say  this  to  their  scholars ;  let  them  proclaim 
it  in  their  lectures.  Let  them  tell  the  truth  and  shame  the 
devil.  Let  them  quit  the  lying ;  quit  it  entirely.  Never  once 
say  that  a  doubtful  thing  is  so,  or  an  hypothesis  a  fact,  but  say 
that  it  is  doubtful,  or,  like  Mr.  Ganot,  that  it  is  *  completely 
unknown.' 

**  Sound  is  an  entity,  radiating  in  all  directions  from  the 
sounding  body  under  its  own  laws,  which  as  yet  we  do  not 
understand,  nor  arc  we  warranted  to  say  that  its  speed  depends 
upon  the  elasticity  and  density  of  the  medium  through  which  it 
passes,  although  it  is  true  that  it  docs  depend  in  some  way 
upon  the  character  of  this  medium,  and  therefore  may  depend 
upon  its  density  and  elastic  force." 

**Thcn,"  I  said,  "this  might  be  true,  although  the  undulatory 
theory  was  not  true." 

•'Certainly,"  she  said;  ''the  undulatory  theory  is  not  true, 
but  the  other  may  be  true.*' 

•*  But  did  not  Mr.  Newton,"  I  asked,  "demonstrate  that  the 
speed  of  sound,  in  an  elastic  fluid,  depended  upon  the  elastic 
force  and  density  of  the  fluid?     His  formula  was  that  its  veloc- 


WIIlSPERmCS.  OFAN   OLD    PINE 


99 


Jtyr    ^wtfBS  directly  as  the  stibdupltcate  ratio  of  the  elastic  force. 
^'^^l-  inversely  as  the  subdiiplicate  ratio  of  the  density.     That  is, 
'^^^  it  was  equal  to  the  square  root  of  its  elastic  force  divided 
hyr-     ^jj(j  square  root  of  its  density.*' 

*^     He  demonstrated  nothing  of  the  kind/'  she  replied,  **for 
*^         theor>'   did  not  agree  with  experiment.      Mr.    Newton    in 
1^       ^Principia'  undertakes  to  derive  the  laws  which  govern  the 
-  «s  that  rule  among  heavenly  bodies.     This  was  a  field  of  his 
■*  choosing*  and  is  handled  with  much  ability.     Man}-  of  his 
^liods  are  exceedingly  ingenious.     All  are  bold,  and  show  a 
^icr  spirit  in  mathematics.     In  section  8»  proposition    41, 
enters   upon   a  discuss'on  of  motion  propagated  in  fluids. 
L5  proposition  is: 

prtuurf  is  not  propagated  through  a  fluid  in  nctiiinear  (iiintivns^ 
^nlns  where  tke  particles  t>f  the  fluid  lie  in  a  right  line'     (Fig.  4) 

If  lite  particles  a,  <^,  r,  d^  e,  lie  in  a  right  line,  the  presjiiire  may  be 
^^eed  dire<nly  propagated  from  it  to  f:  bnt  then  the  particle  c  will  urge 


Fig.  4. 

the  obliqaely  posited  particles/  and  g  obliquely,  and  those  particles/ 
m^g  will  not  sustain  this  pressure,  unless  they  be  supported  by  the  par- 
ticles h  and  k  lying  beyond  them ;  but  the  particles  that  support  them 
•ns  also  pressed  by  them ;  and  those  particles  cannot  sustain  that 


lOO 


ELLEN   OR  THE 


pressure,  without  being  supported  by,  and  pressing  upon,  those  particles 
that  lie  still  farther,  as  /  and  m,  and  so  on  in  infinitum.  Therefore 
the  pressure,  as  soon  as  it  is  propagated  to  particles  that  lie  out  of 
right  lines,  begins  to  deflect  towards  one  hand  and  the  other,  and  will 
be  propagated  obliquely  in  infinitum ;  and  after  it  has  t>egun  to  be 
propagated  obliquely,  if  it  reaches  more  distant  particles  lying  out  of 
the  right  line,  it  will  deflect  again  on  each  hand ;  and  this  it  will  do  as 
often  as  it  lights  on  particles  that  do  not  lie  exactly  in  a  right  line. 

'  Cor.  If  any  part  of  a  pressure,  propagated  through  a  fluid  from  a 
given  point,  be  intercepted  by  any  obstacle,  the  remaining  part,  which 
is  Dof    intercepted,  will  deflect  into  the  spaces  behind  the  obstacle. 


Fig.  5. 


This  may  be  demonstrated  also  after  the  following  manner.  Let  a 
pressure  be  propagated  from  the  point  A  (Fig.  5)  towards  any  part, 
and,   if  it   be   possible,   in   rectilinear    directions ;    and  the   obstacle 


WHISPERINGS    OF   AN    OLD    PINE  Id 

N  B  C  K  being  perforated  in  B  C,  let  all  the  pressure  be  intercepted 
but  the  coniform  part  APQ  passing  through  the  circular  hole 
B  C.  I-«t  the  cone  A  P  Q  be  divided  into  frustums  by  the  transverse 
planes  de,fg,hi.  Then  while  the  cone  ABC,  propagating  the 
pressure,  urges  the  conic  frustum  degf  beyond  it  on  the  superficies 
tie^  and  this  frustum  urges  the  next  frustum  fgih  on  the  superficies 
fg,  and  that  frustum  urges  a  third  frustum  and  so  ///  infinitum ;  it  is 
manifest  (by  the  third  law)  that  the  first  frustum  dc/g  is,  by  the 
reaction  of  the  second  frustum  fgh  /,  as  much  urged  and  pressed  on 
the  superficies  fg,  as  it  urges  and  presses  that  second  frustum. 
Therefore  the  frustum  d  egf  is  compressed  on  both  sides,  that  is, 
between  the  cone  Kde  and  the  frustum  fhig;  and  therefore  (by 
case  6,  prop.  19)  cannot  preserve  its  figure,  unless  it  be  compressed 
with  the  same  force  on  all  sides.  Therefore  with  the  same  force  with 
which  it  is  pressed  on  the  superficies  de,  fg,  it  will  endeavor  to  break 
forth  at  the  sides  df,  eg;  and  there  (being  not  in  the  least  tenacious 
or  hard,  but  perfectly  fluid)  it  will  run  out,  expanding  itself,  unless 
there  be  an  ambient  fluid  opposing  that  endeavor.^  Therefore,  by  the 
effort  it  makes  to  run  out,  it  will  press  the  ambient  fluid,  at  its  sides 
dfy  { g,  with  the  same  force  that  it  does  the  frustum,  fgih ;  and 
therefore,  the  pressure  will  be  propagated  as  much  from  the  sides 
d/yCg,  into  the  spaces  NO,  KL,  this  way  and  that  way,  as  it  is 
propagated  from  the  superficies/^'  towards  PQ.' 

*'It  may  be  noticed  that  Mr.  Newton  nowhere  undertakes  to 
explain  in  what  manner  one  particle  pushes  another,  that  is, 
whether  they  hit  each  other  or  not ;  but  judging  from  the 
whole  of  these  propositions,  it  is  assumed  that  they  do  not  hit 
each  other,  but  operate  in  some  unexplained  way  through  the 
interposition  of  some  other  substance,  or  substances,  the  char- 
acter of  which  is  nowhere  mentioned.     This,  as  will  be  seen,  is 


I02 


ELLEN   OR  THE 


entirely  opposed  to  the  kinetic  theory  of  gases,  now  generally 
accepted  by  scientists. 

'  Proposition  XLIL  All  motion  propagated  through  a  fluid  diverges 
from  a  rectilinear  progress  into  unmoved  spaces..    (Fig.  6) 

'Case  i.  Let  a  motion  be  propagated  from  the  point  A  through  the 
hole  BC,  and,  if  it  be  possible,  let  it  proceed  in  the  conic  space 
BCQP   according  to  right  lines  diverging  from  the  point  A.     And 


Fig.  6. 

let  us  first  suppose  this  motion  to  be  that  of  waves  in  the  surface  of 
standing  water;  and  let  de^  fg,  hi,  kl,  etc.  be  the  tops  of  the  several 
waves,  divided  from  each  other  by  as  many  intermediate  valleys  or 
hollows.  Then,  because  the  water  in  the  ridges  of  the  waves  is  higher 
than  in  the  unmoved  parts  of  the  fluid  K  L,  N  O,  it  will  run  down 
from  off  the  tops  of  those  ridges  e^g,  /,  /,  etc.  ^,/,  /f,  /*,  etc.  this  way 
and  that  way  towards  K  L  and  N  O ;  and  because  the  water  is  more 


WHISPERINGS   OF   AN   OLD    PINE  103 

depressed  in  the  hollows  of  the  waves  than  in  the  unmoved  parts  of 
the  fluid  K L,  NO,  it  will  run  down  into  those  hollows  out  of  those 
unmoved  parts.  By  the  first  deflux  the  ridges  of  the  waves  will  dilate 
themselves  this  way  and  that  way,  and  be  propagated  towards  K  L  and 
N  O.  And  because  the  motion  of  the  waves  from  A  towards  P  Q  is 
carried  on  by  a  continual  deflux  from  the  ridges  of  the  waves  into  the 
hollows  next  to  them,  and  therefore  cannot  be  swifter  than  in  propor- 
tion to  the  celerity  of  the  descent ;  and  the  descent  of  the  water  on 
each  side  towards  K  L  and  N  O  must  be  performed  with  the  same 
velocity;  it  follows,  that  the  dilatation  of  the  waves  on  each  side 
towards  K  L  and  N  O  will  be  propagated  with  the  same  velocity  as  the 
waves  themselves  go  forward  directly  from  A  to  P  Q.  And  therefore 
the  whole  space  this  way  and  that  way  towards  K  L  and  N  O  will  be 
filled  by  the  dilated  waves  rfgr^  shisy  tklt^  vmnv^  etc. 

'That  these  things  are  so,  any  one  may  find  by  making  the 
experiment  in  still  water. 

'Case  2.  Let  us  suppose  that  de^  /^,  A/,  kl^  mn,  represent  pulses 
successively  propagated  from  the  point  A  through  an  elastic  medium. 
Conceive  the  pulses  to  be  propagated  by  successive  condensations  and 
rarefactions  of  the  medium,  so  that  the  densest  part  of  every  pulse  may 
occupy  a  spherical  superficies  described  about  the  center  A,  and  that 
equal  intervals  intervene  between  the  successive  pulses.  Let  the  lines 
de^fg^  h  /,  kly  etc.  represent  the  densest  parts  of  the  pulses,  propagated 
through  the  hole  B  C ;  and  because  the  medium  is  denser  there  than 
in  the  spaces  on  either  side  towards  K  L  and  N  O,  it  will  dilate  itself 
as  well  towards  those  spaces  K L,  NO,  on  each  hand,  as  towards  the 
rare  intervals  between  the  pulses ;  and  thence  the  medium,  becoming 
always  more  rare  next  the  intervals,  and  more  dense  next  the  pulses, 
will  partake  of  their  motion.  And  because  the  progressive  motion  of 
the  pulses  arises  from  the  perpetual  relaxation  of  the  denser  parts 
toward  the  antecedent  rare  intervals ;  and  since  the  pulses  will  relax 


I04  ELLEN   OR  THE 

themselves  on  each  hand  towards  the  quiescent  parts  of  the  medium 
K  L,  N  O,  with  very  near  the  same  celerity ;  therefore  the  pulses  will 
dilate  themselves  on  all  sides  into  the  unmoved  parts  K  L,  N  O,  with 
almost  the  same  celerity  with  which  they  are  propagated  directly  from 
the  centre  A ;  and  therefore  will  fill  up  the  whole  space  K  L  O  N. 

*  And  we  find  the  same  by  experience  also  in  sounds  which  are  heard 
though  a  mountain  interpose;  and,  if  they  come  into  a  chamber 
through  the  window,  dilate  themselves  into  all  the  parts  of  the  room, 
and  are  heard  in  every  corner ;  and  not  as  reflected  from  the  opposite 
walls,  but  directly  propagated  from  the  window,  as  far  as  our  sense 
can  judge. 

*  Case  3.  Let  us  suppose,  lastly,  that  a  motion  of  any  kind  is  propa- 
gated from  A  through  the  hole  B  C.  Then,  since  the  cause  of  this 
propvigation  is  that  the  parts  of  the  medium  that  are  near  the  center  A 
disturb  and  agitate  those  which  lie  farther  from  it ;  and  since  the  parts 
which  are  urged  are  fluid,  and  therefore  recede  every  way  towards 
those  spaces  where  they  are  less  pressed,  they  will  by  consequence 
recede  towards  all  the  parts  of  the  quiescent  medium ;  as  well  to  the 
parts  on  each  hand,  as  K  Tv  and  N  O,  as  to  those  right  before,  as  PQ: 
and  l>y  this  means  all  the  motion,  as  soon  as  it  has  passed  through  the 
hole  13  C,  will  begin  to  dilate  itself,  and  from  thence,  as  from  its 
princijjle  and  center,  will  be  propagated  directly  every  way.' 

"The  supposed  cause  of  these  pulses, — that  is,  the  supposed 
action  of  clastic  force,  —  is  here  most  plainly  pointed  out 
and  is  delightfully  refreshing  as  against  the  muddled  state- 
ments, or  no  statements  at  all,  of  the  textbooks:  'And 
because  the  medium  is  denser  there  than  in  the  spaces  on 
either  side  it  will  dilate  itself  as  well  towards  those  spaces 
on  each  hand  as  towards  the  rare  inten>als  between  the 
pulses ;  and  thence  the  medium,  becoming  always  more  rare 


WHISPERINGS    OF  AN   OLD    PINE  IO5 

ncxi  the  uitenfals,  and  more  dense  next  the  pulse Sy  will 
partake  of  their  motion.  And  because  the  progressive  motion 
of  the  pulses  arises  from  the  perpetual  relaxation  of  the 
denser  parts  toward  the  antecedent  rare  intervals;  and 
since  the  pulses  will  relax  t  Item  selves  on  each  hand 
toivards  the  quiescent  parts  of  the  medium  with  very  near  the 
same  celerity ;  therefore  the  pulses  will  dilate  themselves  on  all 
sides  into  the  unmoved  parts  with  almost  the  same  celerity  ivith 
which  they  are  propagated  directly  from  the  centre;  and, 
therefore,  will  fill  up  the  whole  space.  *  *  *  Then,  since 
the  cause  of  this  propagation  is  that  the  parts  of  the  medium 
that  are  near  the  center  disturb  and  agitate  those  which  lie 
farther  from  it;  and  since  the  parts  which  are  urged  are 
fluid,  and  therefore  recede  every  way  towards  those  spaces 
where  they  are  less  pressed,  they  will  by  consequence  recede 
towards  all  the  parts  of  the  quiescent  medium  ;  as  well  to  the 
parts  on  each  hand  as  to  those  right  before,  and  by  this  means 
all  the  motion,  as  soon  as  it  has  passed  through  the  hole,  will 
begin  to  dilate  itself,  and  from  thence,  as  from  its  principle 
and  center,  will  be  propagated  directly  every  way! 

"And  this  is  all  there  is  of  it,  or  all  there  could  be  of  it. 
Air  will  dilate  and  thus  cause  a  pulse,  not  a  wave,  if  other  air 
surrounding  it  is  more  rarified  than  itself.  And  under 
no  other  possible  circumstances  can  it  do  it.  This  practi- 
cally destroys  the  undulatory  theory  of  sound.  For  during  a 
large  part  of  the  time  when  sounds  occur,  the  conditions  sup- 
posed do  not  take  place,  and  are  impossible.  Surrounding 
air  is  not  quiescent,  but  frequently,  if  not  generally,  more 
condensed    than   the    part   affected  by   the    sound    agitation. 


I06  ELLEN    OR   THE 

This  would  be  especially  true  of  the  agitation  caused  by 
slight  sounds,  which  of  necessity  would  be  constantly  over- 
whelmed by  the  greater  agitation  of  larger  sounds.  And  all 
sounds  would  often,  if  not  generally,  find  the  conditions  of  the 
atmosphere  in  respect  to  density  varied,  and  thus  be  liable  to 
be  stopped  in  their  progress  at  any  moment. 

**Were  the  conditions  possible  or  true,  at  every  meet- 
ing of  a  condensed  wave  from  some  other  sound,  or  from 
any  cause  whatever,  a  thing  which  must  constantly  take 
place,  the  motion  of  our  first  wave  would  be  retarded, 
and,  if  the  next  wave  was  the  larger,  be  entirely  stopped. 
For  its  motion,  being  solely  caused  by  its  tendency  to  enter 
the  less  dense,  it  could  not,  of  course,  advance  against 
the  more  dense.  And  hence  all  the  smaller  sounds,  formed  or 
half-formed,  must  be  constantly  cut  off  by  an  instantaneous 
process.  If  such  a  condition  actually  took  place,  it  would  also 
be  true  that  the  speed  of  these  waves  (or,  the  speed  of  sound) 
would  depend  upon  the  strength  of  the  compression,  and 
therefore  would  vary  continuously,  which  it  does  not  in  fact  do." 

"But,"  I  said,  ''Kllen,  by  Boyle's  law,  compression  and 
density  balance  each  other,  do  they  not?" 

**  Sometimes  the\'  do,"  she  answered.  "  In  the  conditions 
now  supposed  there  is  no  evidence  that  they  could,  though  this 
proposition  of  Mr.  Newton's  rests  upon  the  assumption  that  the 
elastic  force  of  air  is  equal  to  its  condensation. 

"Newton  was  born  in  1642,  and  published  the  *Principia'  in 
1687.     Ganot  says : 

*The  law  of  the  compressibility  of  gases  was  discovered  by  Boyle  in 
1662,  and  afterwards  independently  by  Mariotte  in   1679.     It  is  in 


WHISPERINGS   OF  AN  OLD   PINE 


10; 


England  commonly  called  **  Boyle's  Law,**   and   on   the   Continent 
*•  Mafiotte*s  Law."     It  is  as  follows : 

•  Th€  kmptratuPT  remaining  the  same^  the  volume  of  a  given  quantity 
m  gas  is  inmrsefy  as  the  pressure  whiih  it  dears. 

'This  liw  may  be  verified  by  means  of  an  apparatus  devised  by  Boyle, 

*  ITie  law  also  holds  good  in  the  case  of  pressures  of  less  than  one 
atmosphere.* 

*vBut  only  one  instance  is  given  of  this,  viz.:  air  in  a  tube 
under  pressure  ol  half  an  atmosphere. 

'In  the  experiment  with  Boyle's  tube,  as  the  mass  of  air  remains  the 
same,  its  density  must  obviously  increase  as  its  voUtme  diminishes,  and 
vice  versa.  The  law  may  thus  be  enunciated; — **  For  the  same  tern- 
pemtiire  the  density  of  a  gas  is  proportional  to  its  pressure''  Hence, 
as  water  is  773  times  as  heavy  as  atr,  under  a  pressure  ol  773  atmos- 
pheres air  would  be  as  dense  as  water/ 

**This  law  is  (oundcd  upon  experiments  and  is  known  to  be 
true  only  so  far  as  the  conditions  arc  such  as  existed  when  the 
experiments  were  tried. 

**  But  these  conditions  in  all  cases  were  that  the  gas  consid- 
ered was  all  subjected  to  equal  pressure.  And  hence  the 
experiments,  and  therefore  the  law  founded  upon  them,  can  not 
be  applied  to  tlicsc  hypothetical  condensations  and  rarefactions. 
For  in  this  case  the  whole  body  of  air  considered  is  not  sub- 
jected to  equal  pressure.  But,  on  the  contrary,  by  the 
hypothesis  it  is  subjected  to  unequal  pressure.  And,  therefore, 
with  no  known  principle  preventing,  it  would  be  fairly  pre- 
sumable that  the  speed  of  such  condensations,  did  they  exist, 
would    vary  with    the    force    making    them.     Besides,   further 


I08  ELLEN    OR   THE 

experiments  demonstrated  that  Boyle's  law  is  not  always 
correct.  And  this  especially  enforces  the  fact  that  the  law  can 
be  relied  upon  only  so  far  as  demonstrated  by  experiment. 
Mr.  Ganot  says: 

*The  general  result  of  these  experiments  is  to  show  that  at  high 
pressures  the  volume  is  greater  than  that  required  by  Boyle's  law, 
agreeing  in  this  respect  with  hydrogen  at  ordinary  pressures.  This  is 
well  illustrated  by  the  deportment  of  ethylene  as  given  in  the  following 
table,  where  P  is  the  pressure  in  metres  of  mercury,  and  PV  the  pro- 
duct of  pressure  into  volume,  which  according  to  Boyle*s  law  should  be 
constant : 

Pressure    24      34-8     45-1     55-4     64      72      84     134     214     303 
PV    21*5    i8*4     12-3       9*8       9*4     9*7    10-7     15-1   22*1     29^3 

'  It  will  thus  be  seen  that  the  product  P  V  decreases  with  increasing 
pressure  to  a  minimum,  and  then  increases  again  with  the  pressure. 

*The  pressure  at  which  this  minimum  0/  comprcssibiiity  occmts  \^ 
different  with  different  gases,  as  is  also  the  extent  of  the  deviation  from 
the  law. 

*  At  a  temperature  of  200  this  minimum  occurs  at  the  following  pres- 
sures in  metres  of  mercury  :  nitrogen  and  carbonic  oxide  50,  air  and 
ethylene  65,  oxygen  100,  and  marsh  gas  120.* 

'•  It  will  be  seen  from  Mr.  Newton's  remarks  in  the  above 
propositions,  that  in  proposition  41  he  indirectly  suggests  the 
difficulty  of  many  consecutive  particles  lying  in  a  straight  line, 
saying  that  if  they  did  so  lie  the  pressure  would  indeed  be  propa- 
gated ;  but  that  the  particles  would  urge  the  obliquely  posited 
particles,  and  therefore  the  pressure  soon  begin  to  deflect  in  all 
directions  without  limit. 

**That  the  particles  do  not  to  any  great  extent  lie  in  straight 
lines  is  proven,  according  to  this  hypothesis,  from  the  fact  that 


WHISPERINGS   OF  AN   OLD   PINE  1 1  I 

sound  goes  in  all  directions.  The  corollary  of  this  proposition 
proves  that  if  a  pressure  should  be  in  part  intercepted,  the  other 
portion  of  it  would  obey  this  same  law ;  or  generally,  as  the 
proposition,  that  any  uninterccpted  pressure  in  a  quiescent  fluid 
spreads  in  all  directions.  And  this  from  a  corollary  of  the  prin- 
ciple that  there  is  equal  pressure  in  all  directions  in  a  quiescent 
fluid.  For  in  such  a  fluid  resistance  is  equal  in  all  directions. 
**  According,  then,  to  these  propositions  of  Mr.  Newton  of 
the  motion  of  sound  waves  and  the  cause  of  .hem,  they  can 
advance  so  far  and  only  so  far  as  the  air  in  front  of  them  is 
quiescent  or  less  compressed  than  themselves,  being  stopped 
entirely  by  air  of  equally  compressed  condition  and  annihi- 
lated by  that  of  more.  This,  indeed,  Mr.  Newton  admits  in 
proposition  41,  corollary,  when  he  says:  *  Unless  there  be 
an  ambient  fluid  opposing  that  endeavor.'  But  everywhere 
many  sounds  are  constantly  taking  place,  and  often  at  the  same 
time,  some  mo.e  and  some  less  intense.  If  the  undulatory 
theory  was  true,  as  explained  here  by  Mr.  Newton,  sounds  could 
not  pass  each  other,  but  would  stop,  and  most  sounds,  or  at 
least  many,  could  be  heard  but  very  short  distances,  or  indeed 
not  at  all.  But  this  we  know  is  not  true,  but  that  instead 
sound  i  pass  each  other,  little  sounds  and  greater  sounds,  and 
will  be  heard  always,  or  at  least  generally,  for  distances  propor- 
tional to  their  intensity.  And  so  again  the  theory  is  demon- 
strated not  only  to  be  untrue  but  to  be  impossible,  and  one  that 
no  sensible  person  could  continue  to  consider.  Surely  the  old 
Pine  is  satisfied  with  these  insurmountable  objections  to  the 
theory,  and  will  let  Ellen  now  discuss  something  worth  dis- 
•Uissing." 


112  ELLEN   OR  THE 


IX. 


^^T^HE  old  Pine  sees  that  Ellen  is  right,"  I  said,  *'and  that 
*  there  is  no  possible  explanation  of  the  difficulties  which 
Ellen  suggests;  that  any  theory  containing  them  is  not  only 
impossible  but  idiotic.  And  yet  as  the  whole  scientific  world 
is  teaching  it,  and  as  it  is  very  difficult  always  for  people  to  get 
out  of  a  rut,  the  old  Pine  hopes  that  Ellen  will  still  further  ex- 
pose its  inconsistencies." 

**Very  well,"  she  said.  **In  the  demonstration  Mr.  Newton 
applied  the  third  law  of  motion  to  air.  The  inference  is  that 
he  supposed  all  the  laws  of  motion  to  apply  to  air,  as  indeed^ 
from  the  way  in  which  they  are  stated,  they  would  appear  to. 
But,  if  these  particles  hit  each  other,  it  would  be  impossible 
to  explain  the  system  of  air  waves  contemplated  in  this 
theory,  by  the  laws  of  motion.  For  by  the  theory  the 
particles  vibrate,  and  go  at  a  speed  much  faster  than  the 
vibrating  body;  but  by  the  laws  of  motion  these  particles, 
being  presumably  of  the  same  size,  if  elastic,  would  move 
at  the  speed  of  the  vibrating  body,  imparting  this  same  speed 
to  other  particles  which  they  might  hit,  and  come  themselves 
to  rest.  The  particles  which  they  hit  would  do  likewise,  and 
this  process  be  continued  until  the  motion  was  destroyed  by 
friction.  If  inelastic,  two  equal  particles  hitting  would  con- 
tinue together  at  half  speed.  It  is  evident,  then,  that 
according  to  the  kinetic  theory,  in  which  the  particles  are  sup- 
posed to  hit,  in  some  way  the  laws  of  motion  are  superseded. 


WHISPERINGS    OF  AN   OLD   PINE  II 3 

if  this  undulatory  theory  is  true.  Mr.  Newton  does  not  discuss 
this  part  of  the  subject.  He  mentions  particles  of  air,  but 
apparently  supposes  or  assumes  that  they  are  permanently 
separated  by  some  expansive  and  contractile  substance  or  sub- 
stances which  he  calls  lineolae.  If  this  was  a  fact  such  sub- 
stance must  itlicH  be  composed  of  particles  or  little  bodies 
disconnected, —  else  how  could  we  breath  it,  or  live  in  it, —  and 
these  particles  like  all  matter  be  either  elastic  or  inelastic?" 

**  But  is  it  not  supposed  Ellen,  that  elastic  force  comes  into 
action,  introducing  the  oscillatory  conditions  in  the  sounding 
body,  and  also  accounting  for  the  speed  of  sound?" 

"The  oscillatory  motion  is  impossible,"  she  replied,  ** except 
through  the  action  of  alternating  forces.  But  Ellen  cannot  see 
that  there  are  any  alternating  forces  in  the  transmission  of  sound 
after  it  leaves  the  sounding  body.  For  then  its  movement  in 
every  direction  is  both  constant  and  rapid,  being  in  that  respect 
entirely  different  from  the  motion  of  the  sounding  body. 

**But  Ellen  will  again  —  because  it  won't  hurt  the  old 
Pine  a  bit,  if  she  repeats  a  little  —  call  attention  to  the 
fact  that,  in  these  propositions  of  Mr.  Newton,  the  cause 
of  the  supposed  movement  of  air  waves  is  repeatedly  given  as 
in  proposition  42 : 

'  And  because  the  progressive  motion  of  the  pulses  arises  from  the 
perpetual  relaxation  of  the  denser  parts  towards  the  antecedent  rare 
intervals.' 

** And  again: 

*Then  since  the  cause  of  this  propagation  is,  that  the  parts  of  the 
uiedium  that  are  near  the  center  A  disturb  and  agitate  those  which  lie 


114  ELLEN    OR   THE 

farther  from  it ;  and  since  the  parts  which  are  urged  are  fluid,  and  there- 
fore recede  every  way  towards  those  spaces  where  they  are  less  pressed, 
they  will  by  consequence  recede  towards  all  the  parts  of  the  quiescent 
medium.  *  *  ♦  And  by  this  means  all  the  motion,  as  soon  as  it 
has  passed  through  the  hole  B  C,  will  begin  to  dilate  itself,  etc.* 

"It  is  indeed  quite  refreshing  to  find  thus  an  honest  and 
able  man  who  in  this  extraordinary  theory  was  not  afraid 
to  state  how  he  believed  it  to  be  accomplished;  although 
we  can  hardly  wonder  that  text  books  and  lecturers  on  sound 
omit  all  this,  when  it  is  so  evident  that  such  explanation 
disproves  the  theory.  Present  text  books  are  satisfied  with 
stating  an  incredible  theory  without  undertaking  to  explain  the 
method  of  it,  because  there  is  no  explanation  possible. 

"  It  is  only  partially  true  that  sound  dilates  into  the  sur- 
rounding air,  as  witness  the  following  account  of  the  use  of  a 
megaphone  for  warning  in  fogs: 

'Guilford,  Conn.,  Oct.  14,  1899. 

'At  the  (Tovernment  lighthouse  station  on  Falkner's  Island,  which  is 
directly  off  this  coast,  there  has  just  been  erected  the  largest  megaphone 
in  the  world.  It  is  seventeen  feet  long  and  seven  feet  in  diameter  at 
the  mouth.  It  stands  upon  a  circular  platform  twenty-eight  feet  in 
diameter,  upon  which  it  revolves. 

'The  plan  is  to  direct  it  toward  the  eight  principal  points  of  the  com- 
pass, one  after  the  other  in  regular  rotation,  and  by  means  of  a  different 
signal  sent  in  each  of  these  eight  directions  to  tell  any  vessel  which  may 
be  in  the  line  of  the  axis  of  the  instrument  during  a  fog  the  exact  posi- 
tion of  the  signal  station  with  relation  to  the  ship. 

*  The  great  difficulty  with  sound  signals  as  aids  to  navigation  in  a  fog  is 
that  they  cannot  be  located  with  any  accuracy.     Cases  are  on  record  in 


WHISPERINGS   OF   AX   OLD    PINK  II5 

which  two  officers  standing  on  the  bridge  of  the  same  steamer  have  dif- 
fered as  much  as  ninety  degrees  in  their  estimate  of  the  direction  of  a 
fog  whistle  which  was  distinctly  heard  by  both  of  them.  It  is  common 
for  a  vessel  to  be  kept  on  its  course  under  the  impression  that  a  certaii 
signal  is  several  points  on  the  bow,  >vhen  as  a  matter  of  fact  it  is  deac 
ahead.  If  sound  signals  could  be  located  in  a  fog,  navigation  would  be 
much  less  dangerous. 

*  The  apparatus  which  has  just  been  erected  at  Falkner's  Island,  and 
which  is  the  invention  Of  R.  F.  Foster,  is  intended  to  locate  the  signal 
station  accurately.  When  the  huge  megaphone  is  due  north  of  any 
vessel,  the  ship  will  hear  the  north  signal,  a  short,  a  long  and  short  blast. 
If  it  is  due  west  of  a  ship,  the  vessel  will  hear  three  short  blasts,  and  so 
on,  with  a  different  combination  of  long  and  short  blasts  for  each  of  the 
eight  points  of  the  compass.  The  signals  are  fifteen  seconds  apart,  and 
the  apparatus  makes  a  complete  revolution  in  two  minutes. 

'  In  order  to  facilitate  the  recollection  of  the  code,  all  the  sounds  which 
indicate  the  general  direction  of  west  begin  with  a  short  blast,  and  all 
those  indicating  the  general  direction  of  east  begin  with  a  long  blast. 
The  south  signals  are  all  shorter  than  those  farther  north. 

'  When  the  first  tests  were  made  the  sounding  instmment  used  was  one 
of  the  smallest  sirens  which  could  be  procured,  and  was  blown  with 
steam  at  forty  pounds  and  fed  with  an  inch-and-a-half  pipe.  This  is 
only  one- twentieth  of  the  power  of  the  sirens  at  Sandy  Hook,  Block 
Island,  and  Beaver  Tail.  When  this  little  siren  was  blown  through  the 
seventeen-foot  megaphone  it  was  found  to  be  almost  equal  in  power  to 
the  ten-inch  locomotive  whistle  which  is  part  of  the  regular  installation 
on  the  island,  and  it  could  be  distinctly  heard  at  a  distance  of  ten  miles, 
provided  the  listener  was  in  a  line  with  the  axis  of  the  megaphone. 

'  All  that  was  asserted  by  the  inventor  was  that  the  sound  waves  com- 
ing directly  toward  the  observer  could  be  readily  distinguished  from 
those  sent  forty-five  degrees  from  him,  no  matter  how  far  he  was  from 
the  source  of  the  sound. 


Il6  ELLEN   OR  THE 

'  The  unofficial  tests  were  made  on  Wednesday  by  C.  Lamy  of  the 
Lighthouse  establishment,  on  board  the  Government  boat  Mistletoe, 
the  inventor  being  accompanied  in  a  steam  launch  by  E.  B.  Merriman 
of  Boston,  who  built  the  megaphone,  and  Reuben  E.  Hill  of  Guilford. 

*  To  the  surprise  of  all  it  was  found  that  so  far  from  the  sounds  sent  at 
an  angle  of  forty- five  degrees  being  nearly  equal  to  those  sent  directly 
toward  the  obsen-er,  they  were  absolutely  inaudible  at  all  distances 
beyond  a  mile,  and  even  at  half  a  mile  it  required  the  closest  attention 
to  hear  them  at  all,  while  the  sounds  coming  directly  toward  the  list- 
eners were  extremely  powerful  up  to  eight  miles,  and  at  the  shorter 
distances  of  one  or  two  miles  almost  equal  to  the  immense  steam  whistle, 
which  was  sounded  immediately  after  the  megaphone  so  that  those  in 
the  boat  might  judge  of  their  comparative  strength. 

'These  experiments  completely  upset  all  the  preconceived  ideas  of 
men  who  have  made  a  life-long  study  of  the  peculiarities  of  sound, 
because  they  show  that  it  is  possible  to  confine  a  sound,  even  so 
powerful  as  that  from  a  siren,  and  to  project  it  into  space  in  a  given 
direction  with  the  same  certainty  and  accuracy  that  we  can  project  the 
rays  of  a  searchlight. 

'This  being  so,  there  can  be  no  doubt  of  the  possibility  of  sending  a 
message  to  a  vessel  in  a  fog  by  means  of  a  varying  sound  with  abso- 
lutely as  much  precision  as  it  could  be  sent  in  clear  weather  by  means 
of  a  flashing  searchlight.  If  a  vessel  hears  one  of  these  signals,  which 
says  "  North,'*  it  may  be  certain  that  the  signal  it  hears  lies  directly 
north  of  it,  because  if  it  did  not  the  north  signal  could  not  be  heard 
at  all. 

'  There  are  many  other  uses  to  which  it  is  proposed  to  put  this  system 
of  signalling,  such  as  sending  messages  from  one  part  of  the  army  to 
another  in  the  field  without  any  risk  of  the  enemy's  reading  them,  as 
they  now  do  flag  signals,  because  no  one  not  in  the  direct  line  of  the 
axis  of  the  megaphone  could  hear  anything.     The  same  system  can  be 


WHISPERINGS   OF   AN   OLD    PINE  II7 

used  in  signalling  from  one  vessel  to  another  in  thick  weather  so  as  to 
avoid  collisions.* — Sun. 

**  From  this  account  the  old  Pine  will  see  that  sound  will  act 
like  shot  or  any  other  entity.  Thus,  if  shot  be  placed  upon 
paper  spread  over  gunpowder  lying  upon  the  ground,  and  the 
powder  be  ignited,  the  shot  will  be  thrown  in  all  directions; 
but  if  placed  in  a  gun,  they  will  be  sent  in  the  direction  of  the 
barrel." 

"But,  Kllen,  shot  thus  sent  will  constantly  vary  in 
velocity." 

**  Yes,"  she  said,  "for  they  depend  for  their  motion  upon  the 
force  of  the  gunpowder,  and  arc  retarded  by  friction  of  the  air; 
but,  as  Ellen  thinks,  sound,  like  electricity  or  light,  carries  its 
motive  power  within  itself. 

"  It  is  true  that  sounds,  coming  into  a  chamber  through  a 
window,  dilate  or  spread  themselves.  But  that  doesn't  show 
that  the  air  is  anywhere  cither  condensed  or  rarefied,  but  rather 
that  sound,  like  odor,  is  conducted  through  the  air  in  all 
directions. 

'Proposition  XLIII. — Every  tremulous  both  in  an  clastic  medium 
propagates  the  motion  of  the  pulses  on  every  side  right  fonvard;  but 
in  a  non-elastic  medium  excites  a  circular  motion, 

'Casf.  I.  The  parts  of  the  tremulous  body  alternately  gomg  and 
returning,  do  in  going  urge  and  drive  before  them  those  parts  of  the 
medium  that  lie  nearest,  and  by  that  impulse  compress  and  condense 
them ;  and  in  returning  suffer  those  compressed  parts  to  recede  again, 
and  expand  themselves.  Therefore  the  parts  of  the  medium  that  lie 
nearest  to  the  tremulous  body  move  to  and  fro  by  turns,  in  like  manner 


Il8  ELLEN   OR   THE 

as  the  parts  of  the  tremulous  body  itself  do ;  and  for  the  same  cause 
that  the  parts  of  this  body  agitate  these  parts  of  the  medium,  these 
parts,  being  agitated  by  like  tremors,  will  in  their  turn  agitate  others 
next  to  themselves ;  and  these  others,  agitated  in  like  manner,  will  agi- 
tate those  that  lie  beyond  them,  and  so  on  in  infinitum.  And  in  the  same 
manner  as  the  first  parts  of  the  medium  were  condensed  in  going, 
and  relaxed  in  returning,  so  will  the  other  parts  be  condensed  every 
time  they  go,  and  expand  themselves  every  time  they  return.  And 
therefore  they  will  not  be  all  going  and  all  returning  at  the  same  instant 
(for  in  that  case  they  would  always  preser\'e  determined  distances  from 
each  other,  and  there  could  be  no  alternate  condensation  and  rarefac- 
tion) ;  but  since,  in  the  places  where  they  are  condensed,  they  approach 
to,  and,  in  the  places  where  they  are  rarefied,  they  recede  from  each 
other,  therefore  some  of  them  will  be  going  while  others  are  returning ; 
and  so  on  ///  infinitum.  The  parts  so  going,  and  in  their  going  con- 
densed, are  pulses,  by  reason  of  the  progressive  motion  with  which  they 
strike  obstacles  in  their  way ;  and  therefore  the  successive  j)ulses  pro- 
duced by  a  tremulous  body  will  be  propagated  in  rectilinear  directions ; 
and  that  at  nearly  equal  distances  from  each  other,  because  of  the  ecpial 
intervals  of  time  in  which  the  body,  by  its  several  tremors,  ])roduces  the 
several  pulses.  And  though  the  parts  of  the  body  go  and  return  in 
some  certain  and  determinate  direction,  yet  the  pulses  propagated  from 
thence  through  the  medium  will  dilate  themselves  towards  the  sides,  by 
the  foregoing  proposition ;  and  will  be  propagated  on  all  sides  from 
that  tremulous  body,  as  from  a  common  centre,  in  superficies  nearly 
spherical  and  concentrical.  An  example  of  this  we  have  in  waves 
excited  by  shaking  a  finger  in  water,  which  proceed  not  only  forwards 
and  backwards  agreeably  to  the  motion  of  the  finger,  but  spread  them- 
selves in  the  manner  of  concentric  circles  all  round  the  finger,  and  are 
propagated  on  every  side.  For  the  gravity  of  the  water  supj)lies  the 
place  of  elastic  force.' 


VVHISI'ERINGS   OF   AN   OLD    FINE 


119 


*•  In  case  2  of  this  proposition,  Mr.  Newton  gives  the  com- 
inon  sense  and  correct  phenomenon  happening  when  any  body 
is  thrown  into  the  air,  or  vibrates  in  it.  And  this  because  of 
the  mobility  of  the  air.  a  feature  that  is  as  much  a  part  of  this 
problem  as  light  is  of  creation,  but  which  physicists,  with  a 
stupidity  that  is  idiotic,  neglect  to  consider.     It  is  as  follows: 


*  Case  1.  If  the  medium  be  not  elastic,  then,  because  its  parts  can- 
not be  condensed  by  the  pressure  arising  from  the  vibrating  partii  of  the 
lieinulous  boily,  the  motion  will  be  propagate<l  in  an  instant  towards  the 
jKirts  where  the  medium  yields  most  easily,  that  is,  to  the  parts  which 
the  tretntilous  body  would  otherwise  leave  vacuous  behind  it,  The  case 
is  the  same  with  that  of  a  body  projected  in  any  medium  whatever*  A 
medium  yielding  to  projectiles  does  not  recede  in  infinitum^  but  with  a 
circular  motion  comes  round  to  the  spaces  which  the  body  leaves 
behind  it,  'fherefore  as  often  as  a  tremulous  body  tends  lo  any  part, 
ihe  medium  yielding  to  it  comes  round  in  a  circle  to  the  i>arts  which 
the  botly  leaves  ;  and  as  often  as  the  body  returns  to  the  first  place,  the 
medium  will  be  driven  from  the  place  it  came  roimd  to,  and  return  to 
its  original  place.  And  though  the  tremulous  body  be  not  firm  and 
hard,  but  every  way  flexible,  yet  if  it  continue  of  a  given  magnitude, 
since  it  cannot  impel  the  metlium  by  its  tremors  anywhere  without 
yielding  to  it  somewhere  else,  the  medium  receding  from  the  parts  of 
the  body  where  it  is  pressed  will  always  come  round  in  a  circle  to  the 
parts  that  yield  to  it,* 

**  If  the  first  part  of  this  proposition  was  true,  as  all  particles 
of  air  are  supposed  to  be  set  in  motion  by  every  sound  in  the 
many  directions  in  which  they  He  from  the  sounding  body, 
and,  as  almost  everywhere,  certainly  in  many  places,  there 
arc    xti^Xiy    sounds    constantly    taking    place    at     the    same 


I20  KLLKX   OK   THE 

instant,  these  particles  of  air  would  have  to  go  in  several 
directions  and,  indeed,  often  in  every  conceivable  direction  at 
the  same  instant — a  thing  that  they  certainly  do  not  do.  Or 
else  the  laws  of  sound  would  have  to  be  constantly  suspended; 
and  when  you  rang  a  bell,  or  struck  a  piano,  the  expected 
result  would  materialize  only  when  the  air  surrounding  the 
striking  body  was  not  otherwise  occupied. 

"Case  2  of  the  proposition  is  applied  first  to  an  inelastic 
medium.  But  note  that  Mr.  Newton  says :  *  The  case  is  the  same 
ivith  that  of  a  body  projected  in  any  medium  whatever.  A 
medium  yielding  to  projectiles  does  not  recede  in  injimtum^  but 
luith  a  circular  motion  comes  round  to  the  spaces  which  the  body 
leaves  behind  it.  There/ore  as  often  as  a  tremulous  body  tends 
to  any  part,  the  medium  yielding  to  it  comes  round  in  a  circle  to 
the  parts  ivhich  the  body  leaves  ;  and  as  often  as  the  body  returns 
to  the  first  place,  the  medium  will  be  driven  from  the  place  it 
came  round  to,  and  return  to  its  original  place.  And  though 
the  tremulous  body  be  not  firm  and  hardy  but  every  way  flexible  ^ 
yet  if  if  continue  of  a  given  magnitude,  since  it  cannot  impel 
the  medium  by  its  tremors  anywhere  without  yielding  to  it  some- 
Ik' here  else,  the  medium  receding  from  the  parts  of  the  body 
where  it  is  pressed  will  always  come  round  in  a  circle  to  the 
parts  that  yield  to  it' 

"This  is  the  exact  truth,  and  covers  the  whole  case  of 
sonorous  vibrations.  It  is  hardly  possible  that  it  could  be 
more  forcibly  or  accurately  stated,  and  it  places  Mr.  Newton, 
although  he  did  not  recognize  it,  absolutely  on  the  right  side  in 
sound,  as  well  as  in  light.  For  a  vibrating  is  a  tremulous  body, 
and  admitting  that  such  a  body  cannot  create  a  system  of  con- 


THE  NEW  YCRK 
PUtllC  LIRRART 


A^  :or.  Lt>'X   AND 

i:li.  -  '■  f  •'  ■  •  ».    '.ss 
r 


densati'in- 

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appr-  pr  Ltt 
Had  Mr  :: 
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2«::^r:^--:^ 


Tf'J-i 


'jI.Ij 

MM 

■  >.  f' 

.r     t},.; 

r'  ii 

*''.M 

r*     x'''.' 

j:j.:. 

:>.- 

'■  ','.  / 

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■ « '  - 

I 

THE  BEW  YORK 
PUBLIC  LIBRARY 

Anon.  iUHot  AMa 

1     r                   _L 

^ 

1 

WHISPERINGS    OF   AN   OLD   PINE  123 

densations  and  rarefactions  of  the  air,  for  the  reason  given, 
^projected  in  any  medium  whatever*  there  remains  no  other 
theory  of  sound  but  the  corpuscular,  harmonizing,  as  is  most 
appropriate,  with  Mr.  Newton's  corpuscular  theory  of  light. 
Had  Mr.  Newton  himself  applied  the  reasoning  to  this  theory 
of  sound,  it  would  almost  certainly  have  ended  the  whole 
matter  forever.  Failing  to  do  this,  the  world  could  not  help 
perceiving  that  sound  and  light  are  governed  by  similar  laws, 
and,  obliged  to  quit  Mr.  Newton  as  to  one  of  them  and  led  by 
incompetent  men,  it  blundered  on  the  wrong  side.  But,  as 
Ellen  thinks,  the  mistake  will  be  comparatively  short-lived. 
"  Proposition  44  refers  to  water  in  a  canal,  and  is  unimportant. 

'PROPOsniox  XIA\ — The  Telocity  0/ leaves  is  in  the  subdupUeate  ratio 
of  the  breadths  \jhat  is  in  tJie  ratio  of  square  root"], 

*This  follows  from  the  construction  of  the  following  proposition. 

*  Froi^ositiox  XLVI. — To  find  the  velocity  of  waves, 

*  I^t  a  pendulum  be  constructed,  whose  length  between  the  point  of 
suspension  and  centre  of  oscillation  is  equal  to  the  breadth  of  the 
waves;  and  in  the  time  that  the  pendulum  will  perform  one  single 
oscillation  the  waves  will  advance  forward  nearly  a  space  equal  to  their 
breadth. 

'That  which  I  call  the  breadth  of  the  waves  is  the  transverse  measure 
lying  between  the  deepest  part  of  the  hollows,  or  the  tops  of  the  ridges. 
Let  A  BCD  EH''  (Fig.  7)  represent  the  surface  of  stagnant  water 
ascending  and  descending  in  successive  waves ;  and  let  A,  C,  E,  etc., 
be  the  toj^s  of  the  waves ;  and  let  B,  D,  F,  etc.,  be  the  intermediate 
hollows.  Because  the  motion  of  the  waves  is  carried  on  by  successive 
ascent  and  descent  of  the  water,  so  that  the  parts  thereof,  as  A,  C,  E, 


124  ELLEN   OR  THE 

etc.>  which  are  highest  at  one  time  become  lowest  immediately  after ; 
and  because  the  motive  forCe,  by  which  the  highest  parts  descend  and 
the  lowest  ascend,  is  the  weight  of  the  elevated  water,  that  alternate 
ascent  and  descent  will  be  analogous  to  the  reciprocal  motion  of  the 
water  in  the  canal,  and  observe  the  same  laws  as  to  the  times  of  its 
ascent  and  descent;  and  therefore  (by  Prop.  44)  if  the  distances 
between  the  highest  places  of  the  waves  A,  C,  E,  and  the  lowest  B,  D,  F, 
be  equal  to  twice  the  length  of  any  pendulum,  the  highest  parts  A,  C,  E 
will  become  the  lowest  in  the  time  of  one  oscillation,  and  in  the  time  of 


JD 

Fig.  7. 

another  oscillation  will  ascend  again.  Therefore  between  the  passage 
of  each  wave  the  time  of  two  oscillations  will  intervene ;  that  is,  the 
wave  will  describe  its  breadth  in  the  time  that  the  pendulum  will  oscillate 
twice ;  but  a  pendulum  of  four  times  that  length,  and  which  therefore 
is  equal  to  the  breadth  of  the  waves,  will  just  oscillate  once  in  that  time. 
*CoR.  I.  Therefore  waves  whose  breadth  is  equal  to  3^^  French 
feet  will  advance  through  a  space  equal  to  their  breadth  in  one  second 
of  time  (for  a  pendulum  of  2i\^  French  feet  will  oscillate  in  one  second 
of  time)  ;  and  therefore  in  one  minute  will  go  over  a  space  of  183 J  feet; 
and  in  an  hour  a  space  of  11,000  feet,  nearly. 

*  Cor.  2.  And  the  velocity  of  greater  or  less  waves  will  be  augmented 
or  diminished  in  the  subduplicate  [square  root]  ratio  of  their  breadth. 

*  These  things  are  true  upon  the  supposition  that  the  parts  of  water 
ascend  or  descend  in  a  right  line  ;  but,  in  truth,  that  ascent  and  descent 
is  rather  performed  in  a  circle;  and  therefore  I  propose  the  time 
defined  by  the  proposition  as  only  near  the  truth.* 

'•This   is  a  demonstration   that  water  waves  vary  in  speed 


WHISPERINGS   OF  AN   OLD    PINE 


I 


mih  their  size,  and  of  course  the  h}'pothctical  sound  waves,  if 
like  them,  should  do  the  same.  Water  waves  have  a  maxi- 
mum limit  of  speed  of  about  ^2  feet  a  second  ;  and  they  affect 
the  body  of  the  water  to  only  a  comparatively  slight  depth.  It 
will  be  noticed  that  Mn  Newton  In  this  proposition  correctly 
describes  the  operation  of  water  waves:  *  Because  the  motion 
of  the  ivaves  is  carried  on  bj  snccessive  ascent  and  descent  of 
the  water,  so  that  the  parts  which  arc  highest  at  one  time 
became  lowest  immediately  after;  and  because  the  motive  force  ^ 
by  which  the  highest  parts  descend  and  the  lowest  ascend,  is 
the  iveight  of  the  elevated  water' 

*  pROPosmox*  XLVIL — If  pulses  are  propagated  through  a  fluid ^  the 
several  particles  of  the  fluids  going  and  returning  with  the  shortest 
reciprocal  motion ^  art  always  accelerated  or  retarded  according  to  the 
law  of  the  oscillating  pendulum.     (Fig.  8) 

*  Let  A  H,  BCt  C  D,  etc*,  represent  equal  distances  of  successive  pulses ; 
ABC  the  line  of  direction  of  the  motion  of  the  successive  pulses  propa- 
gated from  A  lo  B ;  E,  F,  G,  three  physical  points  of  the  quiescent 
medium  situated  in  the  right  line  A  C  at  equal  distances  from  each 
other ;  K/,  F/,  G^i^'-,  equal  s[)aces  of  extreme  shortness,  through  which 
those  points  go  and  return  with  a  reciprocal  motion  in  eai  h  vibration ; 
€,  ^^  y,  any  intermediate  places  of  the  same  jjoints  ;  E  F,  Fti,  physical 
lineolae,  or  linear  parts  of  the  medium  lying  between  those  points,  and 
successively  transferreil  into  the  places  €<^,  <^y,  and  f/,/v-  I-et  there 
Ix?  drawn  the  right  line  PS  equal  to  the  right  line  Ya\  Bisect 
the  same  in  O,  and  from  the  centre  O,  with  the  inter\'al  O  P,  describe 
the  circle  SI  Pk  Let  the  whole  lime  of  one  vibration,  with  its  projKir* 
tional  parts,  be  expounded  by  the  whole  circumference  of  this  « ircle 
;ind  it*>  parts,  in  such  sort,  that,  when  any  time  PH  or  PHS//  h  com- 
pleted, if  there  be  let  fall  to  PS  the  perpendicular  H  L  or  hi,  and  there 


..yii. 


126 


ELLEN   OR  THE 


I 


'tt 


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JV.. 


|ii 


\        .'£ 

h 

m         /^ 

'^L 

jf 

L^^ 

be  taken  Ee  equal  to  P  L  or  P/,  the  physical  point  E  may  be  found  in  c. 

A  point,  as  E,  moving  ac- 
cording to  this  law  with  a 
reciprocal  motion,  in  its 
going  from  E  through  c  to 
<r,  and  returning  again 
through  c  to  E,  will  per- 

A.-''    fJ_ :^  form   its  several  vibrations 

with  the  same  degrees  of 
acceleration  and  retarda- 
tion with  those  of  an  oscillating  pendulum.  We 
are  now  to  prove  that  the  several  physical  points 
of  the  medium  will  be  agitated  with  such  a  kind 
of  motion.  Let  us  suppose,  then,  that  a  medium 
hath  such  a  motion  excited  in  it  from  any  cause 
whatsoever,  and  consider  what  will  follow  from 
thence. 

*In  the  circumference  PHS//  let  there  be  taken 
the  equal  arcs  HI,  IK,  or  ///,  tl;  having  the  same 
ratio  to  the  whole  circumference  as  the  equal  right 
lines  E  F,  F  G  have  to  B  C,  the  whole  inter\'al  of 
the  pulses.  Let  fall  the  perpendiculars  I  M,  KN, 
or  /■///,  ^//;  then  because  the  points  E,F,G  are 
successively  agitated  with  like  motions,  and  per- 
form their  entire  vibrations  composed  of  their 
going  and  return,  while  the  pulse  is  transferred 
from  B  to  C  ;  if  P  H  or  PHSA  be  the  time  elapsed 
since  the  beginning  of  the  motion  of  the  point 
E,  then  will  PI  or  P  H  S  /  be  the  time  elapsed  since 
i'»g.  8.  ^j^g  beginning  of  the  motion  of  the  point  F,  and  P  K 

or  THSk  the  time  elapsed  since  the  beginning  of  the  motion  of  the 


\Vinsi»KRlN(;S    OF   AN    OLD    riNE 


127 


therefore  Ec,  F^,  Gy  will  be  respectively  equal   to  PL, 

IPM,  PN,  while   ihe  points  are  going,  and   to  P/,   P///,   P//,  when   the 
|x>mts  arc  returning.     Therefore  €y  or  KG^Gy — Ee  will,  when  the 
|X}iQts  are  going,  be  equal  to  EG — LN,  ainl  in  their  return  ec|ual  to 
EG-|-7ff.     Bui  ey  is  the  breadth  or  expansion  of  the  part  EG  of  the 
medium  in  the  place  cy ;  and  therefore  the   expansion  of   that  part  in 
its  gping  is  to  its  mean  expansion  as  EG^LN  to  EG ;  and  in  its 
return,  as  EG-|-//i  or  EG-f-EN  to  EG.    Therefore  since  LN  is  to  KH  as 
IM  to  the  radius  OP,  and  KH  to  EG  as  the  circumferenre  PHS//P  to 
BC   [by  hypothesis]  ;  that  is,  if  we   [uU  \*  for  the  radius  of  a  circle 
[whose  circumference  is  equal  to  BC  the  inten^al  of  the  pulses,  as  OP 
llo  V    [radii   of   circles  are  as  their  circumferences]  ;  and,  ^A"  afqui\ 
[LN  to  EG   as  IM   to  Vj   the  expansion  of   the  part  EG,  or  of   the 
phpical    point    F  in  the    place   ty,   to   the   mean  expansion   of   the 
[iart  in  its  first  place  EG,  will  be  as  V — ^IM  to  V  in  going,  and 
Lbs  V-fi/w    to   V    in    its    return.      Hence    the    elastic    force    of    the 
[point    F  in  the  place  ey    to  its   mean  elastic  force  in  the  place   EG 

1 


tkaa 


r? — T^mT  to  TT  in  its  going,  and  as  --,  .  ,-  -  to  ,,    in    its    return    [for 
V — IM       V       ,  \-\-im       \  •- 

[the  elastic  force  of  a  gas   is   inversely  as  its  volume].     And  by  the 

[same   reasoning  the  elastic  forces  of  the    iihysical   imints  E  and  G 

f  in  going  are  as  ^     ^     and  ^^    ^^   to    -  ;  and  the  ilifference  of  the 

ifoTces  to  the  mean  elastic  force  of  the  medium  as 


HL— KN 


-^-r       to 


1 


that  is,  as 


HL— KN 


to 


1 


/— VXHU-VXKN+HLXKN        V'  '  VV  V 

[or  as  HI> — KN  to  V  ;  if  we  suppose  (by  reason  of  the  very  short  extent 
[of  the  vibrations)  HE  and  KN  to  be  indefinitely  less  than  the  quan- 
jtily  V,  Therefore  since  the  quantity  V  is  given  [constant],  the  dilTer- 
nrc  vA  the  forces  is  as  HL — KN;  that  is  (because  HL — KN  is 
[^ proportional  to  HK,  and  OM  to  01  or  OP;  and  because  HK  and 
OP  arc  given)  as  OM  ;  that  is,  if  F/be  bisected  in  O,  as  Q<^,     And 


128  ELLEN   OR  THE 

for  the  same  reason  the  difference  of  the  elastic  forces  of  the  physical 
points  c  and  y,  in  the  return  of  the  physical  lineola  cy,  is  as  Q^. 
But  that  difference  (that  is,  the  excess  of  the  elastic  force  of  the  point 
c  above  the  elastic  force  of  the  point  y)  is  the  very  force  by  which  the 
intervening  physical  lineola  cy  of  the  medium  is  accelerated  in  going, 
and  retarded  in  returning;  and  therefore  the  accelerative  force  of 
the  physical  lineola  c  y  is  as  its  distance  from  O,  the  middle  place  of 
the  vibration.  Therefore  (by  prop.  38,  book  i)  the  time  is  rightly 
expounded  by  the  arc  PI ;  and  the  linear  part  of  the  medium  c  y  is 
moved  according  to  the  law  above  mentioned,  that  is,  according  to  the 
law  of  a  pendulum  oscillating ;  and  the  case  is  the  same  of  all  the  linear 
parts  of  which  the  whole  medium  is  compounded. 

*  Cor.  Hence  it  appears  that  the  number  of  the  pulses  propagated  is 
the  same  with  the  number  of  the  vibrations  of  the  tremulous  body,  and 
is  not  multiplied  in  their  progress.  For  the  physical  lineola  cy  as 
soon  as  it  returns  to  its  first  place  is  at  rest ;  neither  will  it  move  again, 
unless  it  receives  a  new  motion  either  from  the  impulse  of  the  tremulous 
body,  or  of  the  pulses  propagated  from  that  body.  As  soon,  therefore, 
as  the  pulses  cease  to  be  propagated  from  the  tremulous  body,  it  will 
return  to  a  state-of  rest,  and  move  no  more.*  " 

**And  how  are  all  these  equations  derived,  Ellen?" 
"The  equation  LN  :  KH::IM  :  OP  is  derived  by  drawing 
a  perpendicular  from  K  to  HL,  at  a  point  that  we  will  call  X, 
and  a  chord  from  K  to  H.  We  would  then  have  tw^o  triangles 
HKX  and  lOM,  whose  corresponding  sides  are  perpendicular 
to  each  other;  for  the  radius  10  bisecting  the  arc  KH  is  per- 
pendicular to  the  chord  of  that  arc,  OM  is  perpendicular  to  HL 
by  construction,  and  IM  being  parallel  to  HL  is  perpendicular 
to  KX.  Therefore  the  triangles  are  similar  and  their  homolo- 
gous sides  proportional. 


WHISPERINGS   OF   AN    OLD    PINE 


129 


"The  equation  LN  :  EG::IM  :  V  is  obtained  by  multiplying 
together  the  corresponding  terms  of  the  two  proportions,  LN  : 
KH::IM  :  OP  and  KH  :  EG:: OP:  V,  and  dividing  both  terms 
of  the  first  ratio  by  KH»  and  both  terms  of  the  second  ratio  by 
OP,  In  doing  this  Mr.  Newton,  following  the  usual  custom  in 
the  differential  calculus  ol  neglecting  small  differences,  assumes 
that  KH,  which  represents  a  chord  in  the  first  proportion,  is 
equal  to  KH  representing  an  arc  in  the  second*  which  is  not 
I  rue. 

**  It  will  be  perceived  here  that  Mr.  Newton  speaks  of  the 
space  between  E  and  G  (which  includes  tbe  particle  F  and  the 
50-caIled  lineolae  EF  and  FG)  and  F,  which  he  here  calls  a 
pointi  as  synonymous,  —  not  an  accurate  manner  of  descrip- 
tion, or  indeed  an  allowable  one,  although  in  harmony  with  the 
iiK'thods  used  in  calculus.  For  i(  the  lineolae  are  something, 
ihcy  and  tlie  point  F  can  not  be  the  same  as  the  point  F,  and 
if  they  are  nothing  they  can  not  expand  and  contract. 

•*Thc  proportion  LN  :  EG  ::  IM  :  V  becomes  by  division  EG 
~LN:EG::V-IM:V  and  by  composition  EG+LN:EG::V+ 
IM:V.  In  the  last  two  proportions  the  first  terms  represent 
the  volumes  of  equal  portions  of  air  at  <y  when  the  particles 
are  going  and  returning  respectively  and  EG  represents  the 
volume  of  the  same  quantity  of  air  at  normal  pressure, 

"To  obtain  the  expression  for  the  difference  of  the  elastic 
forces  at  E  and  G,  let  the  elastic  force  of  the  air  in 
the  place  t  be  represented  by  (E),  the  elastic  force  of  the 
air  in  the  place  y  be  represented  by  (G)  and  the  mean  elastic 

I 


force  of  undisturbed  air  by  (M).     Then  (E)  :  (M)  :: 


V-HL 


I30  ELLEN   OR  THE 

:  — ,  also  (G)  :  (M)  ::      :    — .      If  we  subtract  the  ratios 

V  V— KN      V 

in  the  second  proportion  from  the  corresponding  ratios  in  the 
first,  we  have  (E)-(G)  :  (M)  ::  ^_L__,_-L_^  =  y-  °''  P^""' 

,       ■         .u         u.      »•  V-KN-V+HL  I       . 

formmg     the    subtracUon,      -^^--hl)  (V-KN)      =     V     == 

W^VXKn'^vI^IiT-FH LXKN  =  V  • ""' '' "^  ^^P ""^ "^'^^ 
XKN  and  HLXKN,  as  they  are  small  compared  with  VV,  and 
then  clear  of  fractions  we  have  (E)-(G)  :  (M)::HL-KN  :  V. 

"Here  again  Mr.  Newton  throws  out  certain  small  quantities, 
namely,  VXHL,  VXKN  and  HLXKN  in  the  denominator  of 
the  above  fraction,  on  the  plea  that  they  are  very  small  and 
therefore  omitting  them  would  not  very  much  affect  the  result 
At  the  same  time  he  preserves  in  the  numerator  the  expression 
HL  — KN  which  of  necessity  must  be  less  than  the  quantities 
thrown  out,  and  indeed  less  than  VXHL  or  VXKN  separately, 
and  might  be  less  than  HLXKN.  Certainly  there  can  hardly 
be  a  smaller  quantity  than  the  hypothetical  difference  between 
the  displacements  of  two  contiguous  particles  in  these  supposed 
oscillations.  This  illustrates  the  inaccurate  character  of  much 
of  the  mathematics  which  is  employed  in  such  demonstrations. 

**  Again,  (IC)  — (G)  :  the  mean  elastic  force ::HL—KN  :  V,  in 
which,  since  the  mean  clastic  force  and  V  are  both  constant, 
(K)-(G)  varies  as  HL-KX.  Hut  HL-KN  :  HK::OM  :  01 
(by  similar  triangles),  in  which  HK  and  OI  are  in  a  constant 
ratio ;  therefore  HL— KX  varies  as  OM,  or  (E)  — (G)  varies  as 
OM  or  n</>. 


WinsrERINGS   OK  AN    OLD    PINE 


131 


"This  is  Mr.  Newton's  most  important  theorem  on  sound. 
There  follows: 

•  PlRuposiTloN  XIAllL — Hie  vehdHts  of  pulses  propagakd  in  an  elastic 
fluid  art  in  a  raiitf  e^mpounded  iff  the  subduplicate  ratio  of  the 
fltisiic  foree  directly ^  and  the  subdupiicate  ratio  of  the  density 
iftversefy:  supposing  t/t€  elastic  force  of  the  fluid  to  be  proportional  to 
its  condensation* 

•Cask  l-  If  the  mediums  be  homogeneous,  and  the  distances  of  the 
pulses  in  those  mediums  be  equil  amongst  themselves,  but  the  motion 
in  one  medium  is  more  intense  than  in  the  other,  the  contractions  and 
dilatations  of  the  correspondent  parts  will  be  as  those  motions :  not 
that  this  proportion  is  perfectly  accurate.  However,  if  the  contractions 
and  dilatations  are  not  exceedingly  intense,  the  error  will  not  be  sen- 
sible ;  and  therefore  this  proportion  may  be  considered  as  ph\'sical!y 
exact.  Now  the  motive  clastic  forces  are  as  the  contractions  and 
dilatations ;  and  the  velocities  generated  m  the  same  time  in  equal  parts 
as  the  forces.  Therefore  equal  and  corres|K)nding  parts  of  corre- 
''sponiling  pulses  will  go  and  return  together,  through  spaces  propor- 
tional to  their  contractions  and  dilatations,  with  velocities  that  are  as 
those  spaces;  and  therefore  the  pvilses,  which  in  the  time  of  one  going 
and  returning  advance  fonvards  a  space  equal  to  iheir  breadth,  and  are 
always  succeeding  into  the  places  of  tlie  pulses  that  immediately  go 
before  them,  willj  by  reason  of  the  equality  of  the  distances,  go  forward 
in  lK>ih  mediums  with  equal  velocity. 

*CAsr.  2,  If  the  distances  of  the  pulses  or  their  lengths  are  greater  in 
one  medium  than  in  another,  let  us  suppose  that  the  correspondent 
parts  describe  spaces,  in  going  and  returning,  each  time  proi>ortional  to 
the  breadths  of  the  pulses;  then  will  their  contractions  and  dilatations 
he  c*|ual ;  and  therefore  if  the  mediums  are  homogeneous,  the  motive 
elastic  forcesi  which  agitate  thern  with  a  reciprocal  motion,  will  be  equal 


u^ 


ELLEN   OR  THE 


also.  Now  the  matter  to  be  moved  by  these  forces  is  as  the  breadth  of 
the  pulses ;  anil  the  space  through  which  they  move  every  time  they  go 
and  return  is  in  the  same  ratio.  And,  morem-er,  the  time  of  one  going 
and  returning  is  in  a  ratio  compounded  of  the  subdu|iHcate  ratio  of  the 
matter,  and  the  subduplicate  ratio  of  the  space  ;  and  therefore  is  a.^  the 
space.  But  the  pulses  advance  a  space  equal  to  their  breadths  in  the 
times  of  going  once  and  returning  once ;  that  is,  they  go  over  spaces 
proportional  to  the  times,  and  therefore  are  equally  swift. 

*  Case  3.  And  therefore  in  mediums  of  equal  density  ami  elastic 
force,  all  the  pulses  are  equally  swift.  Now  if  the  density  or  the  elastic 
force  of  the  raetlium  were  augmented,  then,  because  the  motive  force  is 
increased  in  the  ratio  of  the  elastic  force,  and  the  matter  to  be  moved  is 
increased  in  the  ratio  of  the  density,  the  time  which  is  necessary  for 
producing  the  same  motion  as  before  will  be  increased  in  the  subdupli- 
cate  ratio  of  the  density,  and  will  be  diminished  in  the  subduplicate 
ratio  of  the  elastic  force.  And  therefore  the  velocity  of  the  pulses  will 
be  in  a  ratio  compounded  of  the  subduplicate  ratio  [ratio  of  s(iuare 
root]  of  the  density  of  the  medium  inversely,  and  the  subduplicate  ratio 
of  the  elastic  force  directly.  This  proposition  will  be  made  more  i:lear 
from  the  construction  of  the  following  problem/ 

*  pRUPusnujN  XLIX. — The  density  and  ehis tic  font  r/  a  medium  i^eifi^ 
given f  to  find  the  velocity  of  the  pulses, 

'Suppose  the  medium  to  be  pressed  by  an  incumbent  weight  after 
the  manner  of  our  air;  and  let  A  be  the  height  of  a  homogeneous 
medium,  whose  weight  is  equal  to  the  incumbent  weight,  and  whose 
density  is  the  same  with  the  density  of  the  compressed  medium  in 
w^hich  the  pulses  are  propagated.  Suppose  a  pendulum  to  be  con* 
structed  whose  length  between  the  point  of  suspension  and  the  centre 
of  oscillation  is  A  :  and  in  the  time  in  which  that  pendulum  will  perform 
one  entire  oscillation  composed  of  its  going  and  returning,  the  pulse 


-^-^- 


^^ 


wmsrERixus  uf  an  old  i*ine 


will  be  propagated  right  onwards  through  a  space  equal  to  the  c  ircum- 
ference  of  a  circle  described  with  the  radius  A. 

*  For,  letting  those  things  stand  which  were  constructed  in  ]>rop.  47, 
if  any  physical  line,  as  EF  (Fig.  8),  ilescribing  the  space  PS  in 
each  vibration,  be  acted  on  in  the  extremities  P  and  S  of  ever)'  going 
and  return  that  it  makes  by  an  elastic  force  that  is  equal  to  its  weight, 
it  will  perform  its  several  vibrations  in  the  time  in  which  the  same 
might  oscillate  in  a  cycloid  whose  w^hole  perimeter  is  equal  to  the  length 
1*S;  and  that  because  etiiial  forces  will  impel  equal  coqmscles  through 
cviual  spaces  in  the  same  or  etpial  times.  Therefore  since  the  times  of 
the  oscillations  are  in  the  snbdupHcate  ratio  of  the  lengths  of  the  pen- 
dulums [as  proved  in  mechanics],  and  the  length  of  the  pendulum  is 
;<pial  to  half  the  arc  of  the  whole  cycloid,  the  time  of  one  vibration 
jirould  be  to  the  time  of  the  oscillation  of  a  pendulum  whotse  length  h 
I  ill  the  subduplicate  ratio  of  the  length  H  PS  or  PO  to  the  length  A. 
But  the  elastic  force  with  which  the  ph>'sical  lineola  EG  is  urged,  when 
it  is  found  in  its  extreme  places  P,  S,  was  (in  the  demonstration  of 
Prop,  47)  to  its  whole  elastic  force  as  HL — KN  to  V,  that  is  (since  the 
point  K  now  falls  upon  P),  as  HK  to  V  [since  sine  (HL)  and  chord 
(UK)  of  a  very  small  arc  may  be  considered  equal  to  each  other  and 
KN^^O]  :  and  all  that  force,  or,  which  is  the  same  things  the  incum- 
bent weight  by  which  the  lineola  EG  is  compressed,  is  to  the  weight 
of  the  hneola  as  the  altitude  A  of  the  incumbent  weight  to  EG  the 
length  of  the  lineola  [see  hyix)thesis]  j  and  therefore,  ex  aequo^  the 
force  with  which  the  lineola  EG  is  urged  in  the  places  P  and  S  is  to 
the  weight  of  that  lineola  as  HKxA  to  V  x  EG  [multiplying  tlrst  and 
last  i^roportions  together  and  reducing]  ;  or  as  PO  x  A  to  \^';  because 
HK  was  to  EG  as  PO  to  V  [similar  arcs  are  as  their  radii].  Therefore 
since  tJie  times  in  which  equal  bodies  are  impelled  through  equal  spaces 
are  reci[)rocally  in  the  subiuplicate  ratio  of  the  forces  [as  proved  in 
mechanics],   the   time  of   one  vibration,  produced  by  the  action  of 


136  ELLEN   OR  THE 

that  elastic  force,  will  be  to  the  time  of  a  vibration,  produced  by  the 
impulse  of  the  weight  in  a  subduplicate  ratio  of  VV  to  PO  X  A,  and 
therefore  to  the  time  of  the  oscillation  of  a  pendulum  whose  length  is  A 
in  the  subduplicate  ratio  of  VV  to  PO  X  A,  and  the  subduplicate  ratio  of 
PO  to  A  conjunctly  [multiply  the  last  proportion  by  the  following  and 
reduce  :  time  of  a  vibration  of  EG  due  to  its  weight  :  time  of  vibration 
of  a  pendulum  of  length  A ::  y^OP  :  y'A]  ;  that  is,  in  the  entire  ratio  of 
V  to  A.  But  in  the  time  of  one  vibration  composed  of  the  going  and 
returning  of  the  pendulum,  the  pulse  will  be  propagated  right  onwards 
through  a  s])ace  equal  to  its  breadth  BC.  Therefore  the  time  in 
which  a  pulse  runs  over  the  space  BC  is  to  the  time  of  one  oscilla- 
tion coini)ose(l  of  the  going  and  returning  of  the  pendulum  as  V  to  A, 
that  is,  as  BC  to  the  circumference  of  a  circle  whose  radius  is  A  [cir- 
cumferences of  circles  are  as  their  radii].  But  the  time  in  which  the 
jmlse  will  run  over  the  space  BC  is  to  the  time  in  which  it  will  run  over 
a  length  equal  to  that  circumference  in  the  same  ratio ;  and  therefore 
in  the  time  of  such  an  oscillation  the  pulse  will  run  over  a  length  equal 
to  that  ( ircumference. 

'Cor.  I.  The  velocity  of  the  pulses  is  equal  to  that  which  heavy 
bodies  acquire  by  falling  with  an  eijually  accelerated  motion,  and  in 
their  fall  describing  half  the  altitude  A.  For  the  pulse  will,  in  the  time 
of  this  fall,  supposing  it  to  move  with  the  velocity  acquired  by  that  fall, 
run  over  a  space  that  will  be  equal  to  the  whole  altitude  A ;  and 
therefore  in  the  time  of  one  oscillation  composed  of  one  going  and 
return,  will  go  over  a  space  equal  to  the  circumference  of  a  circle 
described  with  the  radius  A  ;  for  the  time  of  the  fall  is  to  the  time  of 
oscillation  as  the  radius  of  a  circle  to  its  circumference. 

*C()K.  2.  Therefore  since  that  altitude  A  is  as  the  elastic  force  of 
'Jie  fluid  directly,  and  the  density  of  the  same  inversely,  the  velocity  of 
.he  i)ulses  will  be  in  a  ratio  compounded  of  the  subduplicate  ratio  of  the 
density  inversely,  and  the  subduplicate  ratio  of  the  elastic  force 
directly. 


WlitSfERINGS    OF   AN    OIJJ    liNE 
^ — i'  pROhisnros  L. — Tt*  fuhi  flu  distances  t*/  the  ffulses^ 


m 


'I*€t  the  mimber  of  the  vibrations  of  the  body,  by  whose  tremor  the 
fmlses  are   |>rodiiced,  be  foond   lo  any  given   time.     By  that  number 
idivide  the  space  which  a  pulse  caii  go  over  in  the  same  time,  and  the 
[.fiart  found  will  be  the  breadth  of  one  pulse* 

*SCHOuuM.  The  last  propositions  respect  the  motions  of  light  and 
tincls-  For  since  light  is  propagated  m  right  lines,  it  is  certain  that  it 
Icannot  consist  in  action  alone  (by  prop.  41  and  42).  As  to  sounds, 
pince  they  arise  from  tremulous  bodies,  they  can  be  nothing  else  but 
I  pulses  of  the  air  propagated  through  it  (by  pro|>.  43).  And  this  is  con- 
['firmeil  by  the  tremors,  which  sounds,  if  they  be  loud  and  deep,  excite 
the  bodies  near  them,  as  we  experience  in  the  sound  of  drums.  For 
^tjuick  and  short  tremors  are  less  easily  excited.  Hut  it  is  well  known, 
that  any  sounds,  falling  upon  strings  in  unison  with  the  sonorous  ladies, 
ptJtcite  tremors  iti  those  strings*  This  is  also  confirmed  from  the 
velocity  of  sounds.     For  ^iince  the  specific  gravities  of  rain  water  and 

I  quicksilver  are  to  one  another  as  about  i  to  135,  and  when  the  mercury 
in  ihc  barometer  is  at  the  height  of  30  inches  of  our  measure,  the  spe- 
cific gravities  of  the  air  and  of  rain  water  are  to  one  another  as  al>out  i 
!o  K70  :  therefore  the  specific  gravity  of  air  and  quicksilver  are  lo  each 
ether  as  i  to  11,890.     'llierefore  when  the  height  of  the  quicksilver  is 
hX  50  inches,  a  height  of  uniform  air,  whose  weight  would  be  sufficient 
to  cora|>ress  our  air  to  the  density  we  find  it  to  be  of,  must  be  e^iual  to 
356,700  inches  or  29,725  feet  of  our  measure.     And  this  is  that  very 
height  of  the  medium,  which  1  have  called  A  in  the  construction  of  the 
foregoing  proposition.     A  circle  whose  radius  is  29,725  feet  is  186,768 
fleet  in  circumference.     And  since  a  pendulum  39 J^  inches   in  length 
[tromplctes  one  oscillation,  composed  of  its  going  and  return,  in  two 
econds  of  time,  as  is  commonly  known  ;   it  follows  that  a  pendulum 
JJ15  feel  or  356*700  inches  in  len^h  wdl  perform  a  like  oscillation 


Mlmiifetfi^ 


138  ELLEN   OR  THE 

in  190J  seconds.  Therefore  in  that  time  a  sound  will  go  right  onwards 
186,768  feet,  and  therefore  in  one  second  979  feet. 

'  But  in  this  computation  we  have  made  no  allowance  for  the  crassi- 
tude of  the  solid  particles  of  the  air,  by  which  the  sound  is  propagated 
instantaneously.  Because  the  weight  of  air  is  to  the  weight  of  water  as 
I  to  870,  and  because  salts  are  almost  twice  as  dense  as  water ;  if  the 
particles  of  air  are  supposed  to  be  of  near^he  same  density  as  those  of 
water  or  salt,  and  the  rarity  of  the  air  arises  from  the  intervals  of  the 
particles ;  the  diameter  of  one  particle  of  air  will  be  to  the  interval 
between  the  centers  of  the  particles,  as  i  to  about  9  or  10,  and  to  the 
interval  between  the  particles  themselves  as  i  to  8  or  9.  Therefore  to 
979  feet,  which,  according  to  the  above  calculation,  a  sound  will 
advance  fonvard  in  one  second  of  time,  we  may  add  ^  J^,  or  about  109 
feet,  to  compensate  for  the  crassitude  of  the  particles  of  the  air :  and 
then  a  sound  will  go  forward  about  1088  feet  in  one  second  of  time. 

'  Moreover,  the  vapors  floating  in  the  air,  being  of  another  spring, 
and  a  different  tone,  will  hardly,  if  at  all,  partake  of  the  motion  of  the 
true  air  in  which  the  sounds  are  propagated.  Now  if  these  vapors 
remain  unmoved,  that  motion  will  be  propagated  the  swifter  through 
the  true  air  alone,  and  that  in  the  subduplicate  ratio  of  the  defect  of 
the  matter.  So  if  the  atmosphere  consist  of  ten  parts  of  tnie  air  and 
one  i)art  of  vapors,  the  motion  of  sounds  will  be  swifter  in  the  sub- 
duplicate  ratio  of  1 1  to  10,  or  very  nearly  in  the  entire  ratio  of  21  to  20, 
than  if  it  Were  propagated  through  eleven  parts  of  true  air :  and  there- 
fore the  motion  of  sounds  above  discovered  must  be  increased  in  that 
ratio.  By  this  means  the  sound  will  pass  through  1142  feet  in  one 
second  of  time. 

'These  things  will  be  found  true  in  spring  and  autumn,  when  the  air 
is  rarefied  by  the  gentle  warmth  of  those  seasons,  and  by  that  means 
its  elastic  force  becomes  somewhat  more  intense.  But  in  winter,  when 
the  air  is  condensed  by  the  cold,  and   its  elastic  force   is  somewhat 


WHTSPERTNCS    OF  AN    OLD   PINE 


»59 


remitted,  the  motion  of  sounds  will  be  slower  in  a  subduplicate  ratio  of 
the  densily ;  and  on  the  other  hnnd,  swifter  in  the  summer. 

'  Now  by  experiments  it  actually  appears  that  sounds  do  really 
advance  in  one  second  of  time  about  1142  feet  of  EngUsh  measure,  or 
1070  feet  of  French  measure. 

'The  velocity  of  soumls  being  known,  the  intervals  of  the  pulses  arc 
known  also.  For  M.  Sauveur,  by  some  experiments  that  he  made, 
found  that  an  open  pipe  about  five  Paris  feet  in  length,  gives  a  sound 
of  the  same  tone  with  a  viol -string  that  vibrates  a  hundred  times  in  one 
second.  Therefore  there  are  near  100  pulses  in  a  space  of  1070  Paris 
feel,  which  a  sound  runs  over  in  a  second  of  time ;  and  therefore  one 
pulse  fills  up  a  space  of  about  lo^^  Paris  feet,  that  is,  about  twice  the 
length  of  the  pipe-  From  whence  it  is  probable,  that  the  breadths  of 
the  pulses,  in  all  sounds  made  in  open  pipes,  are  equal  to  twice  the 
length  of  the  pipes. 

*  Moreover,  from  the  corollary  of  prop.  47,  appears  the  reason,  why 
the  sounds  immediately  cease  with  the  motion  of  the  sonorous  body, 
and  why  they  arc  heard  no  longer  when  we  are  at  a  great  distance  from 
the  sonorous  bodies,  than  when  we  are  very  near  thera*  And  besides, 
from  the  foregoing  principles  it  plainly  appears  how  it  comes  to  pass 
that  sounds  are  so  mightily  increased  in  speaking-trumpets.  For  all 
reciprocal  motion  uses  to  be  increased  by  the  generating  cause  at  each 
return.  And  in  tubes  hindering  the  dilatation  of  the  sounds,  the  motion 
decays  more  slowly,  and  recurs  more  forcibly ;  and  therefore  is  the 
more  increased  by  the  new  motion  impressed  at  each  return.  And 
these  are  the  principal  phenomena  of  sounds.' 

**Ia  this  scholium,  which  Ellen  has  preferred  to  give  in  full 
before  criticism,  it  will  be  noticed  that  Mr.  Newton  says  that 
sounds,  since  they  arise  from  tremulous  bodies,  can  be  nothing 
else  but  pulses  of  the  air  propagated  through  it.     This  is  a  bold 


140  ELLEN   OR  THE 

Statement,  but  not  true.  If  it  was  a  self-evident  truth  it  would 
need  no  confirmation;  but  perceiving  its  unreliability  Mr. 
Newton  adds:  'And  this  is  confirmed  by  the  tremors/  etc.; 
and  further:  *This  is  also  confirmed  by  the  velocity  of  sound/ 
which  is  also  an  error.  For  Mr.  Newton's  theoretical  velocity 
does  not  agree  with  that  of  experiment,  and  to  make  it 
agree  he  makes  another  assumption  that  the  sound  passes 
through  the  air  particles  themselves  instantaneously,  and  also 
that  these  particles  occupy  about  one-ninth  of  the  space.  It  is, 
then,  with  these  hypotheses  added,  that  the  first  statement  is 
confirmed  by  the  velocity  of  sound,  but  these  hypotheses  have 
been  shown  to  be  untrue  and  have  been  entirely  abandoned. 

"Chambers'  Encyclopcedia  says: 

'  Newton  was  the  first  who  attempted  to  deduce  from  mechanical 
principles  the  velocity  of  sound,  but  only  for  the  particular  case  in 
which  each  particle  of  air,  in  the  path  of  the  sound,  is  supposed  to 
move  backwards  and  forwards  according  to  the  same  law  as  the  bob  of 
a  pendulum.  He  showed  that  this  species  of  motion  is  consistent  with 
the  elastic  properties  of  air,  as  given  by  Boyle's  or  Mariotte*s  Law,  viz., 
that  the  pressure  of  air  is  proportional  to  its  density.  The  velocity  of 
sound  in  this  case  is  of  course  to  be  found  from  the  time  which  elapses 
between  the  commencement  of  the  motion  of  any  one  particle  of  air, 
and  that  of  another  at  a  given  distance  from  it,  in  the  direction  in  which 
the  sound  is  moving.  The  numerical  result  deduced  by  Newton  with 
the  then  received  experimental  data  for  the  compressibility  of  air,  was 
979  feet  per  second.  This  investigation  was  very  defective,  applying, 
in  fact,  solely  to  the  special  case  of  a  pure  musical  note,  continually 
propagated  without  lateral  divergence;  yet  the  solution  obtained  by 
Lagrange  from  a  complete  analysis  of  the  question,  gave  precisely  the 
same  mathematical  result. 


WHISPERINGS   OF  AN    OLD    PINE 


MT 


•But,  by  direct  roeasuiements,  carefully  made,  by  observing  at  night 
the  intcrv,il  which  elapses  between  the  flash  and  the  report  of  a  cannon 
Ml  a  known  distance,  the  velocity  of  sound  has  been  fotind  to  be  con- 
fidenibly  greater — in  fact,  about  1090  feet  per  second,  at  the  tempera- 
ture of  freezing  water, 

•Newton  seeks  for  the  cause  of  this  discrepancy  bet^^en  theory  and 
obaen-ation  in  the  idea  that  the  size  of  the  particles  of  air  is  finite  com- 
parctl  with  their  mutual  distance;  and  that  sonnd  is  instantaneously 
projiagated  through  the  particles  themselves.  Thus,  supposing  the 
particles  *to  have  a  diameter  one-ninth  of  the  distance  between  them,  we 
must  add  one-ninth  to  the  space  traveletl  by  sound  in  a  second,  i.  e.,  to 
the  velocity — which  will  thus  be  brought  up  to  (i  +  ^)  979  feet  =  1088 
itct  nearly,  which  is  a  very  close  approximation  to  the  actual  value 

rcn  above. 

'This  is  not  one  of  Newton's  happiest  conjectures — for,  independent 
of  the  fact  that  such  an  assumption  would  limit  definitely  the  amount  of 
compression  which  air  could  unilergo,  and,  besides,  is  quite  inconsistent 
with  the  truth  of  Boyle's  law  for  even  moderate  pressures,  it  would 
result  from  it  that  sound  should  travel  slower  in  rarefied,  and  quicker  in 
condensed  air.  Now,  ecperiment  shows  that  the  velocity  of  sound  is 
jmaffected  by  the  height  of  the  barometer  ;  and,  mdeed,  it  is  easy  to  see 

at  this  ought  to  be  the  case.  For  in  condensed  air  the  pressures  are 
increased  proportionally  to  the  increase  of  condensation,  and  the  mass 
of  a  given  bulk  of  air  is  increased  in  the  same  proportion.  Hence,  in  a 
sound  wave  in  condensed  air,  the  forces  and  the  masses  are  increased 
proportionally,  and  thus  the  rate  of  motion  is  unaltered.  But  the  tem- 
perature of  the  air  Aas  an  effect  on  sound,  since  we  know  that  the 
elastic  force  is  increased  by  heat,  even  when  the  density  is  not  dimin- 
ished ;  and  therefore  the  velocity  of  sound  increases  with  the  tempera- 
ture at  the  rate  of  about  4j4  feet  per  Fahrenheit  degree,  as  is  found 
by  experiment 


^& 


^"'^ 


142  ELLEN   OR  THE 

Newton's  explanation  of  the  discrepancy  between  theory  and  experi- 
ment being  thus  set  aside,  various  suggestions  were  made  to  account  for 
it;  some,  among  whom  was  Euler,  imagining  that  the  mathematical 
methods  employed^  being  only  approximate,  involved  a  serious  error/ 


WHISPERINGS   OF  AN   OLD    DINE 


HS 


^^PROPOSITION  47  is  the    one    upon  which  has    mainly 

*  rested  this  theory  of  sound.  Indeed,  if  Mr.  Airy,  for 
^ome  time  astronomer  royal  in  England,  is  correct,  the  theory 
in  its  present  form  originated  in  these  propositions  of  Mr,  New- 
ton. Thus  Mr.  Airy  in  his  book  on  'Sound  and  Atmospheric 
"Vibrations,*  says: 

*The  idea  of  a  wave  appears  to  have  been  first  entertained  by  New- 
ton, and  was  certainly  first  developed  by  him,  for  the  purpose  of 
explaining  what  till  then  was  totally  obscure,  the  transmission  of  Sound 
through  Air;  it  is  worked  out  in  the  third  book  of  the  "  Principia/*  * 

'*It  will  be  seen  that  proposition  47  is  founded  upon  an 
hypothesis.  *//*  pulses  are  propagated  through  a  fluid/  etc., 
and  this  hypothesis  is  nowhere  proven.  It  iS|  too,  included  in 
the  hypothesis  that  the  particles  go  and  return  in  the  shortest 
possible  motion.  And  this  would  appear  to  be  done  so  as  to 
make  the  chord  and  arc  as  nearly  equal  as  possible,  the 
demonstration  of  the  proposition  depending  upon  this  impos- 
sible equality. 

**  Newton  on  several  occasions  in  his  *  Principia'  remarks  that 
his  principles  are  mathematical,  not  philosophical.  Thus  he 
says  at  the  beginning  of  book  3 : 

*  In  the  preceding  books  I  have  laid  down  the  principles  of  philoso- 
phy; principles,  not  philosophical,  but  mathematical;  such,  to  wit,  as 
we  amy  build  our  reasonings  upon  in  philosophical  inquiries/ 


14^  ELLEN    OR  THE 

"And  after  proving  in  proposition  23,  book  2,  that  'particles 
flying  each  other  with  forces  that  are  reciprocally  proportional 
to  the  distances  of  their  centers,  compose  an  elastic  fluid  whose 
density  is  as  the  compression/  he  adds,  in  the  scholium : 

'  But  whether  elastic  fluids  do  really  consist  of  particles  so  repelling 
each  other,  is  a  physical  question.  We  have  here  demonstrated  math- 
ematically the  property  of  fluids  consisting  of  particles  of  this  kind,  that 
hence  philosophers  may  take  occasion  to  discuss  that  question.* 

"All  of  this  is  equally  applicable  to  this  proposition. 
Whether  pulses  are  propagated  through  a  fluid  whose  particles 
go  and  return  with  the  shortest  reciprocal  motion,  is  a  physical 
question,  which  Mr.  Newton  leaves  for  others  to  discuss. 

"But  this  is  the  fundamental  question  in  this  discussion,  and 
any  propositions  founded  upon  it  as  an  hypothesis,  however 
interesting  they  may  have  been  to  Mr.  Newton  as  an  exercise 
in  mathematics,  are  not  of  practical  importance  to  any  one  else. 

"In  the  discussion  following  he  draws  a  right  line  PS  equal 
to  one  of  these  hypothetical  shortest  oscillations,  or  rather  half 
oscillations,  and  with  this  line  as  a  diameter  he  constructs  a 
circle.  Such  a  circle,  of  course,  is  of  infinitesimal  propor- 
tions, and  to  that  extent  of  the  kind  Mr.  Newton  is  looking  for 
where  the  arc  isn't  very  much  longer  than  the  chord. 

"The  proposition  contains  additional  hypotheses,  or  assump- 
tions, as  to  the  nature  of  the  air  and  elastic  force.  He 
assumes  that  the  whole  time  of  one  vibration  with  its  propor- 
tional parts  be  represented  by  the  circumference  of  this  circle 
and  its  parts,  in  such  a  sort  that  it  will  follow  the  law  of  har- 
monic curves,  and  states  that  a  point  moving  according  to  this 


WHISPERINGS   OF   AN    OLD    liNE 


14; 


law  will  perform  its  vibration  as  an  oscillating  [cycloidal] 
pendulum. 

*•  In  the  further  elucidation  of  the  problem,  it  is  assumed  that 
each  particle,  when  struck,  proceeds  in  a  straight  line  in  its 
whole  half  vibration,  and  then  returns  to  rest  to  its  original 
position;  but  it  is  exceedingly  difficult  to  see  how  in  this  man- 
ner It  can  operate  like  a  pendulum  at  all.  For  a  pendulum 
never  performs  thjs  kind  of  an  antic.  Ellen  never  heard  of  a 
pendulum  cycloidal,  or  any  other  kind,  that  operated  in  this 
way.  They  always  oscillate  about  a  centre.  All  well  regu- 
lated penduhims  certainly  do;  nor  can  EUcn  imagine  so  eccen- 
tric a  pendulum  as  to  oscillate  from  one  end  of  its  line  to  the 
other,  return  and  stop.  But  the  essential  feature  in  this  prop- 
osition that  each  particle  should  make  its  complete  oscillation 
in  the  time  of  a  so-called  wave  length  inckides  such  extraor- 
dinary' action  by  each  of  these  particles,  which,  if  possible  under 
Mr.  Newton's  theory  of  gases,  would  be  impossible  by  the 
kinetic  theory  of  gases. 

•*Mr.  Newton  demonstrated  in  proposition  43  that  a 
system  of  waves  could  not  be  formed  in  a  fluid  medium. 
Now  he  considers  what  would  be  the  effect  and  action 
of  such  a  system  supposing  that  they  could  be  formed. 
This,  as  Ellen  thinks,  is  an  entirely  superfluous  endeavor. 
But  as  this  proposition  has  been  accepted  as  valuable 
by  that  class  of  scientists  who  look  to  authority  for  their 
knowledge,  and  who  have  so  great  a  lack  of  penetration 
as  to  accept  or  treat  a  demonstration  founded  upon  an  hypo- 
thesis  as  if  it  was  the  demonstration  of  the  hypothesis,  so  thai 
the   proposition    has    been   very    generally  used    to    support 


148  ELLEN   OR  THE 

the  undulatory  theory,  it  may  be  worth  while  to  analyze  its 
character. 

"In  the  first  place  Mr.  Newton  assumes  the  elastic  force  of 
air  to  consist  of  a  repellant  force  between  the  particles.  This 
is,  of  course,  in  direct  antagonism  to  the  dynamic  hypothesis, 
or  the  kinetic  theory  of  gases,  so  called,  at  the  present  time 
very  generally  entertained  by  scientists,  but  not  at  all 
by  Mr.  Newton.  For  by  the  kinctit  theory  all  the  particles 
of  air  arc  always  in  motion,  although  the  direction  of 
that  motion  depends  entirely  upon  the  nature  of  the 
last  contact  which  the  particle  made;  and  by  the  kinetic 
theory,  again,  the  number  of  particles  is  practically  infinite,  and 
they  are  moving  in  all  directions.  This  being  so,  it  is  impos- 
sible to  see  how  Mr.  Newton's  proposition  can  be  used  at  all 
by  those  who  accept  the  kinetic  theory  of  gases.  For 
the  proposition  is  founded  upon  the  idea  of  quiescent  air, 
and  can  only  work  where  there  is  quiescent  air;  but  as  practi- 
cally there  is  never  quiescent  air,  whatever  hypothesis  is 
accepted  to  explain  elastic  force,  the  demonstration  and  the 
theory  it  is  intended  to  uphold  arc  not  worth  the  paper  they 
arc  written  on,  although  assuming  the  kinetic  theory  of  gases 
the  absurdities  of  the  theory  arc  infinitely  increased. 

"  By  the  kinetic  theory  the  average  mean  speed  of  the  par- 
ticles of  air  is,  according  to  Ganot,  about  1590  feet  per  second. 
Ganot  further  says : 

'  In  a  gas  the  velocities  of  the  particles  are  unequal ;  since,  even  sup- 
posing that  they  were  all  originally  the  same,  it  is  not  difficult  to  see 
that  they  would  soon  alter.  For  imagine  a  particle  to  be  moving  par- 
allel to  one  side,  and  to  be  struck  centrically  by  another  moving  at  right 


WHISPERINGS   OF  AN   OLD   PINE 


h4 


angles  to  the  direction  of  its  motion,  the  particle  struck  would  proceed 
on  its  new  path  with  increased  velocity,  while  the  striking  particle  would 
rebound  in  a  different  direction  with  a  smaller  velocity. 

'Notwithstanding  the  accidental  character  of  the  velocity  of  any  indi- 
vidual particle  in  such  a  mass  of  gas  as  we  have  been  considering^  there 
will,  at  any  one  given  time,  be  a  certain  average  distribution  of  veloci- 
ties. Now,  from  considerations  based  on  the  theory  of  probabilities, 
Maxwell  inferred  that  some  velocities  will  be  more  probable  than  others 
— ^ihat  there  will,  indeed,  be  one  velocity  which  is  more  probable  than 
any  other.  This  Is  called  the  most  probable  ve/acity.  The  tnean  velocity 
of  the  particle,  as  deduced  above,  is  not  this,  nor  is  it  the  same  as  the 
arithmetical  mean  of  all  the  velocities  j  it  may  be  defined  to  be  that 
Telocity  which,  if  all  the  molecules  possessed  it,  would  give  rise  lo  the 
same  mean  energy  of  the  molecular  impacts  against  the  side  as  that 
which  actually  exists.  This  mean  velocity  is  about  ^^  greater  than  the 
arithmetical  mean  velocity,  and  is  \  that  of  the  most  probable  single 
velocity. 

*  Theoretical  as  well  as  experimental  observations  render  it  possible 
to  determine  with  great  probability  the  length  of  the  path  which  one 
molecule  of  a  gas  traverses  before  it  encounters  another,  which  is  known 
as  i!i\Q  free  path.  This  is  not  a  constant  number  in  one  and  the  same 
gas ;  that  is,  the  paths  which  the  molecules  travel  between  two  impacts 
arc  Dot  equal,  and  the  average  of  these  is  known  as  the  mean  free  path* 
The  length  of  this  depends  on  the  number  of  molecules  in  unit  volume 
of  a  gas,  being  inversely  as  the  density ;  for  it  is  obvious  that  as  the 
density  increases  the  number  of  raolecoles  increases  also,  and  therewith 
the  path  w^hich  one  molecule  travels  before  it  meets  another  will  be  so 
much  the  smaller.  The  mean  free  path  in  different  gases  will  be 
shorter  the  larger  are  the  molecules.  In  nitrogen  measured  under 
standard  conditions  it  has  been  determined  to  be  98.6^1/1  (micromilli- 
nietres),  in  hydrogen  185.5,  and  in  carbonic  acid  68^1/1.    The  frequency 


ISO  ELLEN    OR   THE 

of  the  impacts  has  also  been  determined ;  in  the  case  of  hydrogen  this 
is  9,480  miUions,  and  of  nitrogen  and  air  8,000  millions  per  second.' 

**It  is  further  assumed  in  this  theory  that  the  molecules 
themselves  fill  only  about  a  four-thousandth  part  of  the  whole 
space  containing  them. 

•'Mr.  O.  l'..  Meyer  in  *The  Kinetic  Theory  of  Gases,*  pub- 
lished by  him,  and  one  of  the  most  complete  and  popular  works 
upon  this  subject,  says : 

'When  we  develop  the  theory  of  sound  according  to  the  kinetic 
hypothesis  we  have  also  to  consider  two  sorts  of  motion  which  exist 
without  disturbing  each  other.  In  addition  to  the  molecular  motion 
which  is  present  even  in  a  gas  at  rest  there  are  the  to-and-fro  motions 
which  constitute  the  vibrations  of  sound.  The  latter  motions  spread 
from  one  place  to  another,  and  the  cause  of  this  transmission  is  the 
molecular  motions  which  bring  the  particles  that  execute  the  sound- 
vibrations  into  contact  with  others.  From  this  it  follows  that  the 
velocity  of  propagation  of  sound  cannot  depend  on  the  nature  of  the 
sound  vibrations,  but  only  on  the  molecular  motions. 

'  If  we  paid  no  regard  to  the  variations  in  temperature  which  a  gas 
undergoes  by  condensation  or  rarefaction,  it  would  be  easy  to  answer 
the  question  as  to  the  speed  with  which,  on  the  basis  of  the  assumptions 
of  the  kinetic  theory,  a  sound  wave  is  propagated.  If  sound  consists  in 
alternate  rarefactions  and  condensations  of  the  air,  the  speed  of  its 
propagation  cannot  be  different  from  the  speed  with  which  any 
inequality  of  the  pressure  that  arises  at  any  place  would  spread  through 
air-filled  space.  Now,  according  to  our  theory  the  pressure  arises 
from  the  to-and-fro  motions  of  the  particles,  and  is  exerted  and  carried 
on  from  one  layer  to  another  by  the  same  cause ;  the  velocity  with 
which  a  pressure  or  sound  wave  is  propagated  must  therefore  be  just  as 
great  as  that  with  which  the  particles  of  gas  move  to  and  fro  in  the 


WHISPERINGS   OF   AN    OLD   PINE 


I  ;i 


direction  of  propagation  of  the  wave.  The  value  of  the  component  of 
the  molecular  motion  in  the  given  direction,  and  not  the  resultant 
velocity  of  the  particles,  comes  therefore  into  account  in  the  calculation 
of  the  velocity  of  sound  ;  and  hence  it  follows  at  once  that  the  spied  of 
propagation  of  sound  in  a  g^u  must  i>e  smalier  ihan  the  mean  speed  of 
ihe  moleculut  motion  in  tit  is  gas  ' 

"And  Mr.  S,  F.  Preston,  in  the  'Philosophical  Magazine," 
referring  to  the  propagation  of  sound  in  accordance  with  this 
ihcory,  says: 

•Since,  therefore,  the  portion  of  a  molecule's  path  through  which  it 
is  acted  on  by  other  molecules  of  the  gas  is  vanishingly  small  compared 
with  the  range  of  its  path  throughout  which  it  is  not  so  acted  on,  there 
16  therefore  practically  no  distance  action  between  the  molecules  of  a 
gas,  which  accordingly  can  only  influence  each  other  by  direct  impact. 
The  only  way,  therefore,  one  molecule  of  a  gas  can  influence  another 
is  by  moving  up  to  it  and  striking  against  it.  The  only  way,  therefore, 
t  wave  or  small  impulse  can  be  propagated  from  molecule  to  molecule 
through  a  gas  is  by  ihe  molecule  possessing  the  impulse  moving  up  to 
and  striking  against  another  molecule  j  and  therefore  the  velocity  of 
propagation  of  such  wave  or  utipulse  must  depend  solely  and  entirely 
u|K>n  the  velocity  with  which  the  molecule  moves;  or  the  sole  conceiv- 
able cause  tegulating  the  velocity  of  an  impulse  propagated  from  mole- 
cule to  molecule  is  the  velocity  of  the  moiecule  itself^  or  the  velocity 
wjtli  which  the  molecule  traverses  its  free  path. 


*The  result  of  these  considerations  may  therefore  be  summarized  as 
follows : 

*  Thai  ihe  veioaiy  qf  propagation  of  a  wave  (such  as  a  wave  of 
sound)  in  a  gas  is  solely  determined  hy,  and  proportional  to^  the  velocity 
of  the  molecules  cf  ilie  gas  ;  that  this  velocity  of  propagation  of  the  wavt 


152  ELLEX  OR  THE 

is  notaffecUd  ty  d^msztr^  pressure^  cr  H  the  s^dfic  gravity  of  a  gas,  or 
by  anjthirT  el:€  exc^^tir*  the  z^Ldtj  cf  its  wioUcuUs, 

*  This,  it  may  be  observed,  is  a  condition  following  inevitably  on  the 
acceptance  of  the  kinetic  iheon- ;  and  surely  the  very  simplicity  of  this 
lelati'.n  as  aEcrding  a  def.nite  physical  conception  of  the  condition 
detenninir.g  the  velocity  cf  sound,  ar-d  as  gH'ing  an  insight  into  its 
mo^ie  of  propagation,  would  be  by  itself  sufficient  to  recommend  it  over 
the  old  system.  If  ar.y  ihicg  I  have  written  should  ser\'e  to  divert  the 
attention  cf  others  more  ccmp^tent  than  myself  to  this  interesting  sub- 
ject, the  purpK>se  of  this  paper  will  have  been  served.' 

"From  which  it  results  that  in  accordance  with  these 
theories  ever>'^  particle  of  air  (or  any  gas)  is  supposed  to  be 
always  moving  at  the  same  time : 

'*  First,  at  the  rate  of  about  1590  feet  per  second,  in  con- 
stantly var>'ing  directiDns,  from  which  results  elastic  force; 
second,  with  ever  var>'ing  movement  to  form  heat;  and  third, 
in  an  indefinite  number  of  different  directions  at  the  rate  of 
about  1 1 90  feet  per  second  in  each,  in  its  efforts  to  distribute 
sound. 

**It  will  be  seen,  accepting  this  theor)',  what  a  fatal  delusion 
Mr.  Newton's  conception  was  in  proposition  47,  corollary,  that 
the  lincola  would  come  to  rest  and  move  no  more.  For  there 
is  no  rest  for  these  particles  under  these  theories  any  more 
than  for  the  wicked.  And  if  the  particles  move,  the  lineolae 
must  move. 

'*In  the  'London,  Edinburgh  and  Dublin  Philosophical  Mag- 
azine,' vol.  16,  this  proposition  of  Newton  is  discussed  by  J.  J. 
Watcrston,  who  first  raises  the  question  whether  it  or  similar 
propositions   founded    upon   the   expansion  theory  of   elastic 


WHISPERINGS  OF  AN  OLD   PINE 

arce,  can  be  accepted  by  those  who  believe  in  the  kinetic 
^theory  of  gases.     He  then  says : 

•In  prop.  47  of  book  2  Newton  shows  that  *'if  pulses  are  propagated 
brough  a  fluid,  the  several  particles  of  the  fluid  going  and  returning 
rith  the  shortest  reciprocal  motion  are  always  accelerated  or  retarded 
ccording  to  the  law  of  the  oscillating  pcnJiilura."  It  is  assumed  that 
the  elastic  force  is  proportional  to  the  density;  and  in  the  direction  of 
the  pulse  the  fluid  is  supposed  to  be  divided  into  physical  iintoiae^ 
ick  are  expansible  and  contractile^  and  exhibit  a  force  that  resist* 
impression  inversely  as  their  brevidth.  The  mathemalicai  reasoning 
defines  the  law  by  which  the  breadth  of  these  lineolae,  and  conse- 
quently the  law  of  Ihe  accelerative  force  operating  on  each  corpuscle 
cts,  which  is  thus  found  to  be  the  same  as  a  body  moving  in  a  cycloid 
i  subject  to  under  the  influence  of  gravity. 

'Newton's  fundamental  hypothesis  is,  that  the  particles  of  air  in  the 

lirection  of  the  puke  are  suecessiveh  ^^\\'3X^A  Hi\\k  like  motions;  that 

both  the  dynamic  condition  and  the  static  force  of  repulsion,  which  is 

rdctermined  by  the  length  of  the  line  that  separates  tw^o  adjacent  par- 

ticies  (called  a  lineola),  is  transferred  onwards  in  the  direction  of  the 

from  one  particle  to  the  next  adjacent  in  regular  succession. 

*The  demonstration  takes  account  of  three  orders  of  magnitudes: 

I,  the  breadth  of  a  pulse  (L)  ;  2,  the  breadth  of  an  oscillation  of  a 

jcle   (1/);   Jp  the   length  of   a  lineola    (AJ,   each   considered   as 

Jinitesinial  with  respect  to  the  preceding. 

•If  the  motion  of  a  particle  forward  and  backward  in  the  line  a/cor- 

sponds  to  that  of  a  cycloida!  pendulum,  f.  e.>  if  the  relation  between 

he  accelerative   force   (acting  in  the  line  of  motion),  the  acquired 

Yelocity,  and  the  time  is  the  same  in  the  line  2/  as  in  the  complete 

cycloid,  the  force  in  this  line  must  vary  simply  as  the  distance  (y)  Irom 

its  middle  point.    The  value  thus  assigned  to  the  force  implies  that  8» 


134  ELLEN   OR   THE 

the  difference  between  the  lengths  of  two  adjacent  lineolae,  should  vary 
also  in  this  proportion.  If  a  semi-circle  [circle]  is  described  on  the 
diameter  2/,  y  is  the  cosine  of  an  arc,  of  which  x  being  the  sine,  we  have 
8  varies  as  y  as  dx ;  so  that  the  differential  of  the  lineola  ought  to  be 
equal  to  the  differential  of  the  sine,  and  hence  the  absolute  magnitude 
of  the  deviation  of  the  length  of  a  lineola  from  its  mean  length  ought 
to  be  proportional  to  the  sine. 

*  Thus  if  the  motion  of  a  particle  is  oscillatory,  like  a  complete 
cycloidal  pendulum,  the  required  sequence  of  force  demands  the  above 
specific  sequence  of  change  in  the  distance  of  the  particles.  Again,  if 
the  motion  of  each  particle  is  oscillatory,  the  required  sequence  in  its 
velocity  (viz.,  that  it  should  vary  as  x  the  sine)  demands  also  a  specific 
sequence  of  change  in  the  distance  of  the  particles ;  and  this  sequence 
is  precisely  the  same  as  what  is  required  b^  the  sequence  of  force. 

*To  obtain  a  clear  idea  of  this  (which  is  a  problem  of  pure  mathe- 
matics), we  may  suppose  with  the  same  radius  /  another  semi-circle  to 
be  described,  placed  also  in  the  line  of  the  pulse,  and  removed  to  the 
distance  X  from  the  preceding  semi-circle.  Let  a  third  also  be  drawn, 
removed  the  same  distance  X  from  the  second.  We  have  further  to 
supj)osc  these  semi-circles  divided  into  as  many  parts  (aa^,  a^  a^,,  a, 
a3,  etc. ;  bb^,  b^  b^,  bo  by,  etc. ;  cc^,  c^  c.,,  c,  0.3,  etc.),  beginning  at 
where  the  line  of  pulse  intersects  them  as  X  enters  into  L  (or  — 
number  of  parts).  The  length  of  each  of  these  parts  or  jA'/j  is  thus 
2/7r=:s   (being  infinitesimal  with  regard  to  X). 

*  Having  made  this  construction,  we  have  next  to  consider  that  the 
motion  of  each  particle  to  be  oscillatory  must  be  such  that,  at  the 
instant  when  particle  A  has  traversed  the  versed  sine  of  aan,  the  par- 
ticle B  (next  in  advance  of  A)  being  one  sUp  behind  in  its  motion,  has 
traversed  only  the  versed  sine  of  bbn-i.  and  particle  C  the  versed  sine 
of  ccn-2.     If  B  had  traversed  as  many  steps  as  A,  the  distance  X  thai 


mtSPERTNGS   OF   AN    OLD    PINE 


^55 


^separates  them  would  not  alter;  but  since  it  is  a  step  behind,  AB 

It    ihis   point  less   than   X   by  the  difference    between  vers    aan 

vers  bbn-i5  or  vers  aan  —  vers  aan-ti  which  eqiu'ils  s.  sin   aan-| 

[because  of  similar  triangles  and  the  assumed  equality  of  an  arc  and 

its  chord,  and  the  principle  that  the  base  divided  by  the  hypothenuse 

;  is  equal  to  the  sine  of   the  angle  opposite  the  base].     In  the  same 

way,  C  being  a  step  behind  B,  their  distance  is  less  than  k  by  s,  sin 


Thus  we  have  BC-'BA:= 


I  (sin  aao  —  sin  aan-t)=s  cos  aan-r 


(Here  s,  being  an  absolute  magnitude,  has  to  be  divided  by  the  abso- 
1  lute  radius  /  to  rejiresent  tlie  differential  of  arc.)  At  the  beginning  of 
'the  vibration  ti  =  i.and  cos  aa"=  radius;  hence  with  B  at  the  initial 

point  b,  C  at  c-i  (a  step  back  on  the  returning  half  of  the  previous 

oscillation),  and  A  at  ai  (the  points  on   the  circle  being  supposed 

projected  on  the  diameter),  the  difference 

BC-BA=^=4/(^). 

*  This  initial  amount  determines  the  accelerative  force  acting  at  the 
begmning  of  the  motion  of  each  particle,  which  is  obtained  by  com- 
paring it  wiih  the  reciprocal  of  A^  which  represents  the  whole  static  force 
of  repulsion  between  two  particles  at  the  distance  A  [because  clastic 
force  laries   inversely  as   the   tlist;ince  between    adjacent    particles]. 

This   force   having   lo   suf>port  the  weight   of  particles  (H  being 

I  H 

the  height  of  a  uniform  atmosphere),    -  represents  the  force  -  g,   viz.,, 

A  A, 

a  force  that  in  one  second  i&  capable  of  communicating  a  velocity  of 

H 

— g  feet  f»cr  second. 

*To  obtain  the  value  of  the  initial  force  acting  on  particle  B  when  it 
IS  at  b,  we  have  the  following  proportion  : 


i_ I      H 


5g=Hg4/(£)V 


156  ELLEN    OR  THE 

•'But  I  cannot  see,"  I  said,  "how  this  proportion  is- 
obtained." 

**It  cannot  be  obtained,"  she  replied,  "from  quiescent  air> 
and  this  Mr.  Waterston  refers  to  further  on.  But  assuming 
that  an  agitation  of  the  air  has  happened, — an  aoritation   in  its 

nature  miraculous  because  without  cause, — then,  as  ?ilr.  Waters- 

I  Hg  s2 

ton  states,  -r-  represents  the  elastic  force  -— ,  and  -,-  the  dif- 
ference between  the  lincola  in  front  of  a  particle  and  the  one 
behind  it.     The  force  behind  the  particle  would  then  be 

I 
s^ 

and  that  in  front  of  it  -r-  and  the   effective  force  would  be  the 

difference  between  these.  This  is  the  second  term  in  Mr. 
Waterston's  proportion,  though  as  he  subtracts  the  larger  from 
the  smaller,  the  term  is  negative.  The  fourth  term  may  then 
be  obtained  by  solving  the  proportion  and  dropping  s^  consid- 
ered an  infinitesimal.     This  term  would  also  be  negative. 

"The  initial  force  can  also  be  obtained  by  letting  a^  b, 
and  c  represent  three  consecutive  particles  of  air;  be  and 
ab   the    lineolae   which    separate    them.     Calling    the    differ- 

ence  between   these   lineolae  -j  and    supposing    b  c   to    be    as 

much  greater  than  X  as  ^^  is  less,  we  have  bc=-\-\ — -.    and  ba 

=  X J,      Let  Fi  equal  the  force  pushing  b  towards  a  and 

Fa  the  force   pushing  b  towards   c ;  then  by  Boyle's  law 

F^:5ji::_!_..LandF2:^?::— ^.,  :  — . 


WHISPEKINGS    OF  AN    OLD    PINE 


159 


Subtracting  the  ratios  of  the  first   proportion  from   the  corre- 
sponding ratios  of  the  second,  we  have 


and  solving* 


2~Pl 

.Hg. 
■    A  • 

I 

I 

F.- 

Fi  = 

s 
If  wc  drop('-r)^  considered  as  an  infinitesimal,  the  proportion 

becomes  I^8""F*i^"w'X-jr-,  which  is  the  same  as  that  obtained 
by  Mr.  Waterston. 
**  Mr.  Waterston  continues : 

•The  lime  (t)  Liken  by  a  particle  to  traverse  2 /^  with  this  force 
diminishing  as  the  distance  from  the  center  of  the  semi-circle,  is  the 
same  as  the  time  required  for  one  oscillation  of  a  pendulum  whose 
length  is  /,  if  subject  to  an  influence  of  gravity  equal  to  this  furce, 
and  is  the  same  as  the  time  taken  by  the  pulse  to  travel  through  ^L. 
By  the  law  of  the  pendulum,  r  is  equal  to  ir  multiplied  by  the  square 
foot  of  the  quotient  of  length  cf  j)endulum  by  force  of  gravity,  hence 


'"yl^-&,=i'-^i' 


Hg47       '      VHg 

and  the  velocity  of  the  pulse  per  second  is  v^Hg, 

*This  supposes  Mariotte*s  law  maintained.  The  repulsive  action  is 
necessarily  assumed  to  be  limited  to  adjacent  particles,  not  extending 
tbiough  the  interstices  of  these  to  the  particles  beyond  (for  such  is  the 
ettTaordinary  and  improbable  hypothesis  required  to  deduce  Mariotte'i 
law  from  a  static  repulsive  force).  This  may  be  supposed  subject  to 
modification  during  vibratory  action. 


l6o  ELLEN  OR  THE 

<But  the  hypothesis  upon  which  the  mathematical  demonstradoo 
rests  is  open  to  three  grounds  of  objection:  i.  It  does  not  take 
account  of  the  condition  of  the  front  of  a  pulse  when  the  particles  from 
a  condition  of  rest  enter  into  the  cycle  of  motion  defined  by  the  theory. 
2.  The  force  of  repulsion  between  two  adjacent  particles  required  by 
the  theory  is  extravagantly  large.  3.  The  other  physical  properties  of 
gases  are  not  deducible  from  the  hypothesis. 

'To  these  may  be  added,  that  the  dynamical  theory  of  heat  has  sug- 
gested another  hypothesis  which  is  free  from  these  objections,  and 
which  therefore  claims  a  preference  according  to  Newton's  first  '*  rule 
of  reasoning  in  philosophy,"  viz.,  "  We  are  to  admit  no  more  causes  o£ 
natural  things  than  such  as  are  both  true  and  sufficient  to  explain  their 
appearances.  To  this  purpose  the  philosophers  say  that  Nature  does 
nothing  in  vain,  and  more  is  in  vain  when  less  will  serve ;  for  Nature  is 
pleased  with  simplicity,  and  affects  not  the  pomp  of  superfluous 
causes." 

'  I.  The  theory  does  not  take  account  of  the  condition  of  the  front 
of  the  pulse,  or  rather  of  the  front  of  the  first  of  the  series  of  pulses  of 
which  a  sound  consists.  This  is  apparent  if  we  consider  that  a  particle 
is  represented  by  the  theory  as  at  rest  at  each  extremity  of  its  oscilla- 
tion, ai.d  at  those  points  the  accelerativc  force  is  at  its  maximum,  and  is 
derived  from  the  difference  between  the  lengths  of  the  lineolae  that  issue 
from  the  particle  in  front  and  in  rear.  The  front  lineola  cannot  differ 
from  the  mean  length  so  long  as  the  front  particle  is  at  rest  unaffected  by 
the  advancing  pulse.  The  rear  lineola  is  less  than  the  mean  length  by  a 
certain  small  amount  a.  If  the  front  particle  were  in  action  in  a  pulse 
cycle,  the  length  of  the  front  lineola  would  be  increased  by  the  same 
amount  a  so  that  the  accelerative  force  at  each  extremity  of  the  oscil- 
lation of  a  particle  is  represented  by  2<i ;  and  unless  it  were  so,  the 
condition  required  to  sustain  the  beautiful  relation  of  velocity  and  pro- 
pelling force  would  be  wanting.     But  at  the  front  of  the  first  pulse  the 


WHISPERINGS  OF 


>LD 


151 


Vneola  does  not  diiFer  from  the  mean  length,  so  that  the  accelerative 
force  is  represented  by  */,  and  this  is  only  one-half  the  amount  required 
by  the  theory  to  begin  the  osciilation.  In  tnith,  the  tleiuonstration 
only  applies  to  a  pulse  having  stmilaf  pulses  operating  on  both  sides, 

*  2.  The  force  of  repulsion  between  two  adjacent  particles  required  by 
the  theory  is  extravagantly  large,  l^he  recent  advances  in  the  theory 
of  heat  have,  in  a  measure,  compelled  us  to  realize  the  dynamic  value 
ol  natural  forces.  To  compute  the  absolute  value  of  the  repulsive  force 
acting  between  tiii'O  adjacent  molectiles  of  air,  we  have  to  consider  that 
it  has  to  support  the  gravity  of  the  number  of  molecules  in  the  height 

of  a  uniform  atmosphere  {-r-)  t  *'  '"^^s*  therefore  exceed  the  force  of 
I  gravity  of  one  molecule  in  this  ratio.  Now  the  force  of  gravity  in  one 
*  lecood  can  communicate  a  velocity  of  32  feet  per  second,  so  that  the 

force  of  repulsion  between  two  adjacent    molecules  of  air    must  be 

capable  in  one  second  of  communicating  a  velocity  of  32—  feet.     The 

[  absolute  value  of  A,  the  distance  between  two  adjacent  molecules  of  air, 
wt  can  now  with  great  probability  deduce  from  the  phenomena  of 
capillarity  (Phil.  Mag.,  vol.  xv.,  p.  i).  At  the  boiling  point  of  water 
the  number  of  molecules  of  steam  in  a  cubic  inch  is  the  same  as  the 
nuTDber  of  molecules  of  air  in  the  same  volume.  At  86«»  the  number  o( 
layers  of  aqueous  molecules  in  a  cubic  inch  is  215  millions  (Phil.  Mag., 
vol.  XV.,  p.  11).  Hence  at  ordinary  temperatures  the  distance  between 
two  adjacent  molecules  of  air  must  be  about  -j^^  of  a  millionth  of  ai 

H 
inch,  and  the  value  of  (j^y)'  ^^^  velocity  communicable  in  a  second^ 

is  160  thousand  times  the  velocity  of  light.  Can  we  for  a  mometil 
believe  that  such  a  force  has  any  real  existence,  that  it  is  other  than  a 
mathematical  fiction? 

*  3.  The  other  physical  properties  are  not  deducible  from  the  hypoth- 
esis of  a  static  force  of  repulsion.  The  deductive  power  of  Newton's 
theory  is  confessedly  limited   to  Mariotte's  law  and    the  velocity  of 


^Mt^^m^ 


jnHn^ 


1 62  ELLEN   OR  THE 

sound.  Laplace,  by  the  invention  of  calorific  atmospheres,  is  allowed 
to  have  added  to  these  Dalton  and  Gay-Lussac's  theory  of  expansion; 
but  it  is  a  question  whether  the  reciprocal  action  between  heat  atmos- 
pheres and  molecules,  which  he  Expresses  by  mathematical  symbols, 
can  be  realized  by  the  mind.  In  judging  of  this,  we  must  not  forget 
the  chapter  of  the  Mecanique  Celeste,  in  which  the  author  speculates 
upon  what  the  laws  of  motion  would  have  been  if  force  had  been  as  a 
function  of  the  velocity,  instead  of  as  the  simple  velocity.  What  is  to 
be  expected  from  a  superstructure  resting  upon  such  a  foundation  as 
this  reveals?  Nevertheless,  granting  that  Mariotte's  law,  Dalton  and 
Gay-Lussac*s  law,  and  the  velocity  of  sound  are  represented  by  the 
statical  hypothesis,  we  have  still  Dalton  and  Graham's  law  of  diffusion 
and  diffusive  velocity;  Gay-Lussac*s  law  of  volumes;  Dulong  and 
Petit*s  law  of  specific  heat,  extended  to  the  mo:'e  simple  gaseous  bodies 
by  Haycraft  and  the  French  physicists ;  the  law  of  latent  heat  par- 
tially discovered  by  Gay-Lussac  and  Welter's  experiments;  also  the 
diminution  of  temperature  in  ascending  the  atmosphere, — all  as  yet 
undeduced  from  any  statical  theory  of  elastic  fluids.  It  may  be  that 
additions  to  the  mathematical  hypotheses  of  Laplace  will  be  attempted 
with  the  view  of  extending  their  capacity,  as  indeed  there  seems  to  be 
no  limit  to  this  artificial  and  barren  system  of  procedure,  which  is  as 
far  removed  from  the  simplicity  of  nature  as  the  hideous  epicycles  of 
Ptolemy.' 

*'Mr.  J.  F.  Herschel,  in  his  article  on  Sound  in  the  *  Encyclo- 
paedia Mctropolitana,'  as  the  result  of  a  long  mathematical 
investigation,  says: 

'Hence  it  follows  that  the  velocity  of  sound  is  uniform;  is  inde- 
pendent of  the  nature,  extent,  and  intensity  of  the  primitive  disturbance 
(for  the  arbitrary  functions  do  not  enter  it)  and  is  expressed  by  the 
quantity  we  have  called  a,  that  is  y'2gH.' 


WHISPERINGS   OF  AN   OLD    PINE 


t63 


••  It  will  be  seen  that  the  mathematics  sustain  the  theory,  as 
is  generally  the  case.  He  would  be  a  poor  mathematician 
that  could  not  accomplish  this.  But  Mr,  Earnshaw,  another 
noted  mathematician,  has  shown  by  mathematics  equally  sub- 
stantial and  interesting,  that  the  velocity  of  sound  is  not  uni- 
form, but  varies  with  the  nature,  extent,  and  intensity  of  the 
primitive  disturbance. 

**  At  one  point  of  his  demonstration  Mn  Hcrschcl  takes  occa- 
sion to  criticise  Mr,  Newton,  as  follows: 


'  And  first  it  is  evident  that  since  the  variable  quantity  x  enters  into  all 
the  terms  both  of  rand  f  under  the  functional  characteristics,  these  quan- 
tities regarded  as  functions  of  /,  are  modified  essentially  by  the  values  of 
jr,  which  may  be  regarded  as  a  parameter,  or  constant  element  in  the  com- 
position of  the  functions  expressing  the  nature  of  the  motion  of  any 
assigned  molecule.     If  only  x-\-af,  or  only  .v— «/,  separately  entered 

under  the  characteristics,  since  x-j-(i/=a  i/-}-  -^)  SLnd  x—ai^^  —  a 

a 

{t '—)  the  variation  of  x  would  only  vary  the  origin  of  //  and  the 

motions  of  all  the  successive  molecules  would  be  performed  according 
to  the  same  laws,  only  commencing  at  a  different  epoch  for  each 
molecule ;  but  as  t>oth  these  quantities  are  involved,  that  will  not  be 
universally  the  case.  Consequent iy»  in  general,  it  appears  that  the 
undulation,  or  pulse,  as  it  is  propagated  onward,  becomes  modified 
essentially  in  its  quality  by  the  distance  it  has  passed  over,  it  is  no 
longer  (he  sanu  .ufund^  i.  e.,  not  identical  with  what  would  be  produced 
by  shifting  the  initial  motion  forward.  Its  velocity,  intensity,  and  pitch, 
it  is  truCj  will  remain  (as  we  shall  see)  unaltered ;  but  its  qualify^ 
its  mode  of  action  on  the  ear  (which  must  be  differently  affected  by 
changes  in  the  natirre  of  the  imptilse  made  in  it),  will  undergo  a  change. 


g,,li^ 


^'-  -— ^' 


1 64  ELLEN   OR  THE 

This  establishes  an  essential  difference  between  a  sound  wave  and  such 
a  wave  as  we  took  for  an  illustration,  where  every  point  was  in  succes- 
sion agitated  by  the  same  identical  motion. 

'  Consequently  every  theory  of  sound  in  which  it  is  assumed  that  the 
several  particles  in  a  sounding  column  are  all  in  succession  agitated 
alike,  is  defective.  This  is  the  case  with  Newton's  doctrine  of  the  prop- 
agation of  sound  as  delivered  in  the  47  th  Proposition  of  the  Second 
Book  of  the  'Principia,'  if  there  was  no  other  objection  against  it, 
would  suffice  to  vitiate  the  whole.  This  and  other  unsatisfactory  points 
in  the  celebrated  theory  alluded  to,  were  first  distinctly  perceived  and 
pointed  out  by  Lagrange,  in  the  first  volume  of  the  "Turin  Miscellanies,*^ 
and  an  exact  and  vigorous  investigation  substituted  in  its  place,  in 
which  the  sounding  column  is  regarded  as  consisting  of  a  serits  of 
finite,  insulated  particles,  mutually  repelling  each  other ;  a  mode  of 
conception  which  leads,  by  a  very  complicated  analysis,  to  the  same 
results  as  that  above  stated,  but  which  has  the  advantage  of  setting  in  a 
distinct  light  the  internal  mechanism,  if  we  can  so  term  it,  by  which 
sound  is  propagated. 

*  Moreover,  since  by  differentiating  the  equation  (d)  we  get 

111="^'  [F"(x+at)+f"(x-at)] 

this  will  be  proportional  to  the  accelerating  force  acting  on  the  mole- 
cule. It  IS  therefore  by  no  means  universally  proportional  to  y— x,  the 
distance  of  the  molecule  from  its  point  of  rest ;  and  therefore  another 
assumi)tion  on  which  the  Newtonian  doctrine  of  sound  rests,  viz.,  that 
the  motion  of  each  molecule  successively  follows  the  law  of  a  vibrating 
pendulum,  is  equally  destitute  of  foundation.  In  fact,  Cramer  had 
shown,  before  the  examination  of  Lagrange,  that  any  other  law  of 
molecular  motion  might  be  substituted  in  Newton's  enunciation  of  the 
general  proposition,  and  the  demonstration  would  be  equally  conclusive, 
and  the  resulting  velocity  of  sound  the  same.' 


WHISPEUINGS   OP  AN   OLD   PINE 


165 


"Lagrange  and  Herschel  were  both  eminent  mathematicians, 
among  Uic  most  eminent  of  their  time,  and  Lagrange  perhaps 
of  any  timCp  but  the  hypothesis  of  Lagrange  referred  to  would 
be  wholly  impossible  under  the  kinetic  theory  of  gases. 

**  It  is  also  noticeable  that,  however  M.  Lagrange  may  have 
pointed  out  the  errors  of  Mr.  Newton's  theory,  errors  which, 
as  we  have  seen,  are  very  transparent,  scientists  generally, — 
the  great  body  of  instructors  on  these  subjects^  whether  in  col- 
leges, schools,  or  books, — did  not  think  wise,  whatever  might 
be  ihe  facts,  to  make  any  change  of  base,  but  preferred  to  con- 
tinue to  build  upon  Mr,  Newton's  propositions.  In  this,  their 
object  being  simply  to  have  something  to  teach,  they  \\erc; 
probably  wise.  For  a  little  more  light,  like  that  Lagrange 
threw  upon  the  subject,  was  sure  to  break  up  the  meeting, 
in  showing  how  utterly  without  foundation  was  the  whole 
conception  of  this  theory, 

**Il  appears,  then,  that  Newton  first  formulated  in  its  present 
shape  this  undulatory  theory  of  sound,  and  probably  it  owes  its 
vigorous  life  in  a  great  part  to  this  fact;  although  those  who 
accept  his  demonstration  of  it,  refuse  to  accept  his  theory  of 
light,  in  the  examination  of  which  he  was  much  more  thorough, 
and  spent  far  more  time. 

'*Thc  moral  is  the  danger  of  building  upon  hypotheses.  To 
this  cause  is  principally  if  not  wholly  due  the  fact  that  a  very 
large  part  of  the  science  of  the  present  day  is  entirely  fictitious, 
and  much  of  it  ridiculously  so/' 

**  But  how  could  this  be  avoided  ?  "  I  asked. 

**By  avoiding  it,"  she  said.  '*  Build  only  upon  known  facts. 
Draw  the  line  between  what  you  know  and  what  you  do  not 


1 66  ELLEN   OR  THE 

know,  and  build  only  upon  what  you  know ;  never  upon  what 
you  do  not  know." 

"  But,  Ellen,  it  is  a  common  saying  of  scientists  that  they 
could  never  advance  in  knowledge,  if  they  didn't  employ 
hypotheses." 

"But  they  never  do  advance,'*  she  said.  "They  are  hope- 
lessly in  the  mire,  and  always  have  been,  and  always  will  be,  if 
they  depend  upon  guesses.  For  always  they  forget  that  the 
matter  is  imaginary  and  teach  it  as  truth,  thus  inaugurating 
over  the  world  that  great  mass  of  rubbish  which  is  called 
science,  but  which  is  always  in  time  discarded,  after  having  ful- 
filled its  mission  of  deceiving  one  or  more  generations.  Truth 
never  will  be  reached  this  way,  but  only  by  building  upoo 
known  facts,  no  matter  how  slowly  these  may  accumulate." 


WHISPERINGS   OF  AN   OLD    IINE 


rOQ 


XI. 


B' 


^'DUT  what.  Ellen,  then."  I  askcd»  * 
nd  rest  upon,  since 
to  be   erroneous 


does  this  undulatory 


theory  of  sound  rest  upon,  since  Mr.  New^tor 
stration   has   proved   to  be   erroneous  both   in   princi|: 
in  fact?" 

•* Nothing/*  she  said,  "but  assertion.  Indeed,  so  far  as  Ellen 
knows,  all  that  its  strongest  supporters  and  teachers  claim  for 
it  is  that  it  explains  the  different  phenomena  connected  with 
sound  better  than  any  other  hypothesis.  A  very  senseless 
claim,  because  it  docs  not  explain  them»  and  cannot  explain 
them  at  all" 

**And  how  does  Ellen  think  that  they  should  be  explained?** 

"Through  knowledge,  and  not  by  ignorance/'  she  answered, 
•*  I-argely  by  the  use  of  our  good  sense,  and  not  by  its  surren* 
dtu  But  scientists  often,  if  not  generally,  would  appear  to 
make  the  abandonment  o(  common  sense  an  essential  prelimi- 
nary qualification  to  the  study  of  science.  Ellen  thinks  that 
the  use  of  good  sense  and  the  cultivation  of  it  is  of  far  more 
importance  than  all  things  else  in  the  search  after  knowledge." 

"But  mathematics  are  very  important  in  the  discoveries  of 
physics,  arc  they  not,  Ellen?"  I  asked. 

"They  arc  worse  than  useless/*  she  replied,  "without  the 
^cnsc  to  apply  them;  and  indeed,  generally  they  are  worse 
than   useless.     Every   dead    hypothesis  of  past  centuries  has 


I70  ELLEN   OR  THE 

been  weighted  down  with  them,  and  the  same  treatment  fol- 
lows the  hypotheses  of  the  present,  which  in  time,  with  all  the 
accumulated  rubbish,  will  be  consigned  to  the  general  cem- 
etery where  "  such  matter  always  finally  rests.  There  are 
certain  fields  for  mathematics,  but  the  field  of  good  sense  and 
reason  is  everywhere. 

"Ellen  will  now  review  this  undulatory  theory  of  sound. 
quoting  from  different  authorities  among  its  more  renowned 
supporters.  And  first  from  Professor Tyndall,  whose  book  'On 
Sound*  has  had  a  very  wide  circulation.     Mr.. Tyndall  says: 

'  Applying  a  flame  to  a  small  collodion  balloon  which  contains  a  mw- 
ture  of  oxygen  and  hydrogen,  the  gases  explode,  and  every  ear  in  thii 
room  is  conscious  of  a  shock,  which  we  name  a  sound.  How  was  this 
shock  tranr.iiitteJ  from  the  balloon  to  our  organs  of  hearing?  Have 
the  expbdinj  g.ises  shot  the  air  particles  against  the  auditory  nerve  as 
a  gun  shoots  a  ball  against  a  target  ?  No  doubt,  in  the  neighborhood 
of  the  balloon,  there  is  to  some  extent  a  propulsion  of  particles ;  but 
no  p  irticle  of  air  from  the  vicinity  of  the  balloon  reached  the  ear  of 
any  p?r';on  here  present.  The  process  was  this :  When  the  flame 
touched  the  mixed  gases  they  combined  chemically,  and  their  union 
was  acco.npanie  1  by  the  development  of  intense  heat.  The  heated  air 
expanded  su:l(lcnly,  forcing  the  surrounding  air  violently  away  on  all 
sides.  This  motion  of  the  air  close  to  the  balloon  was  rapidly  imparled 
to  that  a  little  farther  oIT,  the  air  first  set  in  motion  coming  at  the 
same  tim^  to  rest.  The  air,  at  a  little  distance,  passed  its  motion  on 
to  the  air  at  a  greater  distance,  and  came  also  in  its  turn  to  rest. 
Thus  each  shell  of  air,  if  I  may  use  the  term,  surrounding  the  balloon 
took  up  the  motion  of  the  shell  next  preceding,  and  transmitted  it  to 
the  next  succeeding  shell,  the  motion  being  thus  propagated  as  a  /uhr 
or  wui'e  through  the  air.* 


WHISPERINGS    OF  AN    OLD    PINE 


r»upp  >sing  Mr,  Tyndairs  explanation  oi  the  explosion  of 
the  balloon  correct,  that  '  the  heated  air  expanded  suddenly, 
lorcing  the  surrounding  air  violently  away  on  all  sides,*  why 
should  this  cause  sound?  So  will  a  fan  force  the  air  away 
violently  from  all  sides,  w^ithout  making  perceptible  sound. 
This  is  especially  true  of  electric  fans.  And  this  demon- 
strates that  such  movement  of  the  air  is  not  the  cause  of 
sound.  The  supposition  that  the  exploding  gases  shot  air  par- 
ticles against  the  auditory  nerv^e,  is  entirely  superfluous,  Ellen 
wishes  Mr.  Tyndall  had  explained  what  he  meant  by  the  air 
passing  its  motion  on»  then  coming  to  rest.  In  what  does  he 
consider  motion  to  consist?  Perhaps  some  scientist  will 
answer, 

•*\Vhen  gases  explode,  they  unite  chemically  and  occupy 
more  space  than  when  separate,  probably  because  of  heat 
produced,  as  Mr.  Tyndall  explains.  The  air,  by  this  expan- 
sion, is  driven  away  in  all  directions,  and  the  distance  it  is 
driven  will  depend  upon  the  force  of  the  explosion.  It  might, 
or  it  might  not»  extend  throughout  a  room.  It  might  push  out 
all  the  windows,  or  be  strong  enough  to  push  down  the  walls 
of  a  building.  But  all  of  these  operations,  though  they  might 
cause  sound,  arc  not  sound.  Oxygen,  uniting  with  hydrogen, 
as  in  Uiis  experiment,  produces  steam,  which  is  almost  instantly 
ifidcnscd  to  water.     This  condensation  causes  a  vacuum,  and 

is  vacuum  will  be  immediately  filled  by  the  air  pushed  in 
by  gravity  and  elastic  force.  The  sound  caused  by  explosions 
is  the  result  of  shock  or  disturbance,  the  usual  cause,  and  con- 
sists of  infinitesimal  particles  of  electrical  matter.  Mr.  Tyndall 
continues: 


172  ELLEN   OR  THE 

*  In  the  case  of  our  exploding  balloon  the  wave  of  sound  expands  on 
all  sides,  the  motion  produced  by  the  explosion  being  thus  diffused  over 
a  continually  augmenting  mass  of  air.  It  is  perfectly  manifest  that  this 
cannot  occur  without  an  enfeeblement  of  the  motion.  Take  the  case  of 
a  thin  shell  of  air  with  a  radius  of  one  foot,  reckoned  from  the  centre  of 
explosion.  A  shell  of  air  of  the  same  thickness,  but  of  two  feet  radius, 
will  contain  four  times  the  quantity  of  matter ;  if  its  radius  be  three  feet,* 
it  will  contain  nine  times  the  quantity  of  matter ;  if  four  feet,  it  will 
contain  sixteen  times  the  quantity  of  matter,  and  so  on.  Thus  the 
quantity  of  matter  set  in  motion  augments  as  the  square  of  the  distance 
from  the  centre  of  explosion.  The  intensity  or  loudness  of  sound 
diminishes  in  the  same  proportion.  We  express  this  law  by  saying  that 
the  intensity  of  the  sound  ifaries  inversely  as  the  square  of  the  distanced 

"That  the  area  of  concentric  surfaces  increases  as  the  square 
of  the  distance  from  the  center  is  true;  and  therefore  sound  or 
anything  else  distributing  itself  evenly  over  such  surfaces  must 
decrease  on  each  unit  of  surface  in  this  same  ratio.  So,  too, 
anything  so  distributed  having  permanence  of  form,  might  be 
regathcred.  And  thus  sound  can  be,  as  is  fully  illustrated 
by  the  megaphone,  but  Ellen  denies  that  any  system  of  waves 
could  be.  The  thing  is  impossible.  Any  material  thing  could 
be,  like  water,  of  which  waves  are  composed ;  but  waves  could 
not  be.  For  a  wave,  like  a  shadow,  is  a  condition  of  matter 
without  permanence  of  form.  And  this  alone  is  proof  that  the 
undulatory  thcor}-  of  sound  is  not  true. 

"Again  Mr.  Tyndall  says: 

'The  motion  of  the  pulse  must  not  be  confounded  with  the  motion 
of  the  particles  which  at  any  moment  constitute  the  pulse.  For  while 
the  wave  moves  forward  through  considerable  distances,  each  particular 
particle  of  air  makes  only  a  small  excursion  to  and  fro.' 


WHISPERINGS    OF   AN    OLD    VISE 


'/^ 


"Mr  Tyndall  is  now  discussing  his  imaginary  wave  or  pulse. 
Ellen  denies  that  there  is  any  wave,  or  that  In  such  operation 
each  particular  particle  of  air  makes  a  small  excursion  to  and 
fro,  and  states  that  many  particles  make  a  hurried  and,  for 
them,  extensive  excursion,  pushed  by  the  expandin^f  gas,  and 
then  tumble  back  into  the  vacuum  left  by  the  condensed  gas. 
What  right  has  Mr,  Tyndall.  or  any  scientist,  to  make  such  state- 
ments, when  he  cannot  prove  them?  Upon  their  face,  they 
are  untrue.  Nor  can  there  be  any  evidence  advanced  to  prove 
them.  At  the  best  their  existence  is  an  hypothesis^  though 
asserted  here  to  be  a  fact.  It  was  Goethe  who  said  that  the  wise 
man  is  he  who  is  able  to  distinguish  between  the  things 
which  he  knows  and  those  which  he  does  not.  Is  there  no 
scientist  who  thus  distinguishes? 

**Mr.  Tyndall  further  says: 


'The  process  may  be  rudely  represented  by  the  propagation  of  motion 
through  a  row  of  glass  balls,  such  as  are  employed  in  the  game  of 
sakiaire.  Placing  the  balls  along  a  groove,  each  of  them  touching  its 
neighbor^  and  urging  one  of  tliera  against  the  end  of  the  row ;  the 
motion  thus  imparted  to  the  first  bill  is  delivered  up  lo  the  second^ 
the  motion  of  ihe  second  is  delivered  up  to  the  third,  the  motion  of 
the  thiid  is  imparted  to  the  fourth ;  each  ball,  after  having  given  up 
Its  motion,  returning  itself  to  rest.  The  last  ball  only  of  the  row  flies 
away.  In  a  similar  way  is  sound  conveyed  from  particle  to  particle 
through  the  air.  The  particles  which  fill  the  cavity  of  the  ear  are 
finally  dnven  against  the  tympanic  membrane^  which  is  stretched  across 
the  passage  leading  from  the  external  air  to\%'ard  the  brain.  This 
membrane,  which  closes  outwardly  the  "drum"  of  the  car,  is  thrown 
Into  vibration,  its  motion  is  transmitted  to  the  ends  of  the  auditory 


174  ELLEN   OR   THE 

nerve,  and  afterward  along  that  nerve  to  the  brain,  where  the  vibra- 
tions are  translated  into  sound.  How  it  is  that  the  motion  of  the 
nervous  matter  can  thus  excite  the  consciousness  of  sound  is  a  mystery 
the  human  mind  cannot  fathom.* 

"The  process  of  the  balls  is  this:  If  they  touch  they  neither 
perceptibly  move  nor  return.  If  they  do  not  touch,  each  ball 
moves  at  the  same  pace  as  the  ball  which  struck  it, — the  balls 
being  of  the  same  size,  as  shown  in  the  illustration, — and  the 
striking  ball  stops.  That  is,  the  oscillatory  motion  that  is  sup- 
posed to  be  illustrated  by  these  balls  is  not  illustrated,  but 
instead,  a  plain  straightforward  motion. 

"Mr.  Tyndall  is  eminently  correct  that  no  human  mind  will 
ever  fathom  his  recipe  for  making  sound.  Should  he  give  a 
similar  one  for  taste,  or  nutrition,  or  o^dor,  it  would  be  equally 
unfathomable.  The  conception  being  devoid  of  sense  or  reason, 
readily  baffles  the  human  mind.  Not  anything  in  nature  is 
done  in  the  manner  suggested,  which  is  a  conception  advanced 
by  Mr.  Tyndall. 

"Following  the  same  method  he  would  undoubtcly  introduce 
nourishment  into  the  system  by  transmitting  motion  to  the  ends 
of  the  gastric  nerve,  and  afterwards  to  the  stomach,  where  its 
translation  into  nourishment  would  constitute  another  mystery 
which  the  human  mind  would  be  unable  to  fathom. 

"The  nature  of  the  connection  between  the  material  and 
spiritual  or  intellectual,  by  which  sensation,  or  intelligent  per- 
ception, takes  place,  which  Ellen  has  before  referred  to,  has 
always  been  spoken  of  as  unknown,  but  as  Ellen  thinks,  it  may 
be  easily  understood.  For  certain  things  in  close  connection 
are  known.     Thus   nourishment  of  the   body  so  necessary  to 


WHISPERINGS   OF   AN   OLD    PINE  I/S 

the  existence  of  spirit,  in  material  conditions,  is  accomplished 
by  the  introduction  of  outside  material  into  the  body.  Thus 
our  food  and  drink  are  taken  into  the  body,  and  must  be  if 
we  get  benefit  from  them,  and  this  beneiit  is  absolutely  essential 
to  our  continued  existence  in  present  conditions.  And  medi- 
cines, also,  often  in  very  small  quantities,  will  change  condi- 
tions, relieving  the  most  serious  trouble,  but  always  th'^se 
medicines  must  be  taken  into,  or  brought  into  contact  with,  the 
body.  It  is  the  method  for  affecting  all  material  conditions. 
And  hence  we  see  the  great  law  of  the  soul's  continued  material 
existence,  where  new  supplies  of  matter  are  absolutely  essential, 
is  contact,  and  through  contact  assimilation.  There  is  no  other 
way. 

**  The  same  is  true  in  the  outside  universe.  Thus  rain  to 
assist  in  the  growth  of  things,  must  come  in  contact  with  those 
things,  into  which  it  enters,  and  thus  and  thus  only  fulfills  its. 
mission.  That  rain  takes  place  elsewhere,  no  matter  how  near, 
will  not  suffice.  The  law  of  result  is  one  of  contact,  fixed  and 
immutable.  And  it  is  a  contact  of  matter  with  matter ;  and  a 
contact  which  results  in  the  assimilation  of  the  new  material 
with  the  old. 

"In  this  same  way  come  the  sensations  of  touch,  taste,  smell, 
sight  and  hearing.  There  is  no  other  way,  no  other  possible 
way.  To  see,  light  must  reach  the  intelligence  seeing,  directly 
by  the  eyes  and  optic  nerve,  or  perhaps  indirectly  (as  in 
sound)  through  the  bones  of  the  head  or  body.  The  same  is 
true  of  hearing,  smell,  an^  taste ;  with  all  material  must  enter 
the  body,  to  produce  the  sensation. 

"The  sensation  of  touch  is  of  different  character  from  the 


176  ELLEN    OR   THE 

others,  being  entirely  a  matter  of  resistance,  very  useful  in 
locating  objects,  and  also  giving  knowledge  of  form  and  tem- 
perature; the  thing  touched  is  the  thing  causing  the  sensa- 
tion. It  is  noticeable,  too,  that  the  objects  of  the  sensations  are 
quite  different.  Thus  those  of  sight  and  hearing  are  for  the 
instruction  of  the  mind ;  but  those  of  taste  and  smell  are  more 
directly  connected  with  the  body. 

**From  this  we  gather  that  all  sensations  are  due  to  the 
different  effects  of  matter.  But  Ellen  thinks  the  changes  are 
entirely  those  of  matter,  tlie  effect  upon  spirit  depending  upon 
fixed  laws  which  connect  with  the  conditions  of  matter.  That 
is,  the  soul  doesn't  change,  but  perceives  the  changes  in  matter, 
and  from  these  it  gets  its  knowledge,  or  its  pleasure,  in  the  same 
way  as  it  learns  the  time  of  day  from  the  changing  clock, 
or  gets  information  by  the  changing  sounds  of  a  telegraph 
.instrument. 

"In  all  of  this  not  the  person  changes,  but  the  scenes.  And 
these  scenes  represent  the  material  universe,  everything  in 
which  is  made  by  the  combination  of  matter  in  its  different 
conditions  and  proportions.  So  that  we  can  see*that  all  the 
phenomena  of  nature  take  place  because  of  a  change  in  sub- 
stance ;  and  that  all  the  phenomena  of  the  soul's  existence  in 
material  conditions  take  place,  because  of  a  change  in  material 
phenomena. 

**Mr.  Tyndall  continues: 

*  Let  us  look  at  the  matter  in  another  light.  The  mechanical  effect 
of  a  ball  striking  a  target  depends  on  two  things — the  weight  of  the 
ball,  and  the  velocity  with  which  it  moves.  The  effect  is  proportional 
to  the  weight  simply;    but  it   is   proportional   to   the   square  of  the 


WHISPERINGS   OF   AN    OLD    PINE 


^77 


Now  what  is  tme  of  tlie  cannon  ball  strikiDg  a  target  is  also 
of  an  air  particle  striking  the  tympannm  of  the  ear.  Fix  your 
fttention  uix>n  a  particle  of  air  as  the  sound  wave  passes  over  it  j  it  is 
ged  from  its  position  of  rest  toward  a  neighbor  particle,  first  with  an 
ccelerated  motion,  and  then  with  a  retanled  one.  The  fon  e  which 
Irst  urges  it  is  opixjsed  by  the  resistance  of  the  air,  which  finally  slops 
Ihe  particle  and  causes  it  to  recoil.  At  a  certain  point  of  its  excursion 
he  velocity  of  the  particle  is  its  maximum.  The  intemity  of  sound  is 
\roportHmal  to  the  sr/t^are  of  this  maximum  velocity. 
*  The  distance  through  which  the  air  particles  move  to  and  fro,  when 
sound  wave  passes  it,  is  called  the  amplitude  of  the  vibration.  The 
jltensity  of  the  sound  is  pro|>ortional  to  the  square  of  the  amplitude.' 

''It  might  be  a  little  difficult  for  any  one  but  a  scientist  to  fix 

js  attention  upon  an  air  particle  when  the  sound  wave  passes 

^cr  it.     For,  according  to  the  theory,  this  air  particle,  which 

be  sound  wave  is  supposed  to  be  passing  over,  is  a  component 

part  of  that  w*ave;  and  therefore  to  pass  over  it  the  wave  must 

pass  over  itself,  something  that  is  impossible,  although,  to  be 

sure,  it  is  in  perfect  accord  with  every  part  of  this  preposterous 

theory*.     Evidently  Mr.  Tyndall  supposes  that  it  would  be  a  very 

simple  matter  for  a  man  to  crawl  or  pass  over  himself.     And  he 

ems  to  be  unable  to  make  this  distinction,  that  a  state  of 

botion,  in  whatever  that  consists,  might  pass  through  or  over  a 

irticie,  but  that  a  wave,  of  which  this  particle  was  an  integral 

ad  necessary  part,  could  not  do  this,     Wc   have   here   further 

latcmcnts  as  to  the  action  of  this  supposed  particle,  every^  one 

tliem  purely  imaginary.     Ellen   will  discuss  later  the  whole 

>nception  of  oscillatory  motion,  by  which  the  speed  of  sound 

supposed  to  be  accomplished. 


ji^ 


-*■    ^- 


178  ELLEN   OR  THE 

**Mr.  Tyndall  continues: 

'  With  regard  to  the  point  now  under  consideration,  we  must  endeavor 
to  form  a  definite  image  of  a  wave  of  sound.  We  ought  to  see  mentally 
the  air  particles  when  urged  outward  by  the  explosion  of  our  balloon 
crowding  closely  together ;  but  immediately  behind  this  condensation 
we  ought  to  see  the  particles  separated  more  widely  apart.  We  must, 
in  short,  be  able  to  seize  the  conception  that  a  sonorous  wave  consists 
of  two  portions,  in  the  one  of  which  the  air  is  more  dense,  and  in  the 
other  of  which  it  is  less  dense  than  usual.  A  condensation  and  a  rare- 
faction, then,  are  the  two  constituents  of  a  wave  of  sound.* 

**  In  this  case  a  certain  disturbance  caused  by  explosion  is 
supposed  to  have  taken  place  in  the  air.  This  disturbance, 
which,  in  respect  to  its  being  a  movement  of  air  particles, 
is  similar  to  one  made  by  the  movement  of  a  fan,  or  any 
other  body  in  air,  Mr.  Tyndall  christens  a  sonorous  wave. 
What  he  means  by  a  sonorous  wave  doesn't  appear,  or  why  he 
calls  it  a  sonorous  wave,  or,  indeed,  why  he  calls  it  a  wave  at  all. 
If  it  is  a  sonorous  wave,  then  all  movements  of  air  particles 
are  sonorous  waves.  For  it  would  be  impossible  for  air  par- 
ticles to  be  pushed  without  making  the  air  more  dense  in 
the  direction  towards  which  they  moved,  and  less  dense 
behind  them.  The  condition  of  things  referred  to  amounts 
to  a  promiscuous  mingling  of  air  particles  caused  by  an 
expansion  of  gas,  followed  by  the  condensing  of  the  gas 
and  the  reoccupancy  of  its  space  by  the  air,  pushed  in 
by  the  combined  effects  of  elastic  force  and  gravity.  The 
conception  of  a  sonorous  wave,  which  Mr.  Tyndall  says  we 
must  be  able  to  seize,  is  grotesquely  impossible  under  the 
conditions.     It  is  but  the  conceit  of  some  one.  who  not  only 


WHISPERINGS    OF   AN    OLD    PINE 


1/9 


knows  nothing  of  the  matter  he  is  talking  about^  but,  so  far 
as  he  has  explained,  shows  that  he  is  ignorant  of  the  condi- 
tions which  exist.  For  Mr*  Tyndall  does  not  suggest,  and,  so 
far  as  Ellen  knows,  no  text  book  has  suggested »  the  opera- 
tion of  gravity,  one  of  the  principal  forces  involved,  and 
through  which  the  atmosphere  near  the  earth  is  always 
exerting  a  pressure  of  about  filtcen  pounds  to  the  square 
inch,  a  force  that  under  any  conceivable  conditions  would 
destroy  the  whole  system  of  sound  waves  before  a  scientist 
could  count  one*  It  is  here  that  the  infinite  nonsense 
of  condensations  and  rarefactions,  as  connected  with  a  system 
of  air  waves,  is  first  introduced.  The  old  Pine  will  see  that  it 
would  be  impossible  for  any  one  using  reason  to  conceive  that 
a  system  of  air  waves  could  exist  under  such  circumstances. 

**  Mr.  Tyndall  now  speaks  of  experiments  in  a  vacuum,  in 
liydrogen,  and  on  mountains,  showing  that  a  bell  rung  in  a 
vacuum  makes  either  no  sound  or  an  inaudible  one.     He  says: 


*Sir  John  Leslie  found  hydrogen  singularly  incompetent  to  act  as  the 
vehicle  of  the  sound  of  a  bell  rung  in  the  gas.  More  than  this,  he 
emptied  a  receiver  like  that  before  you  of  half  its  air,  and  plainly  heard 
the  ringing  of  the  bell.  On  permitting  hydrogen  to  enter  the  half- 
filled  receiver  until  it  was  wholly  filled,  the  sound  sank  until  it  was 
icarcely  audible.  This  result  remained  an  enigma  until  it  received  a 
iimple  and  satisfactory  explanation  at  the  hands  of  Prof.  Stokes, 
When  a  common  pendulum  oscillates  it  tends  to  form  a  condensation 
in  front  and  a  rarefaction  behind.  But  it  is  only  a  kmkncy :  the 
motion  is  so  slow,  and  the  air  is  so  elastic,  that  it  moves  away  in  front 
before  it  Is  sensibly  condensed,  and  fills  the  space  behind  before  it  can 
become  sensibly  dilated.     Hence  waves  or  pulses  are  not  generated  by 


l8o  ELLEN  OR  THE 

the  pendulum.  It  requires  a  certain  sharpness  of  shock  to  produce  the 
condensation  and  rarefaction  which  constitute  a  wave  of  sound  in  air. 
'The  more  elastic  and  mobile  the  gas,  the  more  able  will  it  be  to 
move  away  in  front  and  to  fill  the  space  behind,  and  thus  to  oppose 
the  formation  of  rarefactions  and  condensations  by  a  vibrating  body. 
Now  hydrogen  is  much  more  mobile  than  air ;  and  hence  the  produc- 
tion of  sonorous  waves  in  it  is  attended  with  greater  difficulty  than 
in  air.  A  rate  of  vibration  quite  competent  to  produce  sound  waves 
in  the  one  may  be  wholly  incompetent  to  produce  them  in  the  other.' 

"From  this  it  would  appear  that  hydrogen  gas  is  not  a  desir- 
able substance  for  the  promotion  of  sound,  and  that  the 
trouble  is  not  wholly,  if  at  all,  due  to  its  lack  of  density.  For 
the"  air  of  half  density  mixed  with  it  would  be  more  dense 
than  before,  and  yet  the  sound  under  these  circumstances 
in  the  above  experiments  was  deadened.  It  would  seem 
that  there  might  be  something  in  hydrogen  antagonistic  to 
sound.  And  this  is  sustained  by  the  fact  reported  by 
those  who  have  made  the  experiments,  that,  after  having 
breathed  hydrogen  gas,  the  voice  is  weak.  Mr.  Tyndall's 
explanation  of  the  difference  of  sound  in  hydrogen  and  in 
air,  is,  as  usual  with  him,  entirely  superficial  and  insuffi- 
cient. It  is,  besides,  dishonest,  because  he  calls  it  satisfactory 
when  it  is  not.  For  the  things  that  he  mentions  in  explanation 
are  true  of  air  or  any  other  gas.  Driven  to  it  not  by  honesty  but 
by  necessity,  Mr.  Tyndall  recognizes  here  for  the  first  time  the 
property  of  mobility,  which  belongs  to  all  fluids  and  gases,  and 
because  of  which  the  undulatory  theory  of  sound  is  impossible. 
The  elastic  force  of  all  gases,  under  the  same  pressure  and  tem- 
perature, is  supposed  to  be  the  same.     The  mobility  of  gases  is 


WHISPERINGS   OF  AN    OLD    PINE 


r8i 


thought  to  vary  with  the  amount  of  viscosity  they  possess,  and 
viscosity  is  ascribed  to  friction  between  the  particles.  Mobih'ty 
IS  also  thought  to  vary  with  the  velocity  of  the  particles  of  a 
gas,  and  the  velocity  of  the  particles  of  hydrogen  is  considered 
to  be  four  times  that  of  air.  But  whatever  difference  of 
mobility  there  may  be  in  gases,  is  here  practically  unimportant, 
as  all  are  sufficiently  mobile  to  prevent  the  formation  of  any 
extended  system  of  condensations  and  rarefactions.  The  air  is 
like  a  great  ocean,  only  more  liable  to  disturbances,  and  these 
disturbances  reach  down  further.  But  as  it  would  be  impos- 
sible for  a  system  of  weaves  formed  of  water  to  take  place  in  the 
body  of  the  ocean,  so  it  would  be  for  a  similar  system,  formed 
of  air,  in  the  body  of  the  air. 

**Mn  Tyndairs  remarks  about  the  pendulum  are  equally 
discreditable.  The  motion  of  a  pendulum  is  often  much  faster 
than  that  of  a  tuning  fork  or  fiddle  string.  As  everything  else 
which  moves  in  air,  it  condenses  the  air  in  front  and  leaves 
rarefaction  behind,  far  more  pronounced  than  that  left  by  a 
fork  or  string,  as  any  one  may  verify  by  experiment  with 
smoke,  but  it  does  not  form  any  system  of  condensations  and 
rarefactions  which  are  propagated.  For,  as  Ellen  has  before 
said,  because  of  the  mobility  of  the  air  this  cannot  be  done. 

"  Mr.  Tyndall's  remark  that  it  requires  a  certain  sharpness  ol 
shock  to  produce  these  hypothetical  sound  waves,  is  also  mere 
assertion  and  entirely  gratuitous.  For  by  the  hypothesis  it 
requires  nothing  of  the  kind.  It  requires  only  the  striking  of 
the  particles  by  the  moving  body.  But  Ellen  will  not  discuss 
further  the  phrase  'sharpness  of  shock*  until  some  scientist  wiD 
attempt  to  explain  what  is  meant  by  it 


182 

'*  Mr,  Tyndall  continues  : 


THE 


'The  motion  of  sound,  like  all  other  motion,  is  enfeebled  by  k 
transference  from  a  light  body  to  a  heavy  one.  AVheti  the  receiver! 
which  has  hitherto  covered  our  bell  is  removed,  you  hear  how  much 
more  loudly  it  rings  in  the  open  air.  When  the  bell  was  covered  the 
aerial  vibrations  were  first  communicated  to  the  heavy  glass  jar,  audi 
afterward  by  the  jar  to  the  air  outside ;  a  great  diminution  of  intensity 
being  the  consequence/ 

'*This  idea  that  the  aerial  vibrations  are  communicated  to 
the  glass  jar,  or  any  other  solid  body,  by  the  mere  slight  move- 
ment of  air  particles,  which  must  be  a  fact  if  this  theory  is 
true,  IS  as  ridiculous  and  senseless  as  it  is  possible  for  the  mind 
to  conceive.  For  it  is  well  known  that  sounds  uttered  in 
enclosed  rooms  may  and  often  do  go  through  thick  walls  of 
brick  or  stone.  And  this  theory  teaches  that  they  go  through 
by  bending  these  walls  in  and  out  They  could  no  more  do  it 
than  a  soap  bubble  could  bend  a  mountain,  or  a  thistle  seed 
knock  over  a  church.  Why  any  sane  person  should  accept 
such  a  proposition, — ^Ellen  doesn't  say  believe,  for  she 
doesn't  think  any  sane  person  could  believe  it,^ — is  inexplic* 
able  to  Ellen.  Or,  why  scientists  should  not  always  remem- 
ber that  not  only  a  cause,  but  a  sufficient  cause,  is  necessary 
for  any  result,  Ellen  cannot  understand.  There  would  seem  to 
be  no  reason  why  one  should  be  a  fool  in  order  to  be  a  scientist. 

'•Again  Mr.  Tyndall  says; 

•The  intensity  of  a  sound  depends  on  the  density  of  the  air  in  whkb 
the  sound  is  generated,  and  not  on  that  of  the  air  in  which  it  is  heanL* 

•  Poisson,  •*  M^canique,"  vol.  ii.,  p.  707. 


WHISPERINGS   OP  AX    OLD    1  INE 


18; 


Supposing  the  summit  of  Mont  Blanc  to  be  equally  distant  from  the 
lop  of  the  Aiguille  Verte  and  the  bridge  at  Chamouni ;  and  supposing 
two  observers  stationed,  the  one  upon  the  bridge  and  the  other  ii|3on 
the  Aiguille :  the  report  of  a  cannon  fired  on  Mont  Hlanc  would  reach 
both  observers  with  the  same  intensity,  though  in  the  one  case  the 
soimd  would  pursue  its  way  through  the  rare  air  above,  while  in  the 
other  it  would  descend  through  the  denser  air  below.  Again,  let  a 
straight  line  equal  to  that  from  the  bridge  at  Chamouni  to  the  summit 
of  Mont  Blanc  be  measured  along  the  earth's  surface  in  the  valley  of 
Chamouni,  and  let  two  observers  be  stationed,  the  one  on  the  summit 
and  the  other  at  the  end  of  the  line :  the  report  of  a  cajinon  fired  on 
the  bridge  would  reach  both  observers  with  the  same  intensity,  though 
in  the  one  case  the  sound  would  be  propagated  through  the  dense  air 
of  the  valley,  and  in  the  other  case  would  ascend  through  the  rarer  air 
of  the  mountain.  Finally,  charge  two  cannon  etjually,  and  fire  one  of 
them  at  Chamouni  and  the  other  at  the  top  of  Mont  Blanc  :  the  one 
fired  in  the  heavy  air  below  may  be  heard  above,  while  the  one  fired  in 
the  light  air  above  is  unheard  below.' 

**  If  sounds  as  the  theory  holds,  was  caused  by  the  vis  viva 
of  the  air  particles  hitting  the  drum  of  the  car,  it  is  difficult  to 
see  how  these  results  could  take  place.  For  the  vis  viva  of  air 
of  half  density  could  not  equal  that  of  air  of  full  density,  unless 
the  air  particles  had  large  additional  velocity.  Again,  too,  we 
are  confronted  with  a  fact  suggesting  that,  as  you  cannot  make 
brick  without  straw,  so  you  cannot  make  sound  without  proper 
material* 

**Mr.  Tyndall  further  says: 


'This  weakening  of   the   sound,    according   to  the  law  of   inverse 
squares,  would  not  take  place  if  the  sound  wave  was  so  confined  as  to 


184 


ELLEN   OR  THE 


prevent  its  lateral  diffusion-  By  sending  it  through  a  tube  with  a 
smooth  interior  surface  we  accomplish  this,  and  the  wave  thus  confined 
may  be  transmitted  to  great  distances  with  very  little  diminution  of 
intensity-  Into  one  end  of  this  tin  tube,  fifteen  feet  long,  I  whisper  in 
a  manner  quite  inaudible  to  the  people  nearest  to  me,  but  a  listener 
at  the  other  end  hears  me  distinctly.  If  a  watch  be  placed  at  one 
end  of  the  tube,  a  i>erson  at  the  other  end  hears  the  ticks,  though 
noboJy  else  does.  At  the  distant  end  of  the  lube  is  now  placed  a 
lighted  candle.  When  the  hands  are  clapped  at  this  end,  the  flame 
instantly  ducks  down  at  the  other.  It  is  not  quite  extinguished, 
but  it  is  forcibly  depressed.  When  two  books,  n  b'.  Fig.  9,  are  clapped 
together,  the  candle  is  blown  out.*  Von  may  here  observe,  in  a  rough 
way,  the  speed  with  which  the  sound  wave  is  propagated.  The  instant 
the  clap  is  heard  the  flame  is  extingiushed.  1  do  not  say  that  the  time 
required  by  the  sound  to  travel  this  tube  is  immeasurably  short,  but 
simply  that  the  interval  is  too  short  for  your  senses  to  appreciate  it. 


i-ifi.  9* 
'That  it  is  a  ////jy  and  not  a  ///jf  of  air  is  proved  by  filling  one  end 
of  the  tube  with  the  smoke  of  brown  paper.  On  clapijing  the  books 
together  no  trace  of  this  smoke  is  ejected  from  the  other  end.  The 
pulse  has  passed  through  both  smoke  and  air  without  carrying  either  ot 
them  along  with  it.* 

**  It  is  perfectly  evident  to  any  sensible  person  that  the  candle 
is  blown  out  by  a  puff  of  air,  just  as  it  is  perfectly  evident  that^ 

*  To  converge  the  puls«  upon  the  flame,  ibc  tube  was  caused  to  end  in  a  conc^ 


WHISPERINGS  OF  AN   OLD   TINE 


I8S 


when  sound  goes  through  a  stone  wall  it  does  not  make  the 
wall  bend  in  and  out,  but  is  carried  through  the  interstices  of 
the  wall  by  some  force  sufficiently  powerful  to  accomplish  this 
result*  Thus,  a  stream  will  find  its  way  through  impediments. 
With  the  stream  the  force  operating  is  gravity;  with  sound, 
unquestionably,  some  force  similar  to  electricity.  Sound 
spreads  through  different  bodies  because  of  its  tenuity.  The 
connection  is  doubtless  interfered  with  or  partly  broken  in 
passing  abruptly  from  one  medium  to  another,  but  sound  is 
able  to  go  through  nearly  all  mediums  and  therefore  it  is  cer- 
tain that  it  Is  of  extreme  tenuity. 

**  There  arc  several  things  to  be  proven  by  this  tube,  but 
none  of  them  are  favorable  to  this  theory  of  sound.  Ellen  had 
a  tube  made,  and  tried  this  experiment. 

**To  demonstrate  that  it  was  a  puff  of  air  that  blew  out  the 
candle,  Ellen  first  clapped  the  books  with  their  sides  or  covers 
towards  the  larger  end  of  the  tube.  In  this  case  the  sound 
would  be  the  same,  but  the  puff  of  air  made  would  be  driven  at 
right  angles  to  the  tube.  Of  course  the  candle  did  not  duck. 
Then  Ellen  tried  the  smoke,  but  had  it  blown  m  at  the  small 
end  of  the  tube  near  the  candle  instead  of  at  the  flange  end, 
fifteen  feet  away.  Clapping  books  again,  as  at  first»  the 
smoke  was  driven  two  Icct  from  the  lower  end.  Mr,  Tyn- 
dall  had  illustrated  the  fact  that  you  cotdd  not  drive  smoke 
through  a  tube  fifteen  feet  long,  with  one  clap  of  books.  Ellen 
found  that  you  could  do  it  with  a  sufficient  number  of  claps, 
Ellen  then  tried  the  experiment  with  a  fan  and  with  the  breath. 
In  neither  case  was  there  any  sound,  but  the  candle  was 
instantly  affected  as    before. 


:*^  ELLEN  ^'R  THE 

•'  Aryi  ::  proves  that  a  puff  of  air.  which  it  would  take  a  fan 
%veral  seconds  to  drive  in  usconfined  air,  may  be  con- 
ducted through  such  a  rube  in  an  indistinguishable  part  of  a 
«econd.  Theso  experiments  are  similar,  excepting  the  tube. 
In  each  ft  is  the  same  lan.  operated  :n  the  same  manner,  and 
affecting^  the  same  or  similar  air.  But  in  one  case  the  action  of 
the  tube  is  added  and  the  ver^-  dinerent  results  are  entirely 
due  to  this.  It  illustrates  completely  and  accurately  the 
differences  which  must  take  place  between  a  pulse  in  a 
tube  and  a  pulse  in  unconnned  air.  The  operation  of  the 
smoke  put  in  at  the  larger  end  shows  that,  as  in  a  longer  and 
smaller  tube  when  a  tight-fitting  piston  is  pushed  in,  each 
successive  layer  ot  air  is  shoved  through  the  tube,  and  in  suc- 
cession comes  out  at  the  small  end :  the  farthest  layer  from  the 
cau'^e  of  disturbance,  that  is  the  one  nearest  the  candle,  going 
out  first  and  causing  the  candle  to  duck.  For  it  is  impossible  to 
have  air.  that  is.  the  particles  of  air.  move  to  any  extent  against 
a  candle  without  causing  it  to  duck.  And  on  the  other  hand, 
sounds  do  not  thus  affect  a  candle  unless  the  normal 
vibration  (4  its  flame  is  the  same  as  that  of  the  body 
soundin;^^  In  that  case  a  Aame  will  be  affected  just  as 
a  pane  of  j^lass  will  vibrate  to  a  clap  of  thunder,  having  the 
same  normal  vibration  as  itself;  or  the  chords  of  a  piano  to 
a  sound  of  the  >ame  pitch  as  themselves.  Thus,  too,  one  tun- 
ing fork  will  be  set  in  vibration  by  the  sounding  of  another  of 
the  same  pitch,  it  is  said,  at  a  distance  of  I  GO  feet.  The  assump- 
tion of  the  scientists  is  that  these  sympathetic  vibrations  take 
place  because  of  air  waves,  particles  of  air,  in  succession  hit- 
ting the  pane  of  glass,  or  tuning  fork,  or  piano  string.     The 


WHISPERINGS  OF  AN  OLD   PINE  1 8/ 

assumption,  too,  is  that  air  waves,  whose  existence  is  imper- 
ceptible to  the  most  sensitive  conditions,  will  do  this.  The 
tremor  of  the  earth  caused  by  a  single  flake  of  snow,  falling 
upon  the  top  of  Mont  Blanc,  could  every  whit  as  easily  accom- 
plish the  result  with  every  piano  on  earth,  as  could  the  hypo* 
thetical  air  waves  with  one  piano,  and,  indeed,  much  more 
probably,  because  the  snow  flake  on  Mont  Blanc  is  something 
real,  whilst  the  air  wave  is  entirely  visionary. 

**It  is  very  evident  that  these  results  come  from  some  appro- 
priate and  extraordinary  force  which  vibration,  or  contact,  the 
cause  of  vibration,  has  introduced.  The  rubbing  of  certain 
bodies  will  produce  electricity.  Very  possibly  electricity,  or 
a  substance  similar  to  electricity  enters  into  the  production  of 
sound. 

"We  can  easily  imagine  that  a  force,  or  substance,  like  elec- 
tricity might  be  able,  by  unknown  laws,  to  get  inside  of  a 
piano  and  make  a  wire  vibrate,  but  we  may  be  perfectly 
sure  that  no  inadequate  cause,  as  the  movement  of  air  par- 
ticles in  the  room  outside  or  anywhere  else,  could  accomplish 
this. 


1 88  ELLEN   OR  THE 


XII. 


^^f^OI^  some  time    it  has  seemed   to   Ellen  that  electrical 
A      conditions   enter     into    sound,    and    she    has    recently 

come  across  the  following  evidence : 

"In    a  letter  of   M.    Oersted,    Professor   of   Philosophy   at 

Copenhagen,  to   Professor  Pictcd  of  Geneva,  upon   Sonorous 

Vibrations,  published  in  the  'Philosophical  Magazine'  in  1806, 

vol.  24,  is  the  following : 

*One  would  suppose  that  the  change  produced  in  elastic  bodies,  by 
the  communication  of  motion,  could  scarcely  be  limited  to  the  simple 
mechanical  displacement  of  the  part,  but  that  in  this  modification  it 
ought  to  have  some  other  more  intimate  action.  Every  kind  of  friction 
produces  not  only  heat,  but  electricity  also.  De  la  Place,  and  Biot, 
have  already  attracted  the  attention  of  philosophers  to  the  first  of  these 
phenomena ;  I  am  of  the  opinion  that  the  latter  of  them  requires  much 
more  attention.  I  always  found  in  my  experiments  that  sand,  or  dust, 
adheres  much  more  to  those  parts  to  which  the  movement  of  the  sonor- 
ous bodies  had  fixed  it,  than  it  did  to  other  parts.  I  have  often  thrown 
fresh  sand  over  a  plate  of  glass,  upon  which  I  had  already  produced  a 
figure.  I  shook  it  gently  after  having  reversed  it,  and  I  always 
remarked  that  the  sand  which  formed  the  figure  remained  adhering, 
while  the  other  part  detached  itself.  The  adherence  of  the  grains  finer 
than  those  of  sand  is  very  remarkable.  I  also  discovered,  with  the 
assistance  of  Coulomb's  eloctrometer,  indications  of  electricity  in  those 
plates  which  had  emitted  a  sound;  but  I  have  not  repeated  these 
experiments  sufficiently  to  enable  me  to  detail  them.  I  discovered  on 
the  above  occasion,  that  the  edges  and  angles  of  bodies  act  upon  Cou- 


WHISPERINGS    OF   AN    OLD    IMNE 


189 


lomb*s  electrometer  almost  always;  and  I  propose  to  myself  a  new 
course  of  experiments  upon  this  subject.  The  celebrated  Ritter,  to 
whom  I  had  communicated  my  experiments  upon  the  part  which  elec- 
tricity acts  in  the  phenomejia  of  sound,  had  long  ago  discovered  that 
the  electrical  pile  of  Volta  is  capable  of  producing  sotmd,  when  a  shock 
is  received  from  it  in  the  ears.  In  a  work  about  to  appear  under  the 
title  of  **  A  System  of  Electrical  Bodies,"  this  great  philosopher  makes 
it  clear  that  a  body  acquires  positive  electricity  by  compression,  and 
negative  by  dilatation.  1  bus  we  may  say,  that  there  are  in  each  sound 
as  many  aJternalives  of  electricity,  positive  and  negative,  as  there  are 
oscillations  ]  but  the  union  of  two  electricities  produce  a  commotion : 
thus  there  are  in  one  sound  as  many  extremely  weak  electrical  commo- 
tions as  there  are  oscillations.  Each  of  these  insulated  commotions 
would  be  absolutely  insensible ;  but  when  received  in  a  very  great  num- 
ber, in  a  period  too  small  to  distinguish  the  one  from  the  other,  they 
always  produce  a  sensible  effect,  especially  since  positive  electricity 
renders  the  organ  more  sensible  for  the  negative  than  it  was  before,  and 
tw  versa.  The  sensible  effect  of  the  union  of  all  these  insensible 
commotions  is  sound.  I  confess  that  these  ideas  of  M,  Ritter  appear 
contradictory  to  all  the  received  opinions  on  the  organ  of  hearing  j  but 
it  must  also  be  confessed  that  our  knowledge  of  all  the  organs  of  sense 
is  as  yet  imperfect,  I  am  of  opinion,  however,  that  the  theory  of  M. 
Ritter  agrees  perfectly  well  with  the  ancient  hypotheses.  As  for  ray 
own  experiments,  they  may  be  easily  repeated  by  any  person,  and  some 
one  perhaps  may  discover  more  than  I  have  here  described.' 

••Dr.  Hans  Christian  Oersted  was  eminent  as  a  physicist  and 
especially  recognized  as  authority  in  electricity.  The  Cham- 
bers* Encyclopaedia  thus  speaks  of  him : 


"In   tSir  Mr,  Oersted  wrote  his  famous  essay  on   the  identity  of 
chemical  and  electrical  forces,  in  which  he  first  developed  the  ideas  on 


190  ELLEN   OR  THE 

which  were  based  his  great  discovery  of  the  intimate  connection  exist- 
ing between  magnetism  and  electricity  and  galvanism.  He  thus  made 
good  his  claim  to  be  regarded  as  the  originator  of  the  new  science  of 
electro-magnetism.  The  enunciation  of  this  theory  was  followed  by 
many  important  experiments  in  regard  to  the  compression  of  water, 
and  by  numerous  other  chemical  discoveries.  The  influence  which 
Dr.  Oersted  exerted  on  the  science  of  the  day  by  his  discoveries,  was 
recognized  by  the  learned  in  every  country,  and  honors  increased  upon 
him  with  increasing  years.' 

**The  following  statement,  suggestive  of  a  similarity  between 
sound  and  electricity,  Ellen  saw  in  the  'London,  Edinburgh 
and  Dublin  Philosophical  Magazine,*  vol.  4,  though  she  did 
not  sec  the  articles  referred  to : 

*  The  investigations  of  Helmholtz  on  the  divergence  of  sound  from 
the  open  end  of  a  cylindrical  tube  (Crelle,  i860),  broke  ground  for  the 
first  time  in  the  knowledge  of  the  manner  in  which  sound  actually 
passes  over  from  the  inside  of  a  tube  into  the  surrounding  air.  The 
work  was  based  on  the  modern  potential  analysis ;  and  some  of  the 
chief  difficulties  in  it  were  overcome  by  giving  to  the  various  expres- 
sions the  meaning  they  would  have  had  in  the  theory  of  electricity,  and 
employing  the  results  that  belong  specially  to  that  theor}\ 

*  Lord  Rayleigh  treated  important  portions  of  the  same  subject  in  a 
paper  in  the  "  Philosophical  Transactions,"  187 1  (Mr.  Strutt  "  On  Reso- 
nance *') .  The  analysis  is  much  simplified,  but  it  is  essentially  the  same 
in  principle  as  Helmholtz's.  The  reference  to  electrical  analogies  is 
used  freely.' 

*' There  is  a  marked  similarity  between  the  laws  governmg 
the  conduction  of  electricity  and  sound  through  solids  in  the 
form  of  wires  or  rods.  Thus  *  Electricity  in  the  Service  of 
Man*  says: 


WHlSrERlNGS   OF  AN    OLD    I  INP 


19! 


*  The  laws  of  the  resistance  of  coatluctors  may  therefore  Vie  collected 
jiB  follows : 

*  t .  The  resistance  of  a  cantiueting  wire  is  proporti&nai  to  its  length. 

*  2.  Tke  resistance  of  a  conducting  wire  is  inversely  proportional  to 
ihe  area  of  its  cross  section. 

*  J.  The  resistance  of  a  conducting  wire  of  a  given  length  ami  Miick- 
ness  depends  upon  ihe  specific  resistance  of  the  material  of  which  it 
is  made** 

"Also  in  rei^ard  to  sound,  the  *  LundoHp  Edinburgh  and 
Dublin  Philosophical  Magazine/  voL  27,  page  548.  says: 

'The  intensity  of  sound  remains  constant  when  one  roil  (conducting 
it)  is  replaced  by  another  of  the  same  material  but  the  dimensions  of 
which  vary  in  the  same  proportion.  By  varying  the  length  alone  the 
intensity  is  changetl ;  in  like  manner  it  is  changed  also  by  varyinji?  the 
?5ection  while  the  length  is  constant.  (The  test  was  made  with  a 
tuning  fork.)* 


*•  Wc  have  seen  that  Newton  expounded  in  its  present  form 
this  theory  of  sound,  a  thing  that  could  not  possibly,  as  Ellen 
thinks,  have  occurred  had  there  then  existed  the  knowl- 
edge of  electricity  which  we  have  to-day.  We  have  seen 
that  light  and  sound  are  largely  governed  by  the  same 
laws.  Hut  this  is  not  more  certain  than  that  electricity,  heat, 
and  light  arc  all  kindred  substances.  At  the  time  of  Newton 
electricity  was  just  beginning  to  be  examined ^  and  was  known 
only  in  its  frictional  form.  Newton  lived  1643— 1727;  Franklin 
began  his  first  experiments  in  electricity  about  1740,  but 
Galvani  did  not  discover  galvanic  electricity  until  1790,  nor 
Volta  the  voltaic  pile  until  1800.     In  1820  Oersted  discovered 


192  ELLEN   OR  THE 

the  action  of  the  galvanic  current  in  the  magnetic  needle. 
Arago  in  1820  and  Davy  in  1821  discovered  the  power  of  the 
electric  current  to  magnetize  iron  and  steel.  Sebeck  discovered 
thermo-electricity  in  1822,  and  in  1831  Faraday  discovered 
induced  currents  of  electricity.  Since  these  dates  have  fol- 
lowed the  great  practical  discoveries  which  to-day  make  elec- 
tricity the  most  remarkable  of  known  forces. 

"And  yet,  although  all  these  greater  discoveries  on  elec- 
tricity were  made  since  Newton's  time,  he  perceived  the  close 
connection  between  electrical  conditions  and  those  of  sound,  as 
is  illustrated  by  the  statement  found  in  '  Hutton's  Mathematical 
Dictionary,'  in  the  article  on  *  Electricity,'  as  follows : 

*  Newton  ascribes  the  action  of  electric  bodies  to  an  elastic  fluid 
which  easily  penetrates  glass,  and  the  emission  of  it  to  the  vibratory 
motions  of  the  parts  of  the  excited  bodies.* 

"It  will  be  seen  here  that  Newton  ascribes  the  emission  of 
electricity  to  exactly  the  same  conditions  that  cause  the  emis- 
sion of  sounds. 

"  Ellen  will  now  resume  her  review  of  Mr.  Tyndall's  book: 

'The  celebrated  French  philosopher.  Blot,  observed  the  transmission 
of  sound  through  the  empty  water-pipes  of  Paris,  and  found  that  he 
could  hold  a  conversation  in  a  low  voice  through  an  iron  tube  3, 120  feet 
in  length.  The  lowest  possible  whisper,  indeed,  could  be  heard  at  this 
distance,  while  the  firing  of  a  pistol  into  one  end  of  the  tube  quenched 
a  lighted  candle  at  the  other.' 

•'Here  aj^ain  vvc  have  a  suggestion,  though  not  a  statement* 
for  ignorance  is  often  cowardly,  that  sound  has  to  do  with 
quenching    a    lighted  candle.      And    it  appears  that  M.    Biot, 


:     ;■:■,'■  >■ 


:-,AKY 


WlIISPERtNGS    OF   AN   OLD    riXi: 

quite  a  noted  scientist,  fell  into  this  delusion.  Regnault, 
another  French  scientist  and  noted  experimenterp  was  also  thus 
misled. 

•*The  distance  that  a  whisper  is  heard  in  a  tube,  as  noted  by 
M.  Biot,  ilhistrates  that  in  a  tube  sound  is  not  dissipated.  In 
this  it  acts  as  any  material  thing  would,  confined  by  a  tube. 

"And  it  must  have  a  certain  and  fixed  consistency,  else 
It  could  not  be  the  correlative  of  the  sensation.  And  this 
consistency  must  be  of  a  kind  that  can  be  reflected,  else  we 
couJd  not  have  echoes,  for  that  which  makes  the  echo  is  the 
correlative  of  that  which  makes  the  sound.  For  under 
favorable  conditions  the  echo  is  almost  a  perfect  duplicate 
of  the  sound.  But  waves  of  water — or,  if  it  was  possible 
for  them  to  exist,  of  air — du  not  have  any  such  con- 
sistency, and  they  cannot  be  reflected  with  form  unchanged, 
any  more  than  a  quart  of  water  could  be  reflected  with  its 
form  unchanged.  And  this  because  v\  the  mobility  of  the 
air.  that  remarkable  quality  in  fluids  which  permits  their  par- 
ticles to  slip  by  each  other  with  such  great  facility  and 
tlius  distinguishes  them  from  solids.  Under  the  laws  of  nature 
the  thing  is  impossible.  Neither  could  any  system  of  waves 
Hnth  their  arrangement  of  particles  unchanged  be  gathered  in 
a  megaphone*  And  therefore  it  is  certain  that  sound,  or  the 
correlative  of  it,  cannot  consist  of  waves  in  any  form,  but 
must  be  an  entity  capable  of  being  both  reflected  and 
gathered, 

**Mr.  Airy»  at  one  time  Astronomer  Royal  of  England,  says 
in  the  *  London,  Edinburgh  and  Dublin  Philosophical  Maga- 
zinc/  vol.  33,  page  404  : 


■^-  -^ 


10  ELLEN   OR  THE 

'  1  have  never  been  able  to  observe  the  smallest  trace  of  reflected 
wave  from  a  surf,  although  at  the  same  time  I  am  utterly  unable  to 
account  for  the  disposal  of  the  vis  viva, 

*  A  broken-headed  sea  is  not  reflected  by  a  vertical  pier.  When  a 
broken-headed  sea  strikes  a  pier  perpendicularly,  it  is  thrown  upwards ; 
when  it  strikes  obliquely,  it  is  partly  thrown  upwards  and  partly  it  runs 
horizontally  along  the  face  of  the  pier.  In  neither  case  is  there  any 
reflection  of  the  broken  head,  or  any  creation  of  a  broken  wave  travel- 
ling in  the  opposite  direction,  although  the  swell  is  reflected  according 
to  the  usually  understood  laws.* 

**  This  shows  how  scientists  have  been  confused  in  regard  to 
the  reflection  of  water.  Broken-headed  seas  are  caused  by  the 
force  of  the  wind,  and  cannot  be  reflected  as  such  when  striking 
a  perpendicular  pier ;  but  a  swell  is  under  the  action  of  gravity, 
both  when  striking  the  pier  and  when  leaving  it,  and  therefore 
is  reflected  with  reverse  form." 

'*But  a  pulse  in  a  tube  is  reflected,  is  it  not,  Ellen?" 
"  h>om  the  further  end  of  the  tube,  if  closed,  it  is  by  necessity 
reflected  because  it  cannot  spread.  That  is,  the  matter  form- 
ing it  is  reflected  in  the  form  of  another  pulse,  but  of  necessity 
also  with  particles  very  differently  situated.  And  since  the 
character  and  quality  of  the  sound  depend  upon  the  arrange- 
ment of  whatever  it  is  that  makes  sound,  this  arrangement  can 
not  be  in  the  slightest  degree  injured  without  affecting  the 
sound,  nor  much  altered  without  destroying  it.  This  fact  is  a 
constant  and  fatal  objection  to  the  theory,  but  is  emphasized  in 
this  case  of  reflection,  where,  by  the  theory,  an  echo  of  the 
original  sound  becomes  impossible. 


WHISPERINGS   OF  AN   OLD    PINE 


197 


"That  the  sensation  o(  sound  must  depend  upon  the  correla- 
tive without,  is  beginning  to  be  recognized  by  scientists.  Thus 
Mr,  Ganot  says : 

*The  tint  If  fr  or  sUimp  or  quaiiiy  is  that  peculiar  property  of  note 
which  distinj^iishes  a  note  when  sounded  on  one  instrument  from  the 


I  ig.  10.  < 

State  note  when  sounded  on  another,  and  which  by  some  is  called  the 
cohr.  Thus  when  the  C  of  the  treble  stave  is  sounded  on  a  violin  and 
on  a  flute,  the  two  notes  will  have  the  same  pitch ;  that  is,  they  are 
Iiroduced  by  the  same  number  of  vibrations  per  second,  and  they  may 
have  the  same  intensity,  and  yet  the  two  notes  will  have  ver>'  distinct 
qualities;  that  is,  their  timbre  is  different. 

*  l£  we  were  to  represent  graphically  a  compound  note,  we  should 
proceed  to  constnicl  a  curve  out  of  simple  notes  of  different  intensities 

P  rig.  u. 

in  the  same  manner  as  fig.  1 1  is  constructed  from  two  simple  notes  of 
equal  intensity  represented  by  fig.  10.  It  is  evident  that  the  resulting 
curve  will  take  different  /tyrms  according  to  the  presence  or  absence 
of  different  harmonics  and  to  their  different  intensities;  in  other 
words,  the  quality  or  timbre  of  the  notes  produced  by  different 
instruments  will  depend  upon  i\it  form  of  the  cune  representing  vibra- 
tions producing  the  sound/ 


**  Deschanel  says ; 


198  ELLEN  OR  THE 

'Musical  sounds  may,  however,  be  alike  as  regards  pitch  and  loud- 
ness, and  may  yet  be  easily  distinguishable.  We  speak  of  the  quality 
of  a  singer's  voice,  and  the  tone  of  a  musical  instrument ;  and  we  char- 
acterize the  one  or  the  other  as  rich,  sweet,  or  mellow,  on  the  one 
hand  ;  or  as  poor,  harsh,  nasal,  etc.,  on  the  other.  These  epithets  are 
descriptive  of  what  musicians  call  timbre — a  French  word  literally  sig- 
nifying stamp,  German  writers  on  acoustics  denote  the  same  quality 
by  a  term  signifying  sound  tint.  It  might  equally  well  be  called  sound 
flavor.     We  adopt  character  as  the  best  English  designation. 

*  Physically  considered,  as  wave  length  and  wave  amplitude  fall  under 
the  two  previous  heads,  character  must  depend  upon  the  only  remain- 
ing point  in  which  aerial  waves  can  diflPer — namely  their  form^  mean- 
ing by  this  term  the  law  according  to  which  the  velocities  and  densities 
change  from  point  to  point  of  a  wave.  Every  musical  sound  is  more  or 
less  mingled  with  non-musical  noises,  such  as  puffing,  scraping,  t\%'ang- 
ing,  hissing,  rattling,  etc.  These  are  not  comprehended  under  timbre 
or  character  in  the  usage  of  the  best  writers  on  acoustics.  The  grada- 
tions of  loudness  which  characterize  the  commencement,  progress,  and 
cessation  of  a  note,  and  upon  which  musical  effect  often  greatly 
depends,  are  likewise  excluded  from  this  designation.  In  distinguish- 
ing the  sounds  of  different  musical  instruments,  we  are  often  guided  as 
much  by  these  gradations  and  extraneous  accompaniments  as  by  the 
character  of  the  musical  tones  themselves. 


*  Character  or  timbre^  which  we  have  already  defined,  must  of  neces- 
sity depend  on  the  form  of  the  vibration  of  the  aerial  particles  by 
which  sound  is  transmitted,  the  word  form  being  used  in  the  meta- 
phorical sense  there  explained,  for  in  the  literal  sense  the  form  is  always 
a  straight  line.' 

'*Prof.  Pietro  Blaserna  in  his  'Theory  of  Sound'  says: 


WHISPERINGS  OF  AX   OLD    I'lNE 


199 


r 


*The  third  characteristic  difference  of  musical  sounds  is  their  quaiity 
or  Hmbre,  Suppose  that  the  same  note  is  sung  by  different  human 
voices,  and  played  on  the  pianoforte,  violin,  flute,  etc.,  it  does  not 
tequjre  a  delicate  musical  ear  to  recognize  that  these  notes,  although  of 
the  same  loudness  and  pitch,  are  nevertheless  dilTerent  from  each 
other*  Our  ear  goes  e\'en  farther  in  this  direction,  and  not  only  dis- 
tinguishes betift'cen  violin  and  flute,  but  even  between  one  violin  and 
another  by  a  diHerent  maker.  The  difference  is  very  marked,  and 
makes  itself  felt  in  a  most  remarkable  manner  in  the  price  of  the  instni- 
ment«  Thus,  for  example,  whilst  an  ordinary  violin  costs  a  few  pounds, 
many  hundreds  are  paid  for  a  good  Stradivaruis  or  N.  Amati,  Tlie 
same  may  be  said  of  all  musical  instruinents,  although  the  difference  of 
price  is  not  so  great  for  most  of  them,  as  the  modern  manufacturers 
arc  in  a  position  to  furnish  them  in  any  desired  number;  whilst  violins 
increase  in  excellence  and  value  with  their  age, 

'The  difference  of  timbre  is  therefore  very  important,  and  very  char- 
acteristic. In  the  human  voice,  which  constitutes  the  most  agreeable 
and  richest  monotone  musical  instrument,  the  variety  is  jmmense. 
There  are  scarcely  any  t^o  individuals  who  have  exactly  the  same 
timbre  of  voice.  Timbre  and  inflection  are  the  safest  means  we  have 
of  recognizing  a  person, 

*But  the  loudness  of  a  note  depends  on  the  width,  height,  and 
length  of  the  oscillations  producing  it.  It  may  then  be  asked,  in  what 
two  oscillations,  of  the  same  width  and  length,  can  differ  so  as  to  pro- 
duce so  marked  a  difference  as  that  of  timbre, 

*  There  are  two  methods  of  procedure  possible  in  the  study  of  differ- 
ent forms  of  oscillation,  and  of  the  causes  that  influence  timbre.  The 
cuivc  of  the  oscillations  may  be  traced  graphically,  and  the  differences 
between  them  may  be  examined  thus,  or  the  sounds  produced  by  dif- 
ferent instruments  may  be  analyzed  in  order  to  see  if,  besides  the 
principal  note  that  is  heard,  there  are  not  other  concomitant  sounds  or 


2CX) 


ELLEN   OR  THE 


noises  which  alter  the  timbre  of  the  simple  note,  and  impress  a  special 
character  on  it.  The  question  will  be  studied  in  this  treatise  by  both 
methods,  and  they  will  be  illustrated  by  the  most  important  examples 
in  each.  As  to  the  form  of  vibrations,  it  will  be  shown  that  account 
must  be  taken  not  only  of  the  width  and  length  of  the  oscillations,  Init 
also  of  the  special  form  of  the  curve  which  represents  them,     llius,  for 


Fig.  12. 

example,  the  curves  i,  2,  3,  in  fig.  12,  have  all  three  the  same  width 
iiby  and  the  same  length  AB ;  but  the  form  is  different  for  each  one  of 
them,  and  it  is  precisely  on  this  special  form  that  that  which  is  called 
timbre  depends.' 

"  The  ordinatcs  of  these  curves  are  assumed  to  represent  the 
velocities  of  the  air  particles  in  the  different  systems  of  waves. 
Ellen  would  like  to  know  whether  the  particles  in  fig.  11  and 
in  2   or  3    of  fig.  12  are  supposed  to  move  according  to  Mr. 


WHISPERINGS   OF  AX   OLD    PINE 


20I 


ton's  proposition,  like  a  cycloidal  penduluni;  that  is, 
whether  these  represent  the  harmonic  curve  of  sines? 

**  Another  fatal  objection  to  the  theory  is  that  it  teaches 
that  sound  goei*  at  tlie  same  speed  in  a  tube  and  out 
of  a  tube.  But  if  it  was  a  matter  of  vis  viva  the  velocity 
would  vary.  For  there  is  the  same  dt^nsity  of  air  in  a  tube 
as  out  of  a  lube,  but  out  of  a  tube  the  mass  is  infinitely 
greater,  and  therefore  if  the  velocity  remained  the  same  the  vis 
vivn  would  be  infinitely  greater,  and  hence  would  be  infinitely 
great:  which  is  infinitely  absurd.  It  follows,  too,  that 
^ound,  if  due  to  vis  viva,  must  diminish  in  speed  from 
beginning  to  end,  which  it  does  not  do.  Ellen  is  accept- 
ing here  what  the  scientists  say  about  vis  viva  —  that  it  is 
half  the  mass  into  the  square  of  the  velocity.  When  a 
piston  is  pushed,  or  gas  is  exploded  in  a  tube,  the  pulse 
formed  will  be  confined,  and  therefore  go  a  much  longer 
distance  and  much  faster  than  in  unconfined  air.  But  sound 
does  not  go  faster.  And  therefore  it  is  certain  that  sound  is 
something  very  different  from  a  pulse  of  air. 

*'Thc  old  I'inc  must  remember  m  all  these  discussions  that 
air  and  all  gases  are  composed  of  little  bodies  which  have  both 
weight  and  extension ;  for  we  can  confine  these  bodies  in  many 
different  vessels  precisely  as  we  would  sand  or  wahiuts;  and 
they  cannot  escape.  But  air  is  not  sound  any  more  than 
pumpkins  or  mountains  are  sound;  though  sound  may 
throw  it  into  vibration.  If  the  old  Pine  wants  a  piano  to 
furnish  his  house  wifli,  he  must  go  to  a  piano  manufactory 
for  it,  where  the  machinery  exists  for  making  it,  or  at 
least  he   must  get  it   somewhere    where,  in  some  manner,  it 


202  ELLEN   OR  THE 

was  procured  from  such  factory.  For  no  other  factory  in  all 
the  universe  can  make  a  piano.  And  so  with  sound.  It  is  all 
made,  every  particle  of  it,  by  sound  factories,  and  these  are 
elastic  bodies.  Ellen  knows  that  the  factories  which  make 
sound  are  very  numerous,  much  more  so  than  those  which 
make  pianos.  Still  they  are  factories,  and  the  sounds,  if 
ever  finished,  must  be  finished  in  them,  just  as  butternuts, 
or  turnips,  or  anything  else  which  nature  makes,  are  finished 
in  the  factories  that  make  them.  That  is  the  way  that 
things  are  made;  and  the  old  Pine  will  have  to  get  all  his 
supplies  ultimately  from  these  sources,  for  there  are  no 
other.  Nor  can  different  things  be  remade  or  altered  to  advan- 
tage ;  certainly  not  sounds,  any  more  than  soap  bubbles  could 
be  after  they  had  been  launched,  though  pianos  or  turnips 
might  be  returned  to  the  factories  and  repaired  or  made  larger. 
"And  thus  sounds  are  turned  out,  and  there  are  millions  of 
them,  and  always  they  flow  off  as  fast  as  they  are  made.  That 
is  what  they  arc  made  for.  And  they  go  up  as  well  as  down, 
and  go  in  all  directions  if  unconfined,  but  act  very  differ- 
ently confined  in  a  tube,  or  directed  by  a  megaphone  or 
speaking  trumpet.  In  these  cases  they  go  straight  ahead. 
There  are  just  so  many  sounds,  every  one  of  them  complete  and 
all  alike,  when  made  by  the  same  vibration.  With  air  not  con- 
fined in  a  tube  they  divide  up  and  go  everywhere,  but  with  it 
confined  they  keep  together  and  strengthen  each  other.  For 
it  is  evident  that  the  results  of  hearing  come  from  an  accumu- 
lation of  sound ;  just  as  thirst  is  quenAed  not  by  a  drop  of 
water  but  by  many  drops,  and  hunger  satisfied  not  by  a  single 
morsel  but  by  a  full  meal.     And  Ellen  thinks  that  this  law  is 


WHISPERINGS   OF   AN*    OLD    PINE  : 

universal  in  nature.  We  see  not  by  a  single  particle  of  light,  but 
by  many  of  them.  We  exercise  not  by  one  step,  but  by  many 
steps.  We  enjoy  scenery  not  by  one  glance,  but  by  many 
glances.  Wc  realize  smell  not  from  the  effect  of  a  single  pr,r- 
ticle  of  odor,  but  as  a  result  of  many  of  these.  And  so  we 
hear  not  from  the  effect  of  a  single  sound,  but  because  of  many 
of  them.  Perhaps  the  old  Pine  would  have  arranged  all  this 
better  if  he  had  created  things?** 

•*No/'  I  said,  'Hhe  old  Pine  is  entirely  satisfied  with  the  way 
things  are  made,  nor  does  he  see  how  they  could  be  improved." 

**\Velli  that's  the  way  they  are  made/*  she  said.  "There  is 
a  wide  limit  of  difference  in  the  intensity  or  quantity  of  things. 
That  sound  is  no  exception  can  be  most  simply  and  fully 
demonstrated  by  the  megaphone.  For  the  megaphone  collects 
the  sound  floating  in  an  extended  surface  of  air,  and  thus  col- 
lected brings  it  to  the  ear  as  a  funnel  conducts  a  fluid,  or  a 
hopper  grain.  Always  the  result  is  to  increase  the  intensity  of 
a  sound,  and  frequently  wc  are  able  thus  to  hear  distinctly 
sounds  which  without  the  megaphone  we  could  not  hear  at 
alL  The  megaphone  will  gather  odor  equally  with  sound, 
which  alone  demonstrates  both  to  be  entitities;  and  Ellen  saw 
another  very  interesting  itlustration  of  this  principle  as  follows: 

•llie  widespread  sail  of  a  shij»,  rendered  concave  by  a  gentle  breeze, 
is  a  good  collector  of  sound.  **  It  happened/'  says  Dr.  Arnoti,  "once 
on  board  a  ship  sailing  along  the  coast  of  Brazil,  far  out  of  sight  of 
hndp  that  the  persons  walking  on  deck,  when  passing  a  particular  spot, 
alwa)*s  heard  very  distinctly  the  sound  of  bells,  varying  as  in  human 
Ttjoicings.  All  on  board  came  to  listen  and  were  convinced  ;  but  the 
phenomenon  was  most   mysterious.     Months  afterwards  it  was  a^Kier- 


^mM^ 


204  ELLEN   OR   THE 

tuned,  tiuLt,  at  the  tiine  of  obfiervatiocu  the  bdLs  o£  the  city  c^  St.  Sal- 
vador, oa  the  Brazilian  coast,  had  been  ringing  on  the  occaaoo  of  a 
festival ;  their  soand,  therefore,  favored  by  a  gentle  wind,  had  traveled 
perhaps  loo  miles  by  smooth  water,  and  had  been  l^roa^t  to  a  focus 
by  the  sail  on  the  particular  spot  where  it  was  Ustened  to.     It  appear^ 
from  this  that  a  machine  might  be  constimted  having  the  same  relatioiS' 
to  sound  that  a  telescope  has  to  sighL"  ' 

"The  human  ear  in  its  flaring  shape  and  Iab3rrinthal  pas — 
sages,  is  evidently  intended  for  the  gathering  and  reflection  of^ 
sound.  And  thus  all  animals  Ii\'ing  in  air,  where  the  passage 
of  sound  is  comparatively  weak,  have  similar  organs,  which 
gather  and  convey  the  sounds  to  the  auditory  nerve ;  but  in 
v^-ater,  where  sounds  have  more  strength,  they  reach  the 
auditor\-  ner\'e  of  fishes  through  the  bones  of  the  head. 

**And  therefore  sound  may  be  scattered  ever>-\vhere  and 
yet  audible  nowhere:  but  if  kept  together  we  can  hear  it 
readily.  This  is  the  reason  that  sound  is  heard  so  far  in  a  tube, 
and  in  the  ec*:'n'.">my  of  nature  there  is  no  other  possible  explan- 
ation :   n» »  other  that  d'-esn't  lead  to  absurdities. 

••Another  peculiarity  of  sound  is  mentioned  by  Francis 
Bacon,  who  says : 

'It  i-  evi'ient,  and  it  is  one  of  the  strangest  secrets  in  sounds,  that 
the  whole  S'ound  i-^  not  in  the  whole  air  only ;  but  the  whole  sound  'is 
also  in  ever\-  part  c:  the  air.  So  that  all  the  curious  diversity  of 
articulate  sounds  oi  the  voice  of  man  or  birds  will  enter  at  a  small 
crannv  unconfused.' 


WHiSI'EklNGS    OF    AN   ULU    I'INE 


20; 


XIU. 


^MT  is»  then,  certain  that  sounds  are  entities;  that  they  are 
^  microscopicaL  and  that  the  mills  which  make  them  turn 
them  out  in  great  quantity  exactly  alike,  just  asscrewsj  or  pins, 
or  bullets  are  made — all  exactly  alike.  For  it  is  no  more 
remarkable  that  sound  should  be  created  in  great  quantities  and 
spread  than  that  mist  should. 

'*  But  what  is  the  cause  o(  sound,  and  in  what  does  its  motion 
consist?*' 

**Tlie  immediate  cause  is  shock,  which  produces  sound, 
and  this  sound  radiates  in  all  directions,  thrown  off  by  the 
vibrating  body.  In  addition  the  vibrating  body  strikes  what- 
ever is  in  its  way,  pushing  it  out  of  the  way  if  light,  and  being 
itselJ  stopped  in  its  vibration  \i  encountering  a  heavy  body* 
Hut  in  no  case  can  it  make  any  body  move  faster  than  it  moves 
itself.  If  anything  struck  by  a  vibrating  body  docs  move  faster 
than  this  agitating  body,  it  is  because  some  new  force  is 
brought  into  action.  Thus  a  tuning  fork  might  hit  some  light 
body  near  enough  to  a  stream  to  throw  it  in,  when  it  might  be 
carried  away  by  the  ctirrent,  or  it  might  throw  some  light 
body  off  a  precipice  and  into  the  unopposed  stream  of 
gravitation »  but  particles  of  air  hit  by  it  are  not  urged  on  in 
their  course  any  faster  than  the  prong  of  the  fork  is  mov* 
ing,  which  is  at  the  rate  of  but  a  few  feet  a  second.  Thus. 
a  4  vibrating  prong  hits  water  it  will  throw  the  drops 
a  few  inches  in  the  direction  of  its  movement,  and  with  a  little 


liiii. 


208  ELLEN   OR  THE 

less  speed  than  it  moves  itself.  The  particles  of  air  it  will  push 
in  similar  manner,  as  can  be  observed  by  the  use  of  smoke. 

"  And  this,  and  this  only,  takes  place  from  the  effect  of  a 
blow  by  the  prong  of  the  tuning  fork.  The  assertion  that  any 
different  result  takes  place  is  but  an  hypothesis,  unproven  and 
untrue. 

"Thus,  in  churning,  the  dasher  hits  the  air  or  anything  else 
in  its  path,  and  drives  it  out  of  the  way ;  but  this  air  or  any- 
thing else  thus  driven  away  is  not  butter — no  more  is  it  sound 
when  a  vibrating  body  hits  it.  There  is  not  a  phenomenon  in 
nature  which  is  not  attended  by  some  incidental  results.  The 
connection  of  things  is  such  that  it  would  be  impossible  for  this 
to  be  otherwise.*' 

"It  is  quite  a  relief,"  I  said,  "to  find  out  that  the  absurd  and 
impossible  hasn't  occurred.  That  is,  that  a  thing  moving  seven 
feet  a  second  hasn't,  by  hitting  something  else,  started  it  oflf 
at  a  pace  of  1090  feet.  Of  course  every  sensible  person  knows 
all  the  time  that  this  doesn't  happen,  as  he  knows  that  a  great 
many  other  things  do  not  happen  which  occasionally  some  of 
the  most  eminent  scientists  say  do.  All  these  instances  but 
illustrate  the  habit  so  prevalent,  indeed  universal  with  scientists, 
of  knowing  so  many  things  that  are  not  so.  And  yet  it  is 
a  relief  to  hear  an  intelligent  exposure  of  all  such  nonsense." 

"Yes,"  she  said,  "it  is  always  a  relief  to  have  a  thing 
explained  so  we  can  understand  it.  And  Ellen  never  could  see 
what  scientists  and  instructors  make  books  for,  to  be  used  as 
text  books  upon  a  subject,  without  explaining  that  subject, 
at  least  in  part.  It  seems  to  Ellen  just  as  if  they  had  mistaken 
their  vocation. 


i 


winsi  ilRings  ok  .vn  old  pfN?: 
'*^^^.  Tvndall  continues: 


-09 


*  The  village  of  Erith  was  some  miles  distint  from  the  magazine,  but 
in  nearly  all  cases  the  windows  were  shattered ;  and  it  was  noticeable 
that  the  windows  turned  away  from  the  origin  of  the  explosion  suffered 
almost  as  much  as  those  which  faced  it.  Lead  sashes  were  employed 
in  Erith  Church,  and  these,  being  in  some  degree  flexible,  enabled  the 
windows  to  yield  to  pressure  without  much  fracture  of  the  glass.  As 
the  sound  wave  reached  the  church  it  separated  right  and  left,  and,  for 
a  moment,  the  edifice  was  clasped  by  a  girdle  of  intensely  compressed 
air,  every  window  in  the  church,  front  and  back,  being  bent  inward. 
After  compression,  the  air  within  the  church  no  doubt  dilated,  tending 
to  restore  the  windows  to  their  first  condition.  The  bending  in  of  the 
windows,  however,  produced  but  a  small  condensation  of  the  whole 
mass  of  air  within  the  church;  the  recoil  was  therefore  feeble  in  com- 
parison with  the  pressure,  and  insufficient  to  undo  what  the  hitter  had 
accomplished.* 

**Hcre  is  another  case  of  the  most  ridiculous  mingling  of 
a  pulse  of  air  caused  by  expanding  gas,  or  the  expanding  gas 
itself,  with  what  Mr  Tyndall  calls  a  sound  wave.  Beyond  all 
possibte  question,  the  windows  were  broken  by  the  same 
force,  or  forces,  that  destroyed  the  magazine.  As  with  the 
tube  where  the  candle  was  blown  out,  Mr.  Tyndall  confused 
puffs  of  air  with  sound,  so  here  he  confuses  exploding  gas 
with  sound.  It  is  not  very  strange  that  he  should »  for  by 
his  theory  this  pulse  is  the  sound  wave.  And,  indeed,  right 
here  the  extreme  folly  and  utter  impossibility  of  this  hypo- 
thetical sound  wave  is  demonstrated*  If  there  is  such  a  thing, 
the  pulse  in  a  tube,  or  the  movement  of  unconfined  air  from 
whatever  cause,  is  it.     But  such  pulse  and    such   movement 


m^M^ 


2IO  ELEEN   OR  THE  ^ 

occur  as  well  without  sound  as  with.  And  th6  sound  alone  is 
not  sufficient  to  produce  it.  Therefore  it  is  certain  that  sound 
is  something  entirely  different  from  a  pulse  of  air,  though  often 
accompanying  it;  as  much  so  as  a  body  floating  in,  or  carried 
by,  water,  is  different  from  the  water  that  carries  it. 

"Mr.  Tyndall,  on  page  52,  begins  his  discussion  of  the 
velocity  of  sound  as  follows : 

*Two  conditions  determine  the  velocity  of  propagation  of  a  sonorous 
wave ;  namely,  the  elasticity  and  the  density  of  the  medium  through 
which  the  wave  passes.  The  elasticity  of  air  is  measured  by  the  pres- 
sure which  it  sustains  or  can  hold  in  equilibrium.  At  the  sea  level  this 
pressure  is  equal  to  that  of  a  stratum  of  mercury  about  thirty  inches 
high.  At  the  summit  of  Mont  Blanc  the  barometric  column  is  not 
much  more  than  half  this  height ;  and,  consequently,  the  elasticity  of 
the  air  upon  the  summit  of  the  mountain  is  not  much  more  than  half 
what  it  is  at  the  sea-level. 

'  *  If  we  could  augment  the  elasticity  of  air,  without  at  the  same  time 
augmenting  its  density,  we  should  augment  the  velocity  of  sound.  Or, 
if  allowing  the  elasticity  to  remain  constant  we  could  diminish  the 
density,  we  should  augment  the  velocity. 

*»»**♦♦♦ 

*The  velocity  of  sound  in  air,  at  the  freezing  temperature^  is  1,090 
feet  a  second. 

*  At  all  lower  temperatures  the  velocity  is  less  than  this,  and  at  all 
higher  temperatures  it  is  greater. 

•With  the  same  elasticity  the  density  of  hydrogen  gas  is  much  less 
than  that  of  air,  and  the  consequence  is  that  the  velocity  of  sound  in 
hydrogen  far  exceeds  its  velocity  in  air.  The  reverse  holds  good  for 
heavy  carbonic-acid  gas.  If  density  and  elasticity  vary  in  the  same 
proportion,  as  the  law  of  Boyle  and  Mariotte  proves  them  to  do  in  air 


WHISPERINGS   OF  AN   OLD    PINE 


211 


temperature   is   presened   constant,    they   neutralize   each 
other's  effects ;  hencCi  if  the  temperature  was  the  same,  the  velocity  of 

Ittound  uix>n  the  sumniits  of  the  highest  Alps  would  be  the  same  as  that 
at  the  mouth  of  the  Thames.  But,  inasmuch  as  the  air  above  is  colder 
than  that  below,  the  actual  velocity  on  the  summits  of  the  mountains  is 
less  than  that  at  the  sea-leveL  To  express  this  result  in  stricter 
language,  the  \*elocity  is  dh-ecily  proportional  to  the  square  root  of  the 

[elasticity  of  the  air;  it  is  abo  inversely  proportional  to  the  square  root 
of  the  density  of  the  air.  Consequently,  as  in  air  of  a  constant  tem- 
perature elasticity  and  density  vary  in  the  same  proportion,  and  act 
oppositely,  the  velocity  of  sound  is  not  affected  by  a  change  of  density, 

I  if  unaccomi:ianied  by  a  change  of  temperature. 

*There  is  no  mistake  more  common  than  to  sui>tx)se  the  velocity  of 

[sound  to  be  augmented  by  density.     The  mistake  has  arisen  from  a 

Imisconception  of  the  fact  that  in  solids  and  liquids  the  velocity  is 
er  than  in  gases.  Dut  it  is  the  higher  elasiicity  of  those  bodies, 
im  relation  h  their  density,  that  causes  sound  to  pass  rapidly 'through 
them.  Other  things  remaining  the  same,  an  augmentation  of  density 
always  produces  a  diminution  of  velocity.  If  the  elasticity  of  water, 
which  is  measured  by  its  compressibility,  was  only  equal  to  that  of  air,  the 
velocity  of  sound  in  water,  instead  of  being  more  than  quadni[>le  the 
velocity  in  air,  would  be  only  a  small  fraction  of  that  velocity.  lk)th 
density  and  elasticity,  then,  must  be  always  borne  in  mind ;  the 
velocity  of  sound  being  determined  by  neither  taken  separately,  but  by 
the  relation  of  the  one  to  the  other. 

"There  is  here  manifested  a  most  monstrous  ignorance  of 
the  meaning  of  the  word  elasticity.  This  is  what  Ellen  has 
referred  to.  In  any  legitimate  use  of  the  word  there  is  no 
truth  whatever  in  these  statements. 

•*  All  text  books  state  that  fluids  are  perfectly  elastic.     If  a 


.^1^ 


212  ELLEN   OR  THE 

thing  was  perfectly  round,  it  would  be  quite  difficult  for  it  to 
be  more  round.  Then  water  and  air  are  equally  elastic,  both 
being  perfectly  so.  For  the  definition  of  elasticity  is  'That 
property  which  enables  a  body  to  resume  its  original  form, 
when  the  force  which  altered  that  form  or  volume  ceases  to  act' 
Water  is  much  denser  than  air.  Then  by  the  formula  that  the 
speed  of  sound  equals  the  square  root  of  the  elasticity  divided 
by  the  square  root  of  the  density,  sound  should  go  much  faster 
in  air  than  in  water.  But  it  goes  about  four  times  as  fast  in 
water  as  in  air.  Take  lead  and  air.  Lead  is  much  more  dense 
and  not  at  all  elastic.  Then  by  the  formula  sound  should 
go  much  faster  in  air,  but  it  does  go  much  faster  in  lead. 
And  thus  again  is  demonstrated  the  falsity  of  the  theory'. 

**It  is  often  impossible  in  reading  scientific  works  upon 
this  subject  to  tell  whether  the  velocity  of  sound  given  for 
different  bodies,  comes  from  experiment  or  theory.  Often, 
if  not  generally,  it  is  from  theory,  and  so  the  proof  given 
that  a  theory  is  true  is  derived  from  the  theory  itself. 
That  is,  this  theory  of  sound  would  require  in  some  sub- 
stance the  speed  of  the  so-called  sound  wave  to  be  about 
four  times  that  in  air,  because  such  substance  is  about 
onc-sixtccnth  as  dense  with  the  same  supposed  elastic  force. 
Therefore  the  scientists  or  text  books,  assuming  the  theory'  true, 
assert,  without  experiment,  that  the  speed  in  this  medium  is 
four  times  as  fast,  and  afterwards  draw  upon  this  statement  to 
prove  the  theory.  The  old  Pine  will  see  that  in  doing  this 
they  have  a  sure  thing,  if  they  are  not  found  out. 

"And  then  again,  where  experiments  are  made,  the  result 
is  questionable   until   verified,   especially  if    made    by   parties 


WHISPERINGS   OF   AX   OLD    PINE 


■13 


cither  unskilled  or  biased  in  favor  of  a  theory.  So  far  as  Ellen 
can  learn,  the  only  experiments  which  have  been  made  to  test 
the  speed  of  sound  were  in  air,  water,  and  iron.  That  in  air 
did  not  at  all  agree  with  the  theory,  and  in  iron  the  speed  was 
about  two-thirds  what  the  theory  called  for.  In  water,  those 
experimenting*  supposed  a  compression  which  would  make 
the  theoretical  agree  with  the  observed  velocity.  Thus  in  the 
*Book  on  Sound  and  Vibrations,*  by  Mr.  Airy,  Ellen  finds 
(page  144)  : 

•  Experiments  made  by  some  philosophers  in  the  compressibility  of 
water,  gave  for  the  compression  produced  by  the  weight  of  one  atmos- 
phere 49.5  millionth  part  of  the  whole.  From  this,  using  formula  sim- 
ilar to  those  in  Article  62,  they  inferred  a  theoretical  velocity  of  1,428 
metres,  agreeing  well  with  that  which  was  observed/ 


"Article  62  says: 

•The  theory  of  the  transmission  of  vibrations  through  fluids  is  embar- 
rassed with  a  complication  from  which  that  of  transmission  through 
solids  is  free.  The  ordinary  laws  of  equality  of  firessure  in  all  direc* 
tions  apply,  apparently,  in  the  same  manner  to  those  sudden  shocks 
which  are  distributed  by  pulses  similar  to  those  of  sound,  as  those 
slower  communications  of  motions  which  are  transmitted  by  visible 
waves.  We  have  remarked,  when  in  a  barge  on  the  sea  at  some 
distance  from  the  vertical  of  the  spot  where  a  large  quantity  of 
gunpowder  was  fired  at  about  60  feet  depth,  that  a  sudden  shock 
was  felt  upwards  at  the  bottom  of  the  barge  long  before  there  was 
the  smallest  sign  of  a  common  wave.  Here  the  shock  had  been 
communicated  by  molecular  transmission  in  the  same  manner  as 
through  an  iron  bar,  but  with  this  difference  of  dispersioDj  that  it 
bad  diverged  through  a  solid  angle/ 


214  ELLEX   OR  THE 

"And  here  is  illustrated  most  completely  how  sound  has 
nothing  to  do  with  waves,  but  in  some  way  is  conveyed  through 
the  water,  swiftly  and  without  its  perceptible  disturbance,  as 
electricity  is  conveyed  through  bodies." 

**But,"  I  said,  **as  Ellen  has  suggested,  doesn't  the  difficulty 
referred  to  come  from  the  use  of  the  wrong  word — that  is,  the 
use  of  *  elasticity' where  *  modulus  of  elasticity' is  intended?" 

**  Ellen  hardly  sees  that  such  change  would  assist  much  in 
the  explanation,  but,  as  she  has  said,  sound  may  be  influenced 
by  the  density  and  elastic  force  of  bodies.  Yet  Ellen  thinks  it 
has  a  speed  of  its  own.  Ellen  does  not  think  that  sound 
is  electricity.  Neither  does  she  think  that  heat,  light,  mag- 
netism, and  electricity  are  all  the  same  thing,  any  more  than 
she  thinks  that  the  different  fluids  which  we  are  acquainted 
with,  like  water,  or  sap,  or  milk,  or  cider,  or  molasses 
are  the  same,  or  that  the  different  gases,  as  oxygen,  nitrogen, 
hydrogen  and  others,  are  the  same.  She  knows  these  are  not 
the  same,  that  they  are  essentially  different,  and  some  of  them 
very  different,  but  they  are  all  fluids  or  gases  and  governed  by 
the  different  laws  which  govern  fluids  and  gases,  and  in  this 
respect  they  are  similar.  And  so  Ellen's  common  sense  tells 
her  it  must  be  with  those  substances  which  are  composed 
of  that  form  of  matter  which  the  great  physicist,  Mr.  Faraday, 
has  suggested  might  properly  be  spoken  of  as  a  fourth 
division  of  matter,  under  the  name  of  radiant  matter.  With 
the  universality  of  nature's  laws  it  would  be  impossible  for 
this  to  be  otherwise.  And  so  we  know  that  there  must  be,  as 
we  know  that  there  arc.  many  different  kinds  of  things  made 
from  radiant    matter,  chief  among   which  are  electricity  and 


WHISPERINGS   OF  AX   OLD    PINE  21 5 

magnetism,  light,  heat,  and  sound.     And  the   first  of  all  the 
series,  and  one  of  the  most  beautiful  and  important,  is  sound. 

"Nor  can  Ellen  think  of  anything  more  foolish  than  to  sup- 
pose that  all  of  these  things  are  the  results  of  the  different 
movements  more  or  less  rapid  of  the  same  material  or  sub- 
stance. This  is  as  utterly  senseless  as  to  suppose  that  water 
is  the  basis  of  all  fluids,  with  a  certain  motion  making  milk, 
with  another  wine,  with  others  molasses,  cider,  beer,  ale, — all 
the  results  of  different  motions  or  vibrations. 


2l6  ELLEN  OR  THE 


XIV. 


^^OOUND  cannot  move  in  a  so-called  vacuum,  but  can  move 
^  in  many  different  bodies.  And  as  it  is  impossible  for 
air  to  enter  many  of  these  bodies,  it  is  certain  that  air  is  not 
essential  to  the  transmission  of  sound,  and  that  sound  is  com- 
posed of  something  far  more  subtle  than  air.  For  air  is  easily 
confined  within  many  different  vessels,  but  sound  is  not.  Air 
cannot  enter  solid  bodies,  but  sound  can,  and  passes  more 
readily  through  them  than  it  does  in  fluids  and  gases.  For 
the  action  of  this  subtle  substance,  air  or  some  other  body  is 
necessary,  just  as  the  earth  is  necessary  as  a  bed  in  order  that 
a  stream  may  exist;  or  the  air  is  necessary  in  order  that  a 
bird  may  fly ;  or,  indeed,  just  as  a  medium  is  necessary  for  the 
existence  of  many  things.  And  thus  as  a  matter  of  fact,  so  far 
as  we  know,  one  medium  always  exists  in  another.  Similar  to 
sound,  electricity  docs  not  readily  pass  through  w-hat  is  called  a 
vacuum,  but  is  conducted  with  greater  or  less  facility  through 
many  different  bodies. 

**It  is  stated  in  the  'Royal  Transactions,'  vol.  26,  page  367, 
that  experiments  by  Hawksbee  show  that  sound  made  by  a  bell 
in  space  filled  with  air  was  not  transmitted  through  a  surround- 
ing vacuum.  Another  experiment  showed  that  sound  was 
conveyed  by  a  tube  from  an  inner  space  filled  with  air  and  con- 
taining the  sounding  bell,  through  a  surrounding  vacuum  to 
the  outside  freely,  but  if  this  tube  was  stopped  by  the  finger 


PIT;!-  'i    ■;.m,:y! 
I  , 


WHISPERINGS   OF 


219 


sound  would  scarcely  be  heard.  The  same  sound  was  not 
prolonged  more  than  in  open  ain  It  also  appeared  from  Mn 
Hawksbee's  experiments  that  when  the  air  was  condensed  in  a 
receiver  the  sound  of  a  suspended  bell  was  stronger  than  in 
natural  air,  and  its  intensity  increased  with  the  degree  oi  con- 
densation, 

"Mr.  J,  F.  Herschel»  in  his  article  on  Sound  in  the  'Encyclo- 
psedia  Metropolitana/  refers  to  the  fact  that  the  intensity  of 
sound  is  diminished  in  rarefied  air»  but  adds: 


*  The  height,  however,  to  which  an  atmosphere,  or  medium  convey- 
ing sound  extends*  far  exceeds  any  attainable  on  mountains,  by  balloons, 
or  even  by  the  lightest  clouds.  The  great  meteor  of  1783  produced  a 
distinct  rumbling  sound,  although  its  height  above  the  earth's  surface 
was  full  50  miles  at  the  lime  of  its  explosion  (see  Philosophical  Trans- 
actions, 1784).  The  sound  produced  by  the  explosion  of  the  meteor 
of  1719,  at  an  elevation  of  at  least  69  miles,  was  heard  as  **  the  report 
of  a  very  great  cannon  or  broadside/*  shook  the  doors  and  windows  of 
houses  and  threw  a  looking  glass  out  of  its  frame  and  broke  it  (Phil. 
Trans,,  vol.  30,  page  97S),  These  heights  are  deduced  by  calculation 
from  observations  too  unequivocal,  and  agreeing  too  well  with  each 
Other  to  allow  of  doubt.  Scarcely  less  violent  was  the  sound  caused  by 
the  bursting  of  the  meteor  of  July  17,  177 1,  near  Paris;  the  height  of 
which,  at  the  moment  of  explosion,  is  assigned  by  LeRoy  at  20,598 
toises,  or  abou  t  25  mi  les  (Mem.  Acad  *  Par.,  1771,  page  668).  The 
report  of  a  meteor  in  1756  threw  down  several  chimneys  at  Aix  in 
Provence,  and  was  taken  for  an  eartliquake.  These  instances  and 
others  which  may  be  adduced  are  sufficient  to  show  that  sound  can  be 
excited  in,  and  conveyed  by,  air  of  an  almost  inconceivable  tenuity 
(lor  such  it  must  be  at  the  heights  here  spoken  of)  provideil  the 
exciting  cause  be  sufficiently  powerful  and  extensive.     It  may  however 


220  ELLEN    OR   THE 

be  contended,  and  not  without  some  probabiiity,-that  at  these  enormous 
heights  sound  may  owe  its  propagation  to  some  other  medium  more 
rare  and  elastic  than  air,  and  extending  beyond  the  limits  of  the  atmos- 
phere of  air  and  vapor.  *  *  The  report  of  the  meteor  of  1783  was 
heard  at  Windsor  Castle  ten  minutes  after  its  disappearance.* 

**Thc  above,  if  observations  were  correct,  would  tend  to  show 
that  sound  takes  place  in  an  atmosphere  of  great  rarity,  and  if 
intense  enough  can  be  heard.  It  ateo  suggests  another  resemb- 
lance between  sound  and  electricity,  for  the  latter  will  pass 
through  a  vacuum  only  when  the  current  is  very  intense.  But  it 
is  certainly  most  doubtful  whether  any  observations  of  the  loca- 
tion of  the  explosion  of  unexpected  meteors,  could  be  reliable. 

**Mr.  Tyndall  next  introduces  one  of  the  most  extraordinary 
fiascos  of  this  theory,  as  follows :  , 

*We  now  come  to  one  of  the  most  delicate  points  in  the  whole 
theor)'  of  sound.  T'he  velocity  through  air  has  been  determined  by 
direct  experiment ;  but  knowing  the  elasticity  and  density  of  the  air,  it 
is  possible,  without  any  experiment  at  all,  to  calculate  the  velocity  with 
which  a  sound  wave  is  transmitted  through  it.  Sir  Isaac  Newton  made 
this  calculation,  and  found  the  velocity  at  the  freezing  temperature  to 
be  916  feet  a  second.  This  is  about  one-sixth  less  than  actual  obser- 
tion  had  i)roved  the  velocity  to  be,  and  the  most  curious  suppositions 
were  made  to  account  for  the  discrepancy.  Newton  himself  threw  out 
the  conjecture  that  it  was  only  in  passing  from  particle  to  particle  of 
the  air  that  sound  required  time  for  its  transmission  :  that  it  moveii 
instantaneously  through  the  particles  themselves.  He  then  supposed 
the  line  along  which  sound  passes  to  be  occupied  by  air  particles  for 
one-sixth  of  its  extent,  and  thus  he  sought  to  make  good  the  missing 
velocity.  The  very  art  and  ingenuity  of  this  assumption  were  sufficient 
to  throw  doubt  on  it ;  other  theories  were  therefore  advanced,  but  the 


WHISPERINGS    OF   AN    OLIJ    PINE  221 

great  French  mathematician,  Laplace,  was  the  first  to  completely  solve 
the  enigma.  I  shall  now  endeavor  to  make  you  thoroughly  acquainted 
with  his  solution.* 

"The  statement  above  that  Sir  Isaac  Newton  found  the 
velocity  of  sound  at  the  freezing  temperature  to  be  916  feet  a 
second  ts  entirely  a  misleading  one,  and  not  true.  For,  as 
Ellen  has  already  explained,  the  whole  calculation  of  Mr.  New^- 
ton  was  based  upon  an  hypothesis  that  there  were  pulses  in 
air,  in  regard  to  which,  the  only  essential  point  in  the  discus- 
sion, Mr.  Newton  advanced  no  opinion  whatever.  And  there- 
tore  the  calculation  of  Mr.  Newlon,  although  it  has  been  used 
to  base  the  undulatory  theory  of  sound  upon,  and  is  the  only 
basis  that  that  theory  has,  is  without  practical  interest.  It  is 
impossible  to  make  this  statement  too  strong.  As  the  basis  of  a 
theory  this  whole  calculation  of  Mr.  Newton  is  absolutely 
without  significance*  nor  did  Mr.  Ntwton  himself  ever  state 
otherwise.  It  seems  to  Ellen  that  text  books  would  do  well  to 
take  this  into  consideration. 

**Why  curious  suppositions,  as  Mr.  Tyndall  states,  were 
made  to  account  for  the  discrepancy  between  theory  and 
experiment  in  the  speed  of  sound,  docs  not  appear.  The 
natural  explanation  would  be  that  the  theory  w^as  false. 

**Mr.  TyndalTs  reason  for  doubting  Mr.  Newton's  explana- 
tion shows  the  innate  honesty  of  a  scientist;  but  Chambers* 
Encyclopaedia,  not  being  so  honest,  says  that  the  fact  that 
sound  went  in  rarefied  air  at  the  same  speed  as  in  normal  air, 
disproved  Mr.  Newton*s  theory.  As  a  matter  of  fact  Mr. 
Ncw^ton's  hypothesis  for  the  discrepancy  between  the  theo- 
retical and  experimental  speed  of  sound,  upon  the  supposition 


222  ELLEN   OR  THE 

that  the  hypothesis  upon  which  he  founded  his  proposition  was 
true,  was  a  very  proper  one.  For  in  a  row  of  elastic  balls 
touching  each  other,  the  motion  passes  much  quicker  than 
where  there  are  spaces  between  the  balls.  We  will  now  see 
with  what  success  Mr.  Laplace  takes  Mr.  Newton's  place, 
although  the  hypothesis  upon  which  Mr.  Newton*s  proposition 
was  based,  being  still  unproven,  the  explanation  has  no  prac- 
tical importance.     Mr.  Tyndall  continues: 

*Into  this  strong  cylinder  of  glass,  which  is  accurately  bored 
and  quite  smooth  within,  fits  an  air-tight'  piston.  By  pushing 
the  piston  down,  I  condense  the  air  beneath  it,  heat  being  at  the  same 
time  developed.  A  scrap  of  amadou  attached  to  the  bottom  of  the 
piston  is  ignited  by  the  heat  generated  by  compression.  If  a  bit  of 
cotton  wool  dipped  into  bisulphide  of  carbon  be  attached  to  the  piston, 
when  the  latter  is  forced  down,  a  flash  of  light,  due  to  the  ignition  of 
the  bisulphide  of  carbon  vapor,  is  observed  within  the  tube.  It  is  thus 
proved  that  when  air  is  compressed  heat  is  generated.  By  another 
experiment  it  may  be  shown  that  when  air  is  rarefied  cold  is  developed. 
This  brass  box  contains  a  quantity  of  condensed  air.  I  open  the  cock, 
and  permit  the  air  to  discharge  itself  against  a  suitable  thermometer; 
the  sinking  of  the  instrument  immediately  declares  the  chilling  of 
the  air.* 

**  Mr.  Tyndall  in  stating  that  *  it  is  thus  proved  that  when 
air  is  compressed,  heat  is  generated,*  left  out  the  words  *in  a 
tube.'  He  told  the  truth,  but  not  the  whole  truth.  He 
assumes  afterwards  that  very  slightly  condensed  unconfined  air 
produces  heat.  There  is  no  evidence  that  this  is  true.  And 
practically  it  is  not  true.  For  it  is  compression  that  produces 
heat,  but  if  a  thing  can   glide  out  of  the  way  of  another,  it  is 


WHISPERINGS   OF   AN   OLD    TINE 


223 


not  much,  if  at  all,  compressed,  Ellen  can  well  imagine  that 
a  scientist  might  suppose  that  air  compressed  in  a  tube  would 
act  the  same  as  though  it  was  unconfincd.  For  this  is  the  way 
they  are  made  up.  They  are  unable  to  see  a  hole  in  a  ladder. 
Nor  do  they  know  that  there  are  any  holes  in  a  skimmer,  but 
suppose  it  is  tight  like  a  quart  cup.  But  Ellen  knows  very 
^m  well  that  the  old  Pine  would  not  be  deceived  this  way/' 
^H  **No/'  I  said,  **thc  old  Pine  can  see  that  the  two  cases  are 

^H      very  different/' 

^^P  '*  And  Ellen  is  happy  to  admit   that   there  is  occasionally  a 

W  scientist  who  distinguishes  between  what  he  knows  and  what 

I  he  does  not.     Thus  Rev.  James  Challis,for  many  years  Pro- 

^^^^Jcssor  of  Astronomy  in  Oxford  University,  England,  and  one 
^^^^^f  the  ablest  mathematicians  of  the  century,  suggested  that 

P 

■  are 

I  . 


'  As  an  experiment  only  showed  that  ihe  effect  is  to  raise  the  temper- 
ature when  the  developed  heat  acts  on  a  very  Umikif  portion  of  air,  we 
are  not  justified  in  supposing  the  same  effect  to  take  place  when  the 
air  is  unlimitetf,  * 


**  But  little  differences  of  this  kind  are  generally  not  considered 
between  scientists.  For  although  the  difference  was  as  great  as 
the  distance  of  the  East  from  the  West,  the  theory  derived  by 
neglecting  it,  if  accepted,  would  be  every  whit  as  good  to  teach, 
and  might  pass  muster  for  a  hundred  years  or  through  the 
lifetime  of  those  most  interested.  It  is  so  much  more  satis- 
factory to  teach  something  and  get  paid  for  it,  than  to  say  that 
you  do  not  know  and  get  no  pay.  Both  profit  and  vanity  are 
interested,  and  the  ready  excuse  is  always  at  handi  if  it  is  not 
true  it's  the  best  we  have.     It  is  thus  that  many  an  hypothesis 


224  ELLEN   OR  THE 

has  done  good  work  for  years,  which  had  hardly  a  leg  to 
stand  on.  But  at  last  all  such  have  to  be  abandoned.  Prob- 
ably no  two  false  ones  have  lived  longer  than  the  Ptolemaic 
sytem  of  astronomy  and  this  undulatory  theory  of  sound. 
And  probably  also  there  were  never  two  important  hypotheses 
more  completely  at  variance  with  true  scientific  and  philo- 
sophical principles.  One  of  them  has  gone,  and  the  other 
totters  to  its  grave. 

**It  is  a  fact  that  compression  produces  heat.  If  iron  is 
struck  with  a  hammer,  heat  is  produced.  But  experiment  shows 
that  less  and  less  is  produced  as  the  iron  is  more  and  more 
compressed,  and  the  statement  is  made  that  it  will  at  last  grow 
cold  under  the  hammer.  And  thus  it  seems  to  be  proven 
that  it  is  the  compression  that  brings  out  the  heat,  the 
striking  itself  or  the  force  exerted  in  pressing  having 
nothing  whatever  to  do  with  the  supply.  The  heat  is,  of 
course,  a  substance  contained  in  things,-  and  it  would 
appear  to  be  the  principal  cause  of  their  expansion.  It  is 
pressed  out  from  bodies,  as  water  is  pressed  out  of  a  sponge." 

"But  the  present  theory  is  that  heat,  too,  is  a  mode  of 
motion ;  that  is,  that  it  is  caused  and  transmitted  by  the  con- 
stant movement  of  the  molepules  of  bodies,  is  it  not,  Ellen?" 
I  asked. 

"Yes,"  she  said,  *'this  is  a  part  of  the  delusion  of  the 
scientists.  For  they  have  gone  quite  mad  on  modes  of  motion, 
and,  as  Ellen  has  had  occasion  before  to  remark,  do  not 
question  the  ability  of  a  body  to  move  in  different  and 
contrary  directions,  or  in  many  of  them  at  the  same 
instant  of    time.     Thus    it    is    assumed    that    the  particles   of 


* 


WHISPERINGS    OF   AN   OLD    PINE  225 

ether,  itself  a  mere  figment  of  the  brainy  by  the  difference  ol 
their  movements  cause  both  heat,  light,  and  all  the  different 
colors.  That  is,  scientists  suppose  that  heat,  light,  and  all  the 
colors,  not  to  mention  electricity  and  magnetism,  are  caused 
by  the  impossible  movements  of  an  imaginary  fluid.  But  it  is 
also  assumed  that  heat  is  produced  by  a  similar  movement  of 
the  molecules  of  solid  bodies,  and  that  different  temperatures 
are  caused  by  different  rates  of  motion.  And  at  the  same 
time  that  the  particles  of  bodies  are  moving  one  way  for 
heatp  It  is  assumed  that  they  are  moving  other  ways  for  sound, 
and  many  different  ways  for  many  different  sounds.  And 
thus,  too.  the  ether,  by  the  theory,  must  vibrate  one  way  for 
electricity,  another  way  for  light,  another  for  heat,  and  a  dozen 
different  ways,  more  or  less,  for  colon  And  so  the  different 
kinds  of  all  these  things,  by  undulatory  theories,  arc  made  by 
different  degrees  or  characters  of  motions.  Thus  Ganot  says, 
in  speaking  of  heat: 

'On  the  second  hypothesis  the  heat  of  a  t>ody  is  caused  by  an 
extremely  rapid  oscillating  or  vibratory  motion  of  its  molecules ;  and 
the  hottest  bodies  are  those  in  which  the  vibrations  have  the  greatest 
velocity  and  the  greatest  amplitude.  At  any  given  time  the  whole  of 
the  molecules  of  a  body  possess  energy  of  motion,  which  is  the  heat 
Oicy  contain.  To  increase  their  temperature  is  to  increase  this  energy ; 
to  lower  their  temperature  is  to  decrease  their  energy.  Hence,  on  this 
view,  heat  is  not  a  substance  but  a  ^omiition  nf  matter^  and  a  condition 
which  can  be  transferred  from  one  boily  to  another.  When  a  heated 
body  is  placed  in  contact  with  a  cooler  one,  the  former  cedes  more 
molecular  motion  than  it  receives;  but  the  loss  of  the  former  is  the 
^uivalent  of  the  gain  of  the  latter. 


226 


ELLEN   OR  THE 


*  1 1  is  also  assumed  that  there  is  an  imponderable  elastic  elher,  wnicn 
pervades  all  matter  aiid  infinite  space,  A  hot  body  sets  this  in  rapid 
vibration,  and  the  vibrations  of  this  ether  being  communicated  to  mate- 
lial  objects  set  them  m  more  rapid  vibration ;  that  is,  increase  their 
temperature.  Here  we  have  an  analog}^  vtith  sound;  a  sounding  body 
is  ill  a  state  of  vibration,  and  its  vibrations  are  transmitted  by  atmos- 
pheric air  to  the  auditory  apparatus  in  which  is  produced  the  sensation 

of  sound* 

•  •#••••• 

'Assuming  that  the  heat  of  bodies  is  due  to  the  motion  of  their  par* 

tides,  we  may  admit  the  following  explanation  as  to  the  nature  of  this 

motion  in  the  various  forms  of  matter : 

*  III  so/iifs  the  molecules  of  even  the  most  rigid  bodies  have  a  kind  of 
vibratory  motion  about  certain  fixed  positions.  This  motion  is  prob* 
ably  very  complex ;  the  constituents  of  the  molecule  may  oscillate 
about  earh  other,  besides  the  oscillation  of  the  molecule  as  a  whole ; 
anil  this  latter  again  may  be  a  to-and-fro  motion,  or  it  may  be  a  rotary 
motion  alxiut  the  center.  In  cases  in  which  externa!  forces,  such  as 
violent  shocks,  act  iipoii  the  body,  the  molecules  may  acquire  fresh 
positions. 

*  In  the  liquid  state  the  molecules  have  no  fixed  positions.  They 
can  rotate  about  their  centers  of  gravity,  and  the  center  of  gravity  itself 
may  move.  But  the  motion  due  to  collisions,  compared  with  the 
mutual  attraction  of  the  molecules,  is  not  sufficient  to  separate  the 
molecules  from  each  other,  A  molecule  no  longer  adheres  to  particular 
adjacent  ones  \  but  it  does  not  spontaneously  Itave  them  except  to 
come  into  the  same  relation  to  fresh  ones  as  to  its  previous  adjacent 
ones.  Thus  in  a  liquid  there  is  a  vibratory,  rotatory,  and  progressive 
motion  of  the  molecules. 

*  In  \\\^  gasemis  state  the  molecules  are  entirely  without  the  sphere  of 
their  mutual  attraction.  They  fly  forward  in  straight  lines  according  to 
the  ordinary  laws  of  mo  Hon,  until  they  impinge  against  other  molecules 


WHISrERrXCS    of   an    r>LD    liiXE 


227 


or  against  a  fixed  envelope  which  they  cannot  penetrate,  and  then  fiy 
off  in  another  direction,  with,  in  the  main,  their  original  velocity.  If 
the  molecules  were  in  space,  where  no  external  force  could  act  upon 
them,  they  wotjld  fly  apart,  and  disappear  in  infinity*  But  if  contained 
in  any  vessel,  the  molecules  continually  impinge  in  all  directions  against 
the  sides,  and  thus  arises  the  pressure  which  a  gas  exerts  on  its  vessel. 
'  The  perfection  of  the  gaseous  state,  or  what  may  be  regarded  as  an 
ideal  gas,  implies  that  the  space  actually  occupied  by  the  molecules  of 
the  gas  is  infinitely  small  compared  with  the  entire  volume  of  the  gas; 
that  the  time  occupied  by  the  impact  of  a  molecule  either  against 
another  molecule,  or  against  the  sides  of  the  vessel,  is  infinitely  small 
in  comparison  with  the  interval  between  any  two  impacts;  and  that  the 
influence  of  molecular  attraction  is  infinitely  small.  When  these  con* 
ditions  are  not  fulfilled  the  gas  partakes  more  or  less  of  the  nature  of  a 
liquid,  and  exhibits  certain  deviations  from  Boyle's  law  (183).  This  is 
the  case  with  all  gases ;  to  a  very  slight  extent  with  the  less  easily  con- 
densable gases,  but  to  a  far  greater  extent  with  vapors  and  the  more 
condensable  gases,  especially  near  their  points  of  liquefaction.  These 
are  now  explained  by  the  modification  which  Van  der  VVaals  has  intro- 
duced into  the  equation  for  gases  (185)/ 


**Thesc  are  the  words  of  one  of  the  ablest  instructors  in 
physics,  who  wants  to  sell  his  book/* 

••And  does  he  not  know  these  things  that  he  states  so  posi- 
tively, Ellen?"  I  asked. 

*•  He  has  not  the  slightest  knowledge  of  them/'  she  answered. 
"They  are  all  hypotheses  about  things  whicht  in  another  por- 
tion of  his  book,  as  Ellen  has  before  nientioned,  Mr.  Ganot 
says  are  completely  unknown.'' 

"And  this  is  what  they  call  science?"  I  said. 

"Yes/*  she  answered,  *'this  is  what  they  call  science,  though 


228  ELLEN   OR  THE 

its  true  name  is  ignorance,  and  a  very  dense  ignorance  it  is. 
But  there  is  also  an  element  of  fraud  in  it ;  for  it  answers  as  a 
basis  for  the  pretense  of  superior  knowledge.  But  Mr.  Ganot, 
it  is  true,  qualifies  by  prefixing  his  statement  with  the  para- 
graph 'Assuming  that  the  heat  of  bodies  is  due  to  the  motion 
of  their  particles,'  etc." 

"And  is  the  ether  composed  of  molecules  or  particles?"  I 
asked. 

**It  is  composed  of  nothing,"  she  said;  "it  being  absolutely 
and  only  a  thing  of  the  imagination.  So  that  it  has  or  may  be 
supposed  to  have  as  many  different  compositions  as  there  arc 
persons  to  imagine  it.  And  hence  it  follows  that  everything 
connected  with  the  undulatory  theories  of  light,  heat,  etc.,  that 
is,  those  that  are  supposed  to  be  formed  from  this  imaginary 
thing  called  ether,  are  without  even  a  basis  of  existence  other 
than  that  of  the  imagination.  And  all  of  these  imaginar>'' 
theories  are  based  upon  this  impossible  one  of  sound." 

"Then,"  I  said,  "there  is  no  truth  in  the  mode  of  motion 
theories?" 

"  None  whatever,"  she  answered.  "  They  only  represent, 
at  the  most,  what  scientists  think  would  be  a  good  method 
of  creation,  though  it  is  perfectly  evident  that  nature  works 
by  a  very  different  method,  the  substantial  one  of  the  combina- 
tion of  the  different  elements  and  substances  in  different 
proportions.     Ellen  likes  nature's  way  the  best." 

"But,"  I  said,  "Ellen,  how  can  scientists  suppose  that 
to  occur  which  all  our  knowledge  shows  us  never  occurs,  and 
is  impossible?" 

"Because  of  their  lack  of  good   sense,  for  ignorance  alone 


1 

■ 

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*                         OX  AHB 
'                                 1 

^H 

1 

1 

WHISPERINGS   OF  AN   OLD    PINE 


231 


'^does  not  explain  it.     Scientists  are  very  prone  to  speak  of  the 

^^doctrines  of  religion  as  superstitions,  but  the  old   Pine  will  see 

^Hthat  the  superstitions  of  science  are  as  dense  as  or  denser  than 

^Mny  that  ever  existed  in  religion;   for  superstition   is  but  the 

belief   of  something   repugnant  to    reason^    and    surely   there 

I  could  be  nothing  more  repugnant  than  that  a  body  is  going 
^  dozen  different  and  contrary  ways,  more  or  less,  or  two 
different  and  contrary  ways  at  the  same  instant, 
•*  But  a  large  if  not  a  principal  part  of  the  enunciations  of 
JKii^ncc,  together  with  the  loads  of  mathematics  with  which  they 
are  encumbered,  are  as  utterly  senseless*  absurd*  and  impossible 
as  the  old  nursery  rhyme, 

•  Hey  diddle  diddle, 
I1ie  cat's  in  the  fiddle, 

The  cow  jumped  over  the  moon  ; 
The  little  dog  laughed  to  see  such  a  rraft, 

And  the  dish  ran  away  with  the  spoon/ 

always  in  nature  the  principle  of  limitation  exists* 
Kof  is  it  difficult,  if  wc  use  good  sense,  to  perceive  the  nature 
>f  this  law.  And  thus  wc  know  that  it  would  be  as  possible 
for  the  cow  to  jump  over  the  moon,  as  for  a  body  to  be  mov- 
ing in  two  opposite  directions  at  the  same  instant  of  time;  or 
^^ven  for  a  thing  to  pass  another  in  any  different  manner  from 
^"that  which  we  see  universally  established  in  nature  for  such  an 
^^occurrence.  For  natural  laws  are  not  only  fixed,  but  they 
^Bire  universal  in  their  character.  Nor  is  any  law  more  certain 
^nhan  that  by  which  things  are  created,  either  naturally  or  arti- 
I  ficially;  for  always  this  law  is  the  same,  and  it  would  be  as 
sensible  to  suppose  that  by  hitting  a  base  ball  it  would  become 


■^  --^^ 


232 


ELLEN    OR   THE 


a  pumpkin,  as  that  by^  a  mere  change  of  movement  in  a  body  it 
would  become  something  else. 

'*  In  unconfined  air  heat  is  not  engendered  by  any  ordinary 
cause  of  condensation.  This  can  be  tested  by  the  movement 
of  a  fan  or  book  or  cloth  indefinitely  continued,  which,  of 
course,  condenses  the  air  far  more  than  does  a  tuning  fork»  or 
fiddle  string,  or  insect  which,  by  rasping  its  leg  against  its  wing, 
makes  a  noise  that  may  be  heard  for  a  long  distance,— *<jr  any 
ordinary  cause  of  sound.  It  is  demonstrated,  too,  by  the  fact 
that  air  condensed  by  wind  is  not  thus  perceptibly  heated. 
In  all  these  cases  the  air  is  moved,  but  not  compressed.  But 
it  is  not  movement  but  compression  that  produces  heat 

**Mr,  Tyndall  continues: 

*  All  that  yoii  have  heard  regarding  the  transmission  of  a  sonorous 
poise  through  air  is,  I  trust,  still  fresh  in  your  minds.  As  the  pulse 
advances  it  squeezes  the  particles  of  air  together,  and  tw'O  results  follow 
from  this  compression.  Firsdy,  its  elasticity  is  augmented  through  the 
mere  augmentation  of  its  density.  Secondly,  its  elasticity  is  augmented 
by  the  heat  of  compression.  It  was  the  change  of  elasticity  which 
resulted  from  a  change  of  density  that  Newton  took  into  account,  and 
he  entirely  overlooked  the  augmentation  of  elasticity  due  to  the  second 
cause  just  mentioned.  Over  and  above,  then,  the  elasticity  involved  in 
Newton's  calculation,  we  have  an  additional  elasticity  clue  to  changes 
of  temperature  produced  by  the  sound  wave  itself.  When  both  are 
taken  into  account,  the  calculated  and  the  observed  velocities  agree 
perfectly. 

*But  here,  without^  due  caution,  we  may  fall  into  the  gravest  error. 
In  fact,  in  dealing  with  Nature,  the  mind  must  be  on  the  alert  to  smie 
all  her  conditions ;  otherwise  we  soon  learn  that  our  thoughts  are  not  id 
accordance  with  her  facts.     It  is  to  be  particularly  noted  that  the 


WHISPERINGS   OF   AN    OLD   PINE 


augnienlation  of  velocity  due  to  the  changes  of  temperature  produced 
by  the  sonorous  wave  itself  is  totally  different  from  the  augmentation 
arising  from  the  heating  of  the  general  mass  of  the  air.  The  average 
temperature  of  ihe  air  is  unchanged  by  the  waves  of  sound.  We  can- 
not  have  a  condensed  pulse  without  having  a  rarefied  one  associated 
with  it.  But  in  the  rarefaction,  the  temperature  of  the  air  is  as  much 
lowered  as  it  is  raised  in  the  condensation.  Supposing,  then,  the 
atmosphere  parceled  ott  into  such  condensations  and  rarefactions^ 
with  their  respective  temperatures,  an  extraneous  sound  passing  through 
such  an  atmosphere  would  be  as  much  retarded  in  the  latter  as  accel- 
erated in  the  former,  and  no  variation  of  the  average  velocity  could 
result  from  such  a  distribution  of  temperature,* 

**  Here  we  have  another  instance  of  scientific  honesty  ;  a  pre- 
tence of  saying  something,  when  there  is  nothing  to  say.  If  the 
augmentation  of  velocity  referred  to  is  different  from  the  aug- 
mentation that  arises  from  heating  the  general  mass  of  the  air, 
how  is  it  accomplished?  That  the  average  temperature  is  un- 
changed, supposing  it  to  be  true,  doesn't  explain  this.  The 
proposition  is  that  any  condensation  of  air  increases  the  heat 
of  the  air  enough  to  add  about  one-sixth  to  the  theoretical 
speed  of  sound.  This  resolves  into  this:  first,  that  con- 
densation of  air  causes  heat;  second,  that  heat  is  caused  in  the 
condensations  of  hypothetical  sound  waves;  third,  that  this 
heat  in  some  way  increases  the  speed  of  sound  so  as  to  make 
a  theorj'  agree  with  experiment,  or  by  about  176  feet  a 
second.  It  is  well  known  that  increase  of  temperature  in  the 
atmosphere  causes  increased  speed  in  sound  of  about  i.i  feet 
lor  every  degree  F.  But  it  is  said  that  the  supposed  increase 
referred  to  by  Mr.  Laplace  does  not  come  in  this  way.  Then 
how  docs  it  come?     Is  it  necessary  for  Ellen  to  tell  scientists 


234  ELLEN   OR  THE 

that  anything  which  is  not  susceptible  of  intelligent  explanation 
is  not  susceptible  of  intelligent  use?  If  it  is  necessary  for  her 
to  say  this,  it  is  only  because  of  the  intolerable  stupidity  of 
those  she  says  it  to. 

"For  always  mind  dominates.  Mind  creates  mathematics, 
not  mathematics  mind.  Things  are  as  they  are  made  by  mind, 
and  they  are  constructed  upon  mathematical  principles 
because  mind  perceives  that  these  are  the  proper  principles  for 
their  construction.  And  nothing  in  all  the  immensity  of  this 
universe  ever  takes  place  contrary  to  reason.  And,  as  Ellen 
thinks,  nothing  takes  place  in  this  material  universe  which 
the  reason  of  man  is  not  able  to  comprehend.  But,  however 
this  may  be,  he  has  no  right  to  make  theory  agree  with 
experiment  by  a  mathematical  operation,  unless  he  can  show 
some  reason  for  such  operation.  This  is  a  self-evident 
truth.  And  therefore  if  no  reason  can  be  given  for  the 
use  of  this  formula,  there  is  no  warrant  for  its  use,  nor 
reason  for  Ellen  to  consider  it.  We  might  just  as  well  add  176 
feet  to  Mr.  Newton's  result,  and  then  say  that  theory  agrees 
with  experiment,  as  to  perform  any  other  mathematical  opera- 
tion, for  which  there  is  no  reason. 

"  By  this  hypothesis  of  Laplace  one-half  of  the  air  is  con- 
stantly overheated,  and  one-half  underheated,  and  this  couldn't 
help  being  noticeable  if  it  meant  any  perceptible  amount  of 
difference  of  temperature,  even  though  the  two  halves  should 
constantly  interchange  conditions.  For  the  old  Pine  will 
remember  that  some  of  the  hypothetical  sound  waves  are  quite 
long,  that  of  the  lower  C  28  feet,  or  having  14  feet  of  condensa- 
tion and  14  of  rarefaction.     And  this  increase  of  heat,  which, 


WHISPERINGS    OF    A\    OLD    PINE 

not  in  the  orditiar>'  way  but  in  some  inexplicable  manner,  is  said 
to  add  1 76  feet  per  second  to  the  speed  of  sound,  must  take 
place  with  every  sound,  even  the  slightest.  How  much  heat  is 
engendered  when  a  tornado  piles  the  air  up  in  condensations 
sufficient  to  snap  like  pipe-stems  the  strongest  trees,  or  sweep 
whole  cities  from  existence,  the  scientists  haven't  yet  reported. 
It  makes  Ellen  pretty  sick  to  discuss  seriously  such  intolerable 
nonsense." 

••Ellen  is  a  good  girl,"  I  said,  *'and  she  may  be  certain  she 
will  ncvxT  have  t<j  discuss  it  but  once.  But  how  does  Mr. 
Tyndall  attempt  to  use  this  explanation  of  Laplace?" 

**  He  thus  continues/'  she  said: 

'Whence,  then,  does  the  augmentation  pointed  out  by  Laplace  arise? 
1  would  ask  your  best  attention  while  I  endeavor  lo  make  this  knotty 

^*  .  f .    f  s'  f    f' 

•    •••##•••    »,^?^* 

i    •?•#••••••  f  f'  J^'  f 

point  clear  to  you.  If  air  be  compressed  it  becomes  smaller  in  volume ; 
if  the  pressure  be  diminished,  the  volume  expands.  The  force  which 
resists  compression,  and  which  produces  expansion,  is  the  elastic  force 
of  the  air.  Thus  an  external  pressure  squeezes  the  air  i>articles 
together ;  their  own  elastic  force  holds  them  asunder,  and  the  particles 
are  in  equilibrium  when  these  two  forces  are  in  equilibrium.  Hence 
it  is  that  the  external  pressure  is  a  measure  of  the  elastic  force.  I^t 
the  middle  row  of  dots,  fif^,  13,  represent  a  series  of  air  particles  in  a 
stale  of  quiescence  betuveen  the  points  a  and  x.    Then,  because  of  the 


236  ELLEN    OR  THE 

elastic  force  exerted  between  the  particles,  if  any  one  of  them  be  moved 
from  its  position  of  rest,  the  motion  will  be  transmitted  through  the 
entire  series.  Supposing  the  particle  a  to  be  driven  by  the  prong  of  a 
tuning  fork,  or  some  other  vibrating  body,  toward  .r,  so  as  to  be  caused 
finally  to  occupy  the  position  a  in  the  lowest  row  of  particles :  at  the 
instant  the  excursion  of  a  commences,  its  motion  begins  to  be  trans- 
mitted to  /'.  In  the  next  following  moments  b  transmits  the  motion  to 
Cy  c  to  dy  d  to  Cy  and  so  on.  So  that  by  the  time  a  has  reached  the 
position  a' y  the  motion  will  have  been  propagated  to  some  point  o'  of 
the  line  of  particles  more  or  less  distant  from  a\  The  entire  series  of 
particles  between  a'  and  o'  is  then  in  a  state  of  condensation.  The 
distance  a'  o\  over  which  the  motion  has  traveled  during  the  excursion 
of  a  to  a,  will  depend  upon  the  elastic  force  exerted  between  the 
particles.  Fix  your  attention  on  any  two  of  the  particles,  say  a  and  />. 
The  elastic  force  between  them  may  be  figured  as  a  spiral  spring,  and 
it  is  i)lain  that  the  more  flaccid  this  spring  the  more  sluggish  would  be 
the  communication  of  the  motion  from  a  to  b ;  while  the  stifTer  the 
spring  the  more  prompt  would  be  the  communication  of  the  motion. 
What  is  true  of  u  and  b  is  true  for  every  other  pair  of  particles  between 
a  and  o.  Now  the  spring  between  every  pair  of  these  particles  is  sud- 
denly stiffened  by  the  heat  developed  along  the  line  of  condensation, 
and  hence  the  velocity  of  propagation  is  augmented  by  this  heat. 
Reverting  to  our  old  experiment  with  the  row  of  boys,  it  is  as  if,  by  the 
very  act  of  i)ushing  his  neighbor,  the  muscular  rigidity  of  each  boy's 
arm  was  increased,  thug  enabling  him  to  deliver  his  jnish  more  promptly 
than  he  would  have  done  without  this  increase  of  rigidity.  The  con- 
densed portion  of  a  sonorous  wave  is  propagated  in  the  manner  here 
described,  and  it  is  plain  that  the  velocity  of  propagation  is  augmented 
by  the  heat  developed  in  the  condensation.' 

"  In  the  above  attempted  explanation  of  Mr.  TyndalK  these 
points   are  noticeable:   first,  that   the    middle  row  of  dots    is 


WHISPERINGS   OF   AN   OLD    PINE  237 

supposed  to  represent  a  row  of  air  particles  in  a  state  of 
quiescence.  But  practically  there  are  no  air  particles  in  a  state 
of  quiescence,  and  under  the  kinetic  theory  of  gases,  which  now 
is  believed  and  taught  by  all  or  nearly  all  scientists  who  accept 
the  undulatory  theory  of  sound,  it  is  assumed,  as  we  have 
before  seen,  that  the  air  particles  are  all  moving,  the  direction 
and  speed  of  their  movements  constantly  varying,  as  they  are 
influenced  by  contact  with  each  other  or  with  anything  else, 
but  that  the  average  speed  of  each  particle  is  about  1900  feet 
per  second.  Particles  understood  to  be  in  such  conditions  as 
these,  are  now,  to  further  the  explanation  of  this  theory,  repre- 
sented by  Mr.  Tyndall  to  be  at  rest.  Ellen  does  not  think  that 
further  discussion  of  Mr.  Tyndall's  suppositions  is  necessary. 
For  they  are  infinitely  stupid  or  infinitely  dishonest,  and  in 
either  case  not  worth  considering." 


238  ELLEN   OR  THE 


XV. 

^^r^UT/'   I    said,  "the  old   Pine  is    anxious  to    understand 
•LJ    better  about  this  celebrated  formula    of  Laplace,    and 
so  hopes  Ellen  will  continue  with  the  explanation." 

**Very  well/'  she  said.  '*The  old  Pine  sees  that  Mr.  Tyn- 
dall's  next  sentence  is  that  if  any  one  of  these  particles  be 
moved  from  its  position  of  rest,  the  motion  will  be  trans- 
mitted through  the  entire  scries.  With  particles  that,  accord- 
ing to  the  theory  of  these  scientists,  are  always  moving,  and 
moving  in  all  conceivable  directions,  it  is  not  only  somewhat 
difficult  to  see  how  they  can  be  at  rest,  but  it  is  also  difficult  to 
see  how  any  particular  motion  can  be  transmitted  through  a 
scries  in  any  particular  direction.  It  is  equally  difficult  to  per- 
ceive how  these  particles  acting  by  the  supposed  laws  that 
govern  them  under  the  kinetic  theory  of  gases  can  transmit 
motion  with  any  uniform  degree  of  speed.  But  all  of  this  is 
included  in  the  supposition  of  Mr.  Tyndall.  And  he  supposes 
the  entire  series  of  particles,  themselves  moving  in  all  direc- 
tions, with  an  average  speed  of  about  1900  feet  per  second,  to 
be  placed  in  a  state  of  condensation  or  rarefaction,  for  an 
indefinite  extent  in  all  directions,  from  the  center  of  disturbance 
by  the  prongs  of  a  tuning  fork  moving  at  a  rate  not  to  exceed 
ten  feet  a  second. 

"The  old  Pine  and  Ellen  know,  and  everybody  on  earth 
*.\'ho   knows   anything  about   it    knows,   that    the   fork    cannot 


WHISPERINGS   OF   AN   OLD    PINE 


affect  the  air  to  any  appreciable  extent  beyond  a  few  inches, 
though  this  theory  supposes  it  to  form  air  waves  extending  a 
long  distance. 

**Lct  us  examine  once  more  the  nature  of  these  hypothetical 
waves.  Take  the  lower  E  of  the  tuning  fork,  whose  condensa- 
tions by  the  theory  are  14  feet  and  rarefactions  of  equal  length* 
Possibly  the  tuning  fork  as  it  begins  operations  may  move 
*.^  of  an  inch.  The  air  particles  then  In  its  way  will  be  pushed 
tliat  distance^  which  is  the  amplitude  of  the  wave.  These 
are  supposed  to  push  other  particles  an  equal  distance,  and 
these  again  others,  the  iinal  result  being  that  precisely  the 
amplitude  of  the  wave  is  added  to  the  normal  air  of  the 
Hrst  condensation  and  constitutes  the  amount  of  added 
air,  which,  spread  somewhat  unequally  over  the  fourteen 
feet  of  condensation,  makes  the  condensation.  This  same 
amount,  withdrawn  from  the  next  fourteen  feet,  is  the  cause 
of  rarefaction.  And  this  is  all  the  cause  there  is  of  cither 
condensation  or  rarefaction.  One-quarter  inch  thickness  of 
air  at  large  estimate  is  distributed  over  fourteen  feet.  This 
means  a  condensation  of  about  r-672  and  a  rarefaction  to  the 
same  extent*  But  the  old  Pine  must  not  forget  that  this  con- 
densed and  rarefied  condition  would  exist  only  directly  in  the 
path  of  the  tuning  fork,  a  surface  of  about  5  inches  by  j^  inch, 
under  the  supposition  that  it  docs  not  spread  laterally,  tlic  fact 
and  the  requirements  of  the  theory  both  being  that  it  spreads 
in  all  directions. 

**  But  a  surface  of  5  inches  by  ^4  inch  in  width  and  a  thick- 
ness varying  from  }■{  inch  at  one  end  to  nothing  at  the  other 
means  about  5-32    of   a  cubic   inch  of  air   to   be  distributed 


242  ELLEN   OR  THE 

somewhat  unequally  over  that  part  of  the  spherical  wave  of 
which  the  first  condensation  consists  of  a  space  of  about  5749 
cubic  feet,  making  an  average  in  round  numbers  of  1-63,579,- 
341  for  this  condensation.  With  each  succeeding  supposed 
condensation  this  would  be  very  much  less,  and  soon  infinitely 
less. 

*'  If  made  by  an  insect,  a  fiddle  string,  or  the  vocal  chords, 
such  condensations  or  rarefactions  would  be  of  such  infini- 
tesimal character  that  it  would  be  absurd  to  undertake  to 
estimate  them.  And  yet  the  smallest  of  them  are  supposed  to 
engender  heat  enough  to  in  some  way  increase  the  speed  of 
sound  by  176  feet  per  second.  And  in  order  to  make  the 
proposition  as  absurd  as  possible,  so  as  to  meet  the  require- 
ments of  science,  it  is  assumed  that  it  does  this  whether  the 
condensation  be  small  or  great. 

*'Mr.  Tyndall  continues: 

*  Having  grasped  this,  even  partially,  I  will  ask  you  to  accompany 
me  to  a  remote  corner  of  the  domain  of  physics,  with  the  view,  how- 
ever, of  showing  that  remoteness  does  not  imply  discontinuity.  Let  a 
certain  quantity  of  air  at  a  temperature  of  0°,  contained  in  a  perfectly 
inexpansible  vessel,  have  its  temperature  raised  1°.  Let  the  same 
quantity  of  air,  placed  in  a  vessel  which  permits  the  air  to  expand 
when  it  is  heated  —  the  pressure  on  the  air  being  kept  constant  during 
its  expansion  —  also  have  its  temperature  raised  i®.  The  quantities  of 
heat  employed  in  the  two  cases  are  different.  The  one  quantity 
expresses  what  is  called  the  specific  heat  of  air  at  constant  volume ;  the 
other  the  specific  heat  of  air  at  constant  pressure.* 

"Thus  far  in  this  paragraph,  though  making  pretences 
having  no  signification  except  to  deceive,  Mr.  Tyndall  has  held 


WniSPERINGS   OF   AN    OLD    PINE 


Hi 


Ris   statements  wJthin    the   line    oi    fact,     But  now»  becoming 
scientific,  he  abandons  facts  and  theorizes  as  follows: 

'  It  is  an  instance  of  the  manner  in  which  apparently  unrelated  natu- 
ral phenomena  are  Ijound  together,  that  from  the  calculated  and 
oliserveil  velocities  of  sound  in  air  we  can  deduce  the  ratio  of  these  two 
specific  heats.  Squaring  Newton's  theoretic  velocity  and  the  observed 
velocity,  and  rlividing  the  greater  scjuare  by  the  less,  we  obtain  the 
ratio  referred  to*  Calling  the  specific  heat  at  constant  volume  Cv,  and 
that  at  constant  pressure  Cp  ]  calling,  moreover,  Newlon*s  calculated 
velocity  V,  and  the  observed  velocity  V\  Laplace  proved  that^ — 

Cp  _  V* 
C^   ^  V^ 

'  Inserting  the  values  of  V  and  V  in  this  equation,  and  making  the 

calctdation^  we  find  — 

Cp 

'Thus,  without  knowing  either  the  specific  heat  at  constant  volume  or 
at  constant  pressure,  Laplace  foimd  the  ratio  of  the  greater  of  them, to 
the  less  to  be  1*42/ 

**  Not  a  single  one  of  these  assertions  is  true.     They  arc  at 
best  but  opinions  of  Mr.  TyndalL 
*'  Mr.  Tyndall  next  says: 

*It  is  evident  from  the  foregoing  formulae  that  the  calculated  velocity 
:  sound,  multiplied  by  the  square  root  of  this  ratio,  gives  the  observed 
velocity/ 

"This  last  remark  is  as  wise  as  to  say  that  four  times  five 
arc  twenty.     Mr.  Tyndall  now  becomes  honest,  as  follows: 

*But  there  is  one  assumption  connected  with  the  determination  of 
this  ratio,  which  must  be  here  brought  clearly  forth.     It  is  assumed 


244  ELLEN    OR   THE 

that  the  heat  developed  by  compression  remains  in  the  condensed 
portion  of  the  loave^  and  applies  itself  there  to  augment  the  elasticity ; 
that  no  portion  of  it  is  lost  by  radiation.  If  air  were  a  powerful 
radiator,  this  assumption  could  not  stand.  The  heat  developed  in  the 
condensation  could  not  then  remain  in  the  condensation.  It  would 
radiate  all  round,  lodging  itself  for  the  most  part  in  the  chilled  and 
rarefied  portion  of  the  wave,  which  would  be  gifted  with  a  propor- 
tionate power  of  absorption.  Hence  the  direct  tendency  of  radiation 
would  be  to  equalize  the  temperatures  of  the  different  parts  of  the  wave, 
and  thus  to  abolish  the  increase  of  velocity  which  called  forth  Laplace's 
correction.* 

*' As  this  formula  of  Mr.  Laplace  is  essential  to  the  undula- 
tory  theory  of  sound  in  its  present  condition,  and  is  assumed  to 
be  correct  and  so  used  by  those  who  hold  the  theory,  it 
will  also  be  desirable  to  see  how  it  has  been  received  by 
critical  judges.  Ellen  finds  that  it  has  been  considered  inappli- 
cable by  many  of  the  ablest  mathematicians,  the  opinions  of 
several  of  whom  she  will  quote  to  the  old  Pine.  And  first  that 
of  Professor  Potter  as  published  in  the  *  Philosophical  Maga- 
zine,' vol.  I   ( 1851 )  : 

Mn  the  last  number  of  the  Magazine,  Mr.  Rankine  says  he  thinks  I 
have  misunderstood  "the  theory  of  Laplace  and  Poisson  as  to  the 
propagation  of  sound  in  gases."  I  assure  him  I  have  never  so  mis- 
understood that  theory  as  to  think  it  to  be  a  solution  of  the  problem,  but 
have  always  considered  it  as  begging  the  question.  It  does  not  look  as 
if  Poisson  looked  ui)on  it  at  all  in  the  light  of  a  strict  solution,  when  he 
had  first,  in  1807,  put  Laplace's  views  into  a  tangible  mathematical 
form  ;  for  he  says,  "  En  admettant  cc  r^sultat,  qu*on  ne  pent  verifier 
par  aucune  experience  directe,  on  fera  disparaitre  la  difference  que 
Newton  a  remarqu^e,  le  premier,  entre  la  vitesse  du  son  donn^e  par 


WHISPERINtiS   OF  AN    OLD    TINE 


caUul,  et  telle  qui  r^sulte  de  1' observation.'*  [In  admitting  this  result, 
which  one  is  not  able  to  verify  by  any  direct  experiuient,  one  will  make 
disappear  the  difference  which  Newton  first  observed  between  the 
velocity  of  sound  given  by  mathematics  and  that  which  results  from 
observation »j  The  amended  calculations  have,  however,  always  been 
far  from  closely  approximate  to  the  true  velocity. 

*  In  showing  the  point  of  failure  in  the  solutions,  I  shall  refer  to  the 
simplest  and  most  improved  form,  as  given  in  Poisson^s  '^'rait^  de 
MticaniqtJe,'*  edition  1^33,  vol  2,  page  695.  He  there  puts  ,^ot  h  equal  to 
the  pressure  in  the  gas  before  dibturbaiice,  ^^  being  the  force  of  gravity, 
m  the  density  of  mercury,  and  //  the  height  of  the  barometric  column. 
In  the  state  of  motion,  and  neglecting  change  of  temperature,  the 
pressure  (/)  will  be  represented  by 

gmh  (i+j), 
where  $  represents  the  condensation  positive  or  negative.     He  then 
says,  **  Nous  supposerons  done  qu'on  ait,  en  general, 

p^^gmh  (i-f  j  +  tr)  ; 
€i  d^signant  une  quantity  de  menie  signe  que  j,  et  qui  en  est  une  cer^ 
taine  fonction.     A  cause  de  la  petitesse  de  j,  on  pent  sup|>oser  cette 
qtiantit^  cr  proix)rtioneUe  a  s,  et  faire 

fi  iiani  un  coefficient  positif  el  ind^pendant  de  j."  [We  will  suppose^ 
then,  that  one  has  the  general  eqimtion/^A'''''^'  ('  -f-^  +  <^)i  ^  repre- 
senting a  quantity  of  the  same  sign  as  s  and  which  represents  some 
function  of  it.  On  account  of  the  smallness  of  s,  one  miy  suppose  thl» 
quantity  a  proportional  to  s  and  to  make  a^0s;  /3  being  a  positive 
coefficient  and  independent  of  s.] 

'  Now  the  only  condition  which  we  have  between  <r  and  s  k,  that 
they  must  be  of  the  same  sign ;  so  that  if  we  put 

and  ejcjiand/  (/)  in  a  series  ascending  by  integral  powers  of  s,  we  must 


246  ELLEN   OR  THE 

have  the  index  of  the  first  term  an  odd  integer ;  and  also  since  j  is  so 
small,  we  might  neglect  all  terms  but  the  first,  and  put 

a  =  pSj  or  (T  =  l3s'\  or  (t  =  Ps^,  etc. 

Now  to  take  the  first  of  these  without  any  reason,  more  than  the  need 
to  procure  a  solution  of  the  problem  under  investigation,  is  a  pure 
assumption ;  and  the  whole  process  fails  with  any  other  power  of  s  than 
the  first. 

'  We  are  thus  thrown  back  on  the  original  popular  view  of  I>aplace  in 
seeking  for  an  explanation.  Sometimes  it  is  so  worded,  as  if  the  accel- 
eration of  the  vibrations  of  the  particles  of  the  medium  by  the  heat  and 
cold  developed,  proved  necessarily  an  acceleration  of  the  velocity  of  the 
propagation  of  the  wave  motion  ;  although  at  the  same  time  it  is  one  of 
the  acknowledged  facts  of  sound,  that  the  velocity  of  propagation  is 
independent  of  the  velocity  and  frequency  of  the  vibrations  of  the 
particles. 

*  The  velocity  of  propagation,  however,  varies  with  the  elasticity  of 
the  medium  for  the  same  vibrating  mass ;  so  that  the  only  way  in  which 
Lai)lace's  view  need  be  taken,  is  that  stated  in  my  paper  on  Sound  in 
the  February  number,  by  considering  the  heat  or  cold  developed  by  the 
first  pulse  which  is  transmitted  ;  and  this  leads  to  consequences,  as 
there  shown,  which  are  contrary  to  experience. 

*  Mr.  Rankine  is,  however,  in  error  when  he  supposes  an  objection 
would  also  nold,  since,  ()ecause  "  every  wave  nuist  consist  of  a  com- 
pressed and  a  dilated  part,  the  different  parts  of  a  wave  would  travel 
with  different  velocities,"  for  this  would  only  make  the  waves  unsym- 
metrical  in  form.* 

"The  'Philosophical  Magazine,'  vol.  9,  thus  reports  the  con- 
tents of  a  paper  read  by  the  Rev.  Samuel  Earnshaw,  of  Shef- 
field, England,  an  eminent  mathematician,  at  one  of  the 
meetings  of  the  Philosophical  Society : 


WmSI'ERINGS   OF   AS  OLD    VISE 


'-47 


\ 


'The  author  explained  that  the  theory  of  sound  must  still  be  consid- 
ered imperfect,  in  consequence  of  resting  on  an  ai)proxtmate  step  in 
the  malhcmatical  part  of  the  investigation.  The  results  were  exhibited 
m  a  simple  numerical  fonn,  and  made  use  of  to  explain  several  inter- 
esting phenomena,  such  as  the  unsling  away  and  divergence  of  sound; 
the  peculiarity  on  which  the  sweetness  of  musical  sounds  depends  on 
the  rapidity  and  intensity  of  its  formation,  but  not  on  the  length  of  the 
sound  wave.  11ie  more  violent  the  genesis  of  a  wave  of  sound,  the 
more  raj)id  should  be  its  transmission.  It  had  been  one  of  his  greatest 
discouragements  in  comparing  theorj^  with  experiment,  to  find  that 
experimenters  on  soimd  appeared  to  agree  unanimously  that  all  sounds, 
whether  gentle  or  violent,  travel  with  the  same  speed.  On  this  point 
theory  and  experiment  seemed  to  be  discordant ;  experimenters  had 
said  that  there  was  no  difference  in  the  sjjeed  of  the  human  voice,  and 
the  report  of  a  cannon,  but  the  mathematical  theory  showed  that  the 
tf^pott  of  the  cannon  should  travel  more  quickly  than  that  of  the 
human  voice/ 

•'The  following  able  article  by  Mr,  Earnshaw  is  published  in 
the  *  Philosophical  Magazine,'  vol.  19: 

'  1  am  perfectly  aware  the  problem  of  the  propagation  of  soimd  is 
considered  to  have  been  solved ;  but  notwithstanding  this  I  venture  to 
offer  the  following  new  solution  to  the  notice  of  the  philosophic  world  ; 
because  it  not  only  leads  to  a  numerical  result  quite  different  from  any 
before  obtained  from  theory,  and  agreeing  better  with  experimentj  but 
likewise  furnishes  some  new  results  of  an  unexpected  character,  and 
affords  besides  a  glimpse  into  a  department  of  nature  which  has  hitherto 
remained  hermetically  sealed.  Laplace's  ingenious  suggestion  of  a 
change  of  temperature  due  to  a  sound  wave,  brought  the  result  of 
theory  so  very  near  to  that  of  experiment,  that  it  has  been  thought 
unreasonable  to  require  a  closer  agreement.    But  it  is  confessed  that 


'^     ^ 


248  ELLEN   OR  THE 

the  experiment  by  which  the  effect  of  a  change  of  temperature  is 
obtained  is  one  that  is  remarkably  difficult  to  manage, —  one  also  in 
which  errors  of  observation  are  greatly  magnified  in  the  result :  this  is 
shown  to  be  so,  from  the  great  differences  between  the  results  of  differ- 
ent experimentalists ;  and  I  think  I  may  say  that  the  requisite  value  of 
the  coefficient  (commonly  denoted  by  k)  is  much  greater  than  Dalton*s 
experiments  warrant,  and  than  what  would  have  been  conjectured  a 
priori  to  be  its  value.  In  looking  also  at  the  determinations  of  its 
value,  and  also  of  the  value  of  the  velocity  of  sound,  I  am  a  little  sus- 
picious that  modern  experimentalists  have  suffered  themselves  to  be 
biased  by  a  desire  to  make  experiment  and  theory  agree.  At  any  rate, 
if  we  compare  experiments  made  since  181 6,  when  Laplace  announced 
his  theorem  for  the  correction  of  Newton's  result,  with  those  previously 
made,  it  is  impossible  not  to  notice  a  very  sudden  and  startling  change ; 
and  in  the  same  spirit  the  value  of  k  has  been  gradually  growing  in  the 
hands  of  experimentalists  till  it  is  now  large  enough  really  to  justify  the 
opinion  which  has  been  expressed,  that  to  Laplace  is  due  the  honor  of 
having  completed  the  solution,  which  was  begun  in  England,  of  the 
problem  of  the  propagation  of  sound.  And,  to  speak  candidly,  it  must 
be  confessed  that  Laplace's  sagacious  suggestion  undoubtedly  has  the 
air  of  a  irra  causa,  although  it  requires  a  larger  development  of  heat 
by  the  sound  wave  than  seems  probable.  But  its  great  defect,  if  I  may 
be  allowed  to  consider  it  defective,  is  that  the  result  it  gives  does  not 
come  up  to  the  exi)eriment.  The  theoretical  velocity,  after  being 
amended  by  Laplace's  suggestion,  still  falls  short  of  the  experimental 
velocity  by  24  feet,  if  we  take  this  last  to  be  1090  feet ;  and  by  76  feet, 
if  we  take  the  velocity  of  sound  to  be  1142  feet  as  determined  by  Der- 
ham,  Flamsteed,  Halley,  and  the  Florentine  Academicians.  It  should 
be  remembered,  also,  that  theory  might  a  priori  be  expected  to  give  a 
result  exceeding,  rather  than  falling  short  of,  experiment;  for  theory 
assumes  the  elasticity  and  fluidity  of  the  atmosphere  to  be  perfect,  and 


WHISPERINGS   OF  AN   OLD    PINE 


249 


wchavc  reason  lo  think  both  are  really  in  a  slight  degree  imperfect; 
ind  this  is  not  likely  to  accelerate,  but  rather  to  retard  (if  it  at  all 
affect)  the  propagation  of  sound  waves.  Upon  the  whole,  after  t  on- 
sidering  the  matter  in  as  imx>artial  a  spirit  as  possible,  candor  obliges 
me  to  confess  that  Laplace's  suggestion  does  not  furnish  a  suffickni 
cause.  I  do  not  deny  that  it  may  Ije  a  cause  ;  but  it  is  not  the  whole. 
There  is  a  cause,  still  unrevealed,  for  the  defect  of  the  theoretical 
velocity.  Euler  considered  that  some  part  of  the  error  of  theory  might 
be  due  to  the  incorrectness  of  assuming 

dx 
previously  to  integrating  the  differential  equation  ;  and  certainly,  as 
this  was  an  art>itrary  step,  it  was  reasonable  to  sup[K)se  it  might  in  some 
way  have  the  effect  of  making  the  theoretical  result  smaller  than  it 
would  be  were  the  equation  integrated  without  making  use  of  approx- 
imate steps.  When,  therefore,  1  succeeded  in  integrating  it  without 
approximate  steps,  I  was  disappointed  to  find  that  the  theoretical 
velocity  of  a  sound  wave  remained  the  same  as  before/ 

**Rev.  James  Challis,  Professor  of  Astronomy  at  the  Uni- 
versity of  Oxford,  England,  as  before  mentioned,  thus  discusses 
the  Laplace  formula: 

*  As  my  name  has  been  mentioned  in  connection  with  the  discussion 
HOW  going  on  in  your  journal  respecting  the  theoretical  velocity  of 
lound,  and  as  I  have  already  ventured  to  call  in  question  the  tisual 
metho<i  of  accounting  for  the  excess  of  the  observed  velocity  above  the 
Newtonian  value,  1  beg  to  be  allowed  to  say  a  few  words*  in  explanation 

;  my  views  on  this  subject. 


•The  received  methoii  of  accounting  for  the  difference  between  the 
Newtonian  and  the  observed  value  of  the  velocity  of  sound  rests  on 


250  ELLEN   OR  THE 

hypotheses.  Now  as  it  is  contrary  to  sound  philosophy  to  explain  by 
an  hypothesis  what  may  be  explained  without  an  hypothesis,  I  am  com- 
pelled by  my  reasoning  to  conclude  that  these  hypotheses  are  inadmis- 
sible. To  reconcile  this  conclusion  with  what  is  observed  respecting 
the  effect  of  heat  developed  by  sudden  condensation  of  the  air,  I  sug- 
gested that  as  experiment  only  showed  that  the  effect  is  to  raise  the 
temperature  when  the  developed  heat  acts  on  a  very  limited  portion  of 
air,  we  are  not  justified  in  supposing  the  same  effect  to  take  i)lace  when 
the  air  is  unlimited ;  and  that  the  developed  heat,  being  in  the  first 
moment  of  its  generation  in  the  state  of  radiant  heat,  and  being  allowed 
to  radiate  indefinitely,  does  not  sensibly  change  the  temperature  of  the 
air  at  the  position  where  it  is  generated.  This  is  the  supposition  which 
Professor  Stokes  alludes  to  in  the  April  number  of  the  "  Philosophical 
Magazine,"  page  306. 

*As  some  advocates  of  I-aplace's  theory  are  of  opinion  that  that 
theory  assigns  a  vera  causa  for  the  excess  of  the  velocity  of  sound 
above  Newton's  value,  in  refutation  of  that  opinion  I  appeal  to  Laplace's 
exposition  of  his  own  views.  It  is  clear  that  he  thought  it  necessary  to 
establish  the  theory  upon  certain  laws  of  the  action  of  caloric  on  the 
atoms  of  matter,  of  the  atoms  of  caloric  on  each  other,  and  of  the 
relations  of  free  and  latent  heat.  But  in  the  existing  state  of  our 
knowledge  of  the  theory  of  heat,  these  laws  can  only  be  regarded  as 
hypothetical.  The  supporters,  however,  of  Laplace's  theory,  instead  of 
referring  to  these  views,  have  substituted  hyi)Otheses  of  a  different  kind, 
leading  to  the  same  results.  In  the  article  by  Professor  Stokes  already 
referred  to  (page  306),  these  hypotheses  are  introduced  in  the  following 
terms:  "That  in  the  case  of  small  sudden  condensations  (ixjsitive  vx 
negative)  the  increase  of  temperature  is  ultimately  proportional,  caeteris 
paribus,  to  the  condensation,  will  not,  it  is  presumed,  be  called  in 
question."  In  this  sentence  there  are  involved  three  distinct  and 
unsupported  hypotheses :  first,  that  there  is  increase  of  temperature  in 


WHISPERINGS   OF   AN   OLD   PINE  25 1 

fluid  of  unlimited  extent,  experiment  only  proving  that  this  is  the  case 
when  the  fluid  is  confined  within  narrow  limits ;  secondly,  that  this 
increment  of  temperature  is  in  exact  proportion  to  the  increment  of 
density ;  thirdly,  that  the  increments  of  temperature  are  simultaneous 
with  the  generation  of  the  increments  of  heat  by  which  they  are  pro- 
duced, whereas  all  analogy  would  lead  us  to  expect  that  time  must 
elapse  between  the  effect  and  the  generation  of  the  cause  producing  the 
effect.  For  these  reasons  I  assert  that  Laplace's  theory,  in  whatever 
way  it  be  viewed,  rests  on  hypotheses. 

*  It  is  unnecessary  for  me  to  make  any  remark  on  the  investigation 
by  which  Professor  Stokes  determines  the  effect  of  the  radiation  of  heat 
on  the  propagation  of  sound,  because  that  investigation  proceeds  on 
the  hypothesis  of  that  very  increase  of  temperature,  the  reality  of  which 
it  has  been  the  purport  of  the  foregoing  observations  to  call  in  question, 
and  the  object  of  it  is  to  calculate  the  effect  of  radiation  due  to  such 
increase  of  temperature.* 


2  52  ELLEN   OR  THE 


XVT. 

^^IVAANY  other  similar  criticisms  might  be  produced,  but 
^^  ^  Ellen  will  only  add  the  following  article,  published 
in  the  'Quarterly  Journal,*  vol.  26,  by  Henry  Meikle,  in 
review  of  an  article  by  Mr.  Ivory  upholding  or  accepting  the 
Laplace  theory.  Mr.  Ivory  is  one  of  that  class  of  mathemati- 
cians like  Mr.  Stokes,  Mr.  Rankine,  and  numerous  others,  who 
have  gained  an  easy  notoriety  by  much  ciphering  in  the  line  of 
authority.  Mr,  Meiklc  is  one  of  the  few  with  ability  and 
honesty  enough  to  work  from  an  independent  basis,  accepting 
only  what  is  correct  and  criticising  what  is  wrong. 

*  In  the  article  011  sound  inserted  in  the  "  Edinburgh  Philosophical 
Journal"  for  October,  1827,  I  had  acquiesced  in  the  theory  of  the  late 
celebrated  Marquis  I^place,  so  far  as  it  appeared  to  go,  and  only  sug- 
gested some  small  additions  to  it.  But  since  writing  that  article,  I 
have  examined  more  closely  the  investigation  of  that  eminent  mathe- 
matician, given  in  the  "Conn.  desTems"  pour  Van  1825, and  "M^canique 
Celeste,"  torn,  v.,  page  119,  and  am  now  convinced  that  it  is  in  itself 
objectionable  in  several  respects,  independently  of  any  thing  which  I 
formerly  hinted  :  so  that  my  proposed  amendments  on  this  theory  are 
as  nothing  compared  with  the  thorough  reform  it  would  require ;  the 
result  being  neither  deduced  from  correct  principles,  nor  by  means  of 
an  accurately  managed  calculus.  The  like  objections  attach  to  Mr. 
Ivory's  view  of  it,  given  in  the  "Philosophical  Magazine"  for  July,  1825, 
page  1 1 .  To  this  I  shall  principally  direct  my  remarks  at  present,  be- 
cause it  is  better  known  in  this  country,  and  is  given  in  a  more  detached 


■ 

THE  KKW  YORK 
PUBMC  I.IBRART ' 

tlLOltN  fOUSOATIOKi 

^B 

WHISPERINGS   OF  AN  OLD    PINE 


:3s 


fann  than  that  of  M.  LapLue,  which,  though  essentially  the  same,  and, 
in  fact,  the  groujiLlwork  of  the  other,  is  ruriously  interwoven  with  some 
untenable  spctula lions  regarding  heat.* 

'Considerable  obscurity  pervades  Mr,  Ivory*s  investigation,  especially 
in  laying  down  the  first  principles,  which  are  both  inconsistent  and 
defective.  Several  of  the  most  important  circumstances  are  overlooked 
altogether;  but,  as  will  be  seen  from  extracts  which  soon  follow,  the 
leading  idea  by  which  the  process  is  meant  to  be  regulated  is  briefly 
this :  A  minute  cylinder  of  air,  whose  length  varies  without  either 
changing  its  mass  or  diameter,  is  supposed  to  be  acted  on  by  an  accel- 
erating force^  till  it  move  over  a  small  space  z,  and  then  abandoned  to 
move  uniformly  with  the  velocity  so  acquired  along  a  straight  line  x.\ 


•  In  the  **Conn.  des  Terns  '*  for  1826,  M.  Poisson  has  treated  the  sub- 
ject in  a  more  general  way,  with  the  view  of  emljracing  cases  where 
the  medium  is  not  uniform.  The  length  of  his  Memoir  would  render 
it  tedious  fully  to  discuss  its  merits  \  but,  so  far  as  regards  the  ordinary 
case  of  sound  traversing  the  horizon,  it  is  not  materially  different 
from  that  about  to  be  examined. 

t  This  notion  seems,  in  the  first  instance,  to  be  borrowed  from 
that  usually  given  in  elementary  bcMjks  on  mechanics ;  where  it  is, 
in  effect,  shown  that  if  a  series  of  equal  and  perfectly  elastic  lx»dies, 
such  as  cylinders,  be  placed  contiguous,  having  their  axes  in  a 
straight  line  ;  and  if  an  impulse  be  given  to  either  extreme  cylinder,  it 
will  communicate  an  e<jual  imj)ulse  to  the  next,  and  this  to  the  next, 
etc,  till  the  whole  series  be  mn  oyer.  But  to  this  is  joined  the  assump- 
lion,  that  the  velocity  with  which  the  imijulse  is  propagated  along  the 
series  is  the  same  as  the  velocity  of  the  first  cylinder  would  have  been, 
if  alone,  or  projected  by  itself, — a  coincidence  for  which  I  know  no 
reason,  nor  can  I  believe  it  to  l>e  nossible.  Hut  admitting  it  to  be  true, 
smce,  as  we  shall  presently  see,  the  velocity  of  the  projected  cylinder 
must  be  proportional  to  the  projecting  force,  how  does  this  consist  with 
the  rate  of  pro|xigation  being  likewise  assumed  to  be  ever  the  same  in 
the  same  state  of  the  medium?  S<jme,  perhaps,  could  tell  us  that  the 
series  of  cylimlers  propagate  the  im|:iu!se,  as  if  there  were  so  many 
isochronous  pendulums;  but  where  is  the  proof?  and  I  may  again 
ask  how  such  a  determinate  velocity  of  sound  can  be  aptly  repre- 
sented by  the  precarious  velocity  with  which  the  cylinder  may  be  pro- 
jected?    For,  at  all  events,  the  calculus  is  conducted  with  reference  to 


256  ELLEN  OR  THE 

*This  latter  motion  is  intended  to  represent  that  of  sound,  and  its 
velocity  is  assumed,  without  either  proof  or  probability,  to  be  always 
the  same,  and,  consequently,  without  either  decrease  or  end,  in  air  of 
the  like  density  and  pressure.  It  is  further  supposed,  that  the  cylinder 
always  moves  over  a  space  equal  to  its  own  length  during  the  constant 
fluxion  of  time  //t,  and  that  it  does  so  whether  in  passing  over  z  or  x. 

'  Now  without  enlarging  on  the  faint  enough  resemblance  between 
this  leading  idea  and  the  propagation  of  sound,  it  may  be  observed, 
before  entering  on  further  particulars,  that  either  the  space  z,  no  matter 
how  small,  must  be  always  of  the  same  magnitude,  and  therefore  the 
intensity  or  loudness  of  sound  always  the  same  in  air  of  the  like  condi- 
tion, which  is  contrary  to  universal  observation ;  or  else,  the  accelerat- 
ing force  must  be  everywhere  inversely  proportional  to  the  space  z. 
Without  some  condition  of  this  nature,  the  final  velocity  with  which  the 
cylinder  is  projected,  or  the  velocity  of  sound,  cannot,  as  our  author 
assumes,  be  always  the  same  in  the  same  medium.  For,  to  attain  the 
same  final  velocity,  the  circumstances  must  be  similar  to  those  of  a 
weight  descending  an  inclined  plane  of  a  given  height ;  where,  abstract- 
ing from  friction  or  other  resistance,  the  accelerating  force  is  inversely 
as  the  plane's  length.  But,  in  the  case  before  us,  the  law  of  the  force 
accelerating  the  cylinder  must  be  of  a  very  opposite  description ;  for, 
as  we  shall  aftenvards  see,  in  order  that  the  velocity  of  sound,  as 
deduced  by  this  sort  of  investigation,  may  be  independent  of  the 
intensity,  or  of  the  degree  of  condensation,  the  elasticity  of  the  air 
would  require  to  be  either  independent  of,  or  to  vary  inverse/y  as,  the 
density,  which  are  alike  absurd ;  but  here  the  elasticity  is  supposed  to 
vary  iiirectly  as  the  \  power  of  the  density. 


a  projected  cylinder.  But  supposing  the  investigation  were  to  relate 
only  to  "  the  vibrations  of  a  line  of  air,"  it  would  not  be  less  objection- 
able ;  as,  for  instance,  what  could  we  make  of  the  curious  absurdity,  to 
be  shortly  noticed,  of  the  small  cylinders  of  air  being  compressed  till 
infinitely  i/ense,  at  the  turn  of  each  vibration  ? 


WHIsrERINOS  OF  AN  OIJi   I'INE 


2S7 


'That  the  above  arc  not  the  only  serious  charges  which  may  be 
brought  against  Mr.  Ivory's  investigation,  will  appear  from  the  following 
extracts;  lo  which  I  shall  subjoin  some  remarks,  for  the  pur|JOse  of 
poinling  out  a  few  more  oC  the  tacit  asstimptions  antl  undefmed  steps, 
which  are  not  unfrequent»  and  for  setting  their  merits  and  iiiuUial  rela- 
tions, whi(?h  are  sometimes  curious,  m  a  proper  point  of  view  : 

'"Conceive  a  slender  horizontal  tube  of  an  indefmite  lengthy  con- 
taining air  in  a  state  of  equilibriam ;  and  let  .v,  reckoned  from  a  fixed 
point  in  the  axis  of  the  tube,  be  the  distance  of  a  small  cylinder  of  air 
within  the  tube,  the  thickniss  (length)  of  which  is  equal  to  dx,  Sui>- 
pose  now  that  the  cylinder  is  pushed  forward  by  some  force  to  the  dis- 
tance x  +  s  from  the  fixed  point,  and  that  it  occui)ies  the  length 
dx+tfs  in  the  axis.* 


•  It  is  not,  however,  this  movement  of  the  cylinder  over  the 
space  2  that  is  considered  in  the  sequel  of  the  investigation;  but 
its  retracing  of  it  occasioned  by  the  natural  tendency  of  the  air  to 
regain  its  equilibrium,  and  which  accelerates  the  cylinder  back  over  the 
8pace  z  towanis  the  assumed  point  from  which  Ihe  distance  jiH-s  was 
reckoned.  A  concussion  or  tremor  is  thus  produced  in  the  air,  and 
proixtgaied  from  atom  to  atom  along  the  line  x;  and  it  is  conceived 
that  tliis  tremor  or  sound  moves  i;/^/(/i?rw/j' along  jr  with  the  velocity, 
whatever  that  be,  which  the  cylinder  has  acquired  during  its  accelera- 
tion over  the  line  :^.  This  supposed  uniform  %'elocity  of  the  cylinder 
projectetl  along  .v  is  further  conceived  to  be  the  same  with  the  velocity 
it  happens  to  have,  whenever  its  density  equals  the  mean  actual  density 
of  the  medium.  If  so,  how  does  this  consist  with  the  well  known  fact, 
that  the  series  of  aerial  vibrations  conducting  sound  through  the  atmos- 
phere alw^iys  get  feebler  and  feebler  as  they  become  more  distant  from 
the  scmorous  body,  and,  consequently,  the  velocities  of  the  atoms 
slower  and  slower  at  those  similar  points  of  their  vit>rations  in  which 
the  den*iities  of  the  cylinders  become  equal  to  the  mean  density  of  the 
mediuiu?  IJut  ample  reason  maybe  given  for  the  fundatneulal  fact 
just  staled,  though  Mr.  Ivory  has  entirely  overlooked  both  it  and  the 
reason.  For  admitting  that  the  motion  of  the  cylinder  were,  as  he 
assumes,  uniform  in  a  lube,  yet  in  the  free  air  sound  is  sent  off,  as  from 
a  radiant  point,  in  every  open  direction  not  opi>osed  to  the  wind. 
Nay,  sound  reaches  many  a  place  by  a  cun  ilinear  route,  even  without 
being  reflected*     It  is  therefore  plain,  that  the  area  of  each  wave  or 


251 


OR 


*''It  is  to  be  ot>serv*e(l  that  tfj:  is  in\^riably  of  the  same  niagoitudCi 
whatever  be  the  position  of  the  small  cylinder  of  air,  and  that  ti%  alone 
varies  in  different  places  of  the  ttibe,  and  at  different  times.  It  follows, 
therefore,  that  x  is  independent  on  the  time  /,  and  5  is  a  function  of 
X  and  /.  It  is  to  be  observed  too,  that  the  air  is  supposed  to  undergo 
very  small  tondensations  and  rarefactions  in  proportion  to  its  original 
bulk  ill  the  state  of  equilibrium  ;  that  is,  dz  must  be  considered  as  very 
smal!  when  compared  to  dx  *     l.et  p'  denote  the  density  of  the  air  in 


spherical  shell  of  air,  to  which  the  tremor  is  communicated  in  succession, 
will  increase  as  fast>  at  least,  as  the  square  of  its  radius,  or  of  its  dis- 
tance from  the  radiant  point.  In  other  words,  the  number  of  atoms  or 
the  mass  to  be  successively  set  in  motion  will,  supf>osing  the  medium 
uniform,  increase  as  fast,  at  least,  as  the  stjuare  of  its  distance  frora  the 
sonorous  body.  This  is  a  very  different  thing  from  saying  off  hand» 
that  **  the  cylinder  in  motion  has  always  the  same  mass,'*  Hence,  as 
might  easily  be  shown  from  known  principles,  the  motion  of  sound  com- 
puted on  projectile  principles,  instead  of  being  uniform^  ought  to 
decrease  as  fast,  at  least,  as  the  reciprocal  of  the  distance  from  its  source 
decreases. 

Sir  Isaac  Newton's  view  of  ihe  subject  is  incomparably  more  con- 
sistent than  the  one  before  us.  He  supposed  all  the  vibrations  in  the 
same  uniform  medium  to  be  isochronous,  or  performed  in  equal  tiroes, 
however  different  their  lengths,  and,  consequently,  however  different 
the  velocities  of  the  atoms  at  like  points  of  their  vibrations.  Indeed,  it 
is  easy  to  see  that  there  is  no  way  in  which  the  velocity  of  sound  could 
be  uniform,  but  by  the  vibrations,  however  different  in  length,  being 
isochronous.  Newton,  and  his  earlier  followers,  were  well  aware  of  this 
circumstance  ;  but  vibrations  of  different  lengths  are  quite  at  variance 
with,  and  cannot  enter  as  an  element  into,  the  refined  mode  of  viewing 
sound  under  the  emblem  of  a  projected  cylinder,  going  on  for  ever,  as 
the  theory  implies,  without  either  det  rease  of  %xlocity  or  of  loudness, 
There  is,  however,  no  reason  to  think  that  every  *- once ivable  or  possible 
kw  of  elasticity  in  air  would  give  isot  hronous  vibrations ;  nor  am  I 
aware  that  such  has  been  proved,  from  legitimate  theoretical  principles, 
to  hold  of  even  one  particular  law,  far  less  of  that  which  belongs  to  the 
atmosphere. — H.  M. 

•  It  would  be  difficult  to  reconcile  almost  any  of  these  remarks 
either  with  each  other,  or  with  the  very  opposite  principles  acted 
on  in  the  rest  of  this  research.  As,  for  instance,  by  strictly  fol- 
lowing up  the  leading  princiiiles  of  the  investigation,  it  appears  that  di. 


WUlSPERlNtiS   OF    AN    lHJ)    I'lM-: 


^59 


tquilibrio^  and  p  the  variable  density  of  the  agitated  cylinder ;  then, 
ihe  masses  of  the  two  cylinders  being  the  same,  their  densities  will  be 
reciprocally  as  the  volumes  :  therefore 


dx 


p'      iix^tiz 


iix 


ii% 


the  jiowers  of  the  small  fraction     -  l>eing  rejected.*      This  e*|twliun,  it 

may  be  remarked,  im|>ltes  the  continuity  of  the  fluid, f  nince  the  cylinder 
in  motion  has  always  the  same  masi>.     Let  F*'  denote  the  elastic  force 


instead  of  being  incomparably  smaller  than  //.v,  must  occasionally  equal 
it ;  and  that  the  condensation,  in  place  of  being  trifling,  must  l>e  infi- 
niU.  For,  here  the  length  of  the  cylinder  is  iix^dz^  which  binooiral  is 
likewise  used  as  the  fluxion  of  z;  no  matter  how  curious  and  umlelined 
the  notation,  whit  h  Laplace,  however,  avoids.  Eiut  when  the  cylinder 
reaches  its  utmost  distance  from  the  assumetl  point  from  which  jr-f-s  is 
reckoned,  and  is  about  to  return  toward  that  point,  its  velocity  ^^; 
and,  therefore*  the  lluxion  of  the  space  =  ^/KV-l-i/r=:f;,  and  iix=i—tiz. 
Or,  more  properly,  r/.v— //c  =  f/,  an<l  Jx:^dz,  For  in  this  case,  the 
fluxion  of  the  s[>ace,  or  the  length  of  the  cylinder,  is  obviously  the  dif- 
ffrcnce  and  not  the  st/m  of  Jx  ami  dz^  because  dx  is  constant. 
Hence,  also,  at  the  turn  of  the  motion,  the  length  of  the  cyliniler  is 
md/iifij(f  or  its  density  is  infinik :  a  consequence,  though  absurd,  yet 
inse]mrable  from  the  tacit  hypothesis  whit  h  makes  the  cylinder  always 
move  over  a  space  equal  to  its  own  length,  during  the  constant  iLixion 
of  time  //t.  It  is  therefore  certain,  that  the  length  of  the  cylinder  can- 
not consistently  represent  its  velocity,  or  coincide  with  the  fluxion  of 
the  space,  as  our  author  so  conveniently  assumes  it  to  do,  wilhoyt  offer- 
ing the  least  reason  for  such  illegitimate  procedure.  It  is  almost 
necdlrss  to  add  that  the  *tme  assumption  involves  various  other  incon- 
sistencies, or  to  remark  that  the  shattering  of  windows  and  crazy  build- 
ings, the  shaking  of  houses  at  considerable  distances,  the  occasional 
deafening  of  persons,  with  many  similar  effects,  could  neither  be  pro- 
dnced  by  small  vibrations,  nor  slight  condensations ;  though  infinite 
ones  would  be  unnecessary. — H.  M. 

•  Since,  as  wc  have  seen,  d%  sometimes  equals  dx^  this  frac- 
tion is  occasionally  considerable,  or  even  equal  lo  unit ;  and,  there- 
fore, its  powers  cannot  warrajiiably  lie  rejected,  either  here,  or  again 
a  little  alter  in  taking  the  fluxions,  —  IL  M. 

t  True,  a  i-ontinuity\  but  only  in  one  <lirection  through  the  tube ; 
whereas,  in  open  air,  the  continuity  is  in  all  directions, — H,  M. 


26o  ELLKN   OR  THE 

of  the  air  /;/  equilibrio,  and  P  the  like  force  of  the  agitated  cylinder ; 
then,   if   we   adopt   the   law   of  Boyle  and   Mariotte,  we   shall  have 

L-p  . 

and  this  equation  would  lead  us  to  the  result  obtained  by  Newton.* 
But  if,  according  to  the  observation  of  Laplace,  we  reason  noore 
agreeably  to  what  actually  takes  place  in  nature,  and  suppose  that  the 
elastic  force  of  the  agitated  cylinder  is  exerted  while  it  retains  the  whole 
of  its  absolute  heat,  the  preceding  formulae  (D)t  will  furnish  this 
equation. 


*  We  shall  afterwards  see  this  to  be  a  mistake.  —  H.  M. 

t  The  formulae  referred  to  make  the  cube  of  the  pressure 
vary  as  the  fourth  power  of  the  density,  which  I  consider  to  be  the 
true  law,  though  Mr.  Ivory  has  since  renounced  it  as  incorrect,  without 
giving  any  admissible  reason ;  but  when  he  adopted  this  ratio,  in  the 
place  from  which  he  now  quotes  it,  he  did  so  for  an  erroneous  reason, 
as  I  have  hinted  in  the  *  Edin.  Phil.  Jour.'  for  January,  1827.  However, 
I  do  not  think  such  a  ratio  applicable  to  the  investigation  of  the 
velocity  of  sound,  especially  in  the  suppositious  case  of  the  tube  before 
us.  For  though,  \n  favorable  circumstances,  sound  be  propagated  in 
every  oj)en  direction  from  the  sonorous  body,  yet  it  does  not  appear 
that  the  air  acts  there  exactly  in  its  fluid  character.  Because  sound 
which  first  passes  through  the  tube,  and  then  into  the  open  air,  does 
not  proceed  from  the  mouth  of  the  tube,  as  from  a  sonorous  body,  in 
every  direction,  which  it  wouhl  do  if  the  particles  acted  on  each  other 
with  ecjual  force  in  every  direction.  On  the  contrary,  sound,  as  is 
well  known,  diverges  but  in  a  small  degree  after  quitting  a  long  tube 
which  merely  conducts  it ;  and  I  rather  doubt  if  it  would  diverge  at  all, 
were  it  not  for  the  friction  or  resistance  which  the  vibrating  particles 
suffer  from  their  contact  with  air  which  is  not  in  the  direction  of  the 
tube.  From  this  we  should  be  led  to  infer,  that  the  particles  of  air 
conveying  sound  through  a  narrow  tube,  especially  the  ideal  one  free 
from  friction,  only  vibrate  in  the  direction  of  the  axis.  If  so,  the  elas- 
ticity of  air  conducting  sound  through  the  tube  should  not  be  estimated 
according  to  the  above  law,  but  more  nearly  as  in  the  inverse  ratio  of 
the  squares  of  the  variable  longitudinal  dnnensions ;  because,  as  I  have 
shown  on  a  former  occasion,  the  particles  of  air  repel  each  other  with 


W!nSPERTNGS   OF  AN   OLD    PINE 


261 


'**Take  the  fluxions  making  .v  only  variable*  and  divide  by  the 
cqud  quantities  p  {dx-^-dz}  and  p  dx ;  then 

dj!S 


d?      ^     ,     T[ 
f,(dx-^dz         ^*   p 


*'•  Now,  P  is  the  elastic  farce  of  the  air  in  the  tube  at  the  distance 
.v-Ks  from  the  assumed  point  in  the  axis,  an4  P  +  //P  is  the  like  force 
of  the  air  at  the  distance  x+z-^-dx-\-dsi  wherefore  ^P  is  the  effective 
force  urging  the  intervening  cylinder  towards  the  assunied  point :  and 
as  the  mass  moved  is  equal  to  p{dx-\-dz)f  the  quotient  is  the  accelera- 
tion of  each  particle,  other\^'ise  expressed  by  — '-— 5;-|-  wherefore 

L,  dr^ 


ddz_.      P' 


dr 


dds„ 
dx^' 


But  wc  have  already 
totally  different  from 


forces  inversely  as  the  squares  of  their  distnnres. 
seen  that  the  actual  case  of  the  atmosphere  is 
that  of  the  tube,— H.  M. 

•  This  is  a  curious  injunction,  more  likely  to  embarrass  and 
mislead  the  reader  than  anything  else ;  for  the  etiuation  in  hand  does 
not  involve  .T  at  all ;  and,  besides,  Mr.  Ivory,  in  the  face  of  this  strict 
precept,  makes  lx)th  P  and  dz  variable, — H.  M. 

t  Viz.  one  of  the  usual  differential  expressions  for  an  accel- 
erating force,  llie  second  fluxion  of  the  space  being  ddz^  and  the 
undefined  symlxil  //t  denoting  the  constant  fluxion  of  the  time.  It  is 
from  this  step  that  it  becomes  more  particularly  obvious  that  the  length 
of  the  cylinder  is  a  measure  of  its  velocity,  being  always  equal  to  the 
minute  space  described  during  the  constant  moment  of  time  dt.  Not 
the  shadow  of  a  reason  is  either  given  or  supposed  necessary  to  assign 
why  the  length  of  the  cylinder  should  not  rather  have  had  some  other 
relation  to  its  velocity  than  that  just  mentioned,  which  we  have  already 
seen  to  be  impossible.  Hut  the  gratuitous  assumptions  in  this  investi- 
gallon  are  so  numerous  and  important  that  they  would  have  rendered  it 
null  and  void  as  a  mathematical  production,  although  no  inconsistency 
had  presented  itself.  For  were  such  assumptions  to  be  tolerated  in 
mathematics,  there  is  no  problem,  however  difficult,  but  they  could 
solve  with  the  utmost  facility.  A  curious  instance  of  their  irresistible 
f)Owers  is  noticed  in  the  'Philosophical  Magazine^  for  December,  1822, 
where  I  have  shown  that  the  demonstration  which  Mr.  Ivory  supposed 
he  had  given  of  Euclid's  Twelfth  Axiom,  in  the  number  for  Xfarch  pre- 
ceding, owes  all  its  virtue  to  an  assumption  fully  equivalent  to  the  axiom 
itselfj  which  was  the  very  point  to  be  proved  '.— H.  M. 


262  ELLEN  OR  THE 

'Were  every  thing  correct  about  this   equation  and  the  mode  by 

which  Mr.  Ivory  has  obtained  it,  the  velocity  would  obviously,  as  he  lo 

effect  states  it,  be 

dx_    '4P' 

and  since  both  dx  and  dg  are  constant,  the  velocity  would  be  uniform, 
and  always  the  same  in*  air  of  the  same  density  and  pressure.  But 
another  notable  error  and  inconsistency  have  here  evaded  notice,  by 
the  manoeuvre  of  twice  rejecting  the  higher  powers  of  //s,  seemingly 
for  the  purpose  of  rendering  the  calculus  manageable,  though,  as  we 
shall  presently  see,  there  was  no  call  or  necessity  for  it  on  that  account. 
Whether  M.  Laplace  or  Mr,  Ivory  were  aware  of  this  circumstance,  I 
could  not  pretend  to  say ;  but  one  thing  is  certain,  that  further  defects 
of  the  investigation  become  sufficiently  apparent,  when  none  of  these 
powers  have  been  discarded.     For  in  this  way  we  have 

Y~^dx->rdz^  ' 
*  Take  the  fluxions,  making  dx  and  P'  constant,  which  gives 

'^'—~'^Tx^dz^    ^~dx—~^^~p'^    ^  dx' 

Multiply  by  P'  and  divide  by  p(dx  +  dz)=zp' dx,  as  before,  and  we 

have 

_dP    ___4_PVp  v^v''''''^--^-^^ 
p(dx-{-dz)  3p^'p'^       dx'^         //t^' 

'  Hence  the  velocity  of  sound  should  be 

dr         p  \     Zp 

which,  though  a  very  different  expression  from  the  former,  is  uniform 
or  independent  of  the  degree  of  condensation,  because  dx  and  dr  are 
constant ;  and  yet  it  is  afTected  by  the  intensity  or  degree  of  condensa- 
tion, because  p  is  so  afTected. 


\VllIM't:KIN(;s   Ol-    AN   OLD    riNF. 


i6i 


^Wc  have  thus,  even  when  working  more  correctly,  obtained  a 
result  which  is  evidently  contradictory  or  absurd.  Nor  lan  it  be 
ftdmitted  as  an  excuse,  to  say,  that  p  and  p'  are  nearly  equal ;  for  we 
have  already  seen  that  the  principles  acted  on  in  this  investigation 
imply  that  p  may  exceed  p'  in  any  proix)rtion. 


'  By  using  unit  for  the  index  of 


we  do  not,  when  nothing 


is  omitted,  obtain  Newton's  result,  as  Mr.  Ivory  alleges,  btit  the  ver)' 
different  expression 

p'  \  p 

which  is  just  as  absurd  as  the  other.  Indeed,  when  in  this  mode  of 
investigation,  none  of  the  powers  of  //s  have  been  rejected,  the  velocity 
can  never  come  out  uniform  or  inde|*endent  of  the  degree  of  condensa- 
tion, and  be  at  the  same  time  real  or  possible.  For,  taking  the  only 
two  supposable  cases,  —  were  the  index  ^  ^,  neither  the  elasticity  of 
aifi  nor  sotmd,  which  depends  on  it,  cotdd  exist ;  and  were  the  index 
=  — I,  the  elasticity  would  vary  trntrstfy  2ls  the  density,  which  is  a 
perfect  contradiction,  not  to  mention  that  the  velocity  of  sound  would 
come  out  an  im (possible  quantity. 

•  Any  further  evidence  would  be  superfluous  lo  show  that  this  sort 
of  investigation  is  not  only  inefficient,  but  full  of  error  and  incongruity, 
view  it  which  way  we  will ;  and  that  it  will  be  alike  unfortunate  for 
this  theory  whether  the  motion  of  sound  ultimately  turn  out,  from 
experiment,  to  be  imiform  or  retarded;  for,  independently  of  that,  the 
result  is  anything  but  a  fair  logical  deduction  from  correct  data.  I 
have  as  yet  confined  my  remarks  to  Mr.  Ivory's  investigation  in  the 
"  Philosophical  Magaicine  '*  for  July,  1825.  His  other  solution  grafted  on 
it,  and  given  in  that  journal  for  April,  1827,  is  one  way  or  other  liable 
to  all  the  above  mentioned  objections/ 

•*This  article  of  Mr.  Mcikle  is  one  of  the  very  few  that  Ellen 
has  ever  seen,  written  by  a  mathematician,  that  doesn't  run  16 


264  ELLEN   OR  THE 

absurdities.  That  is,  it  is  one  of  the  few  especially  able  artkks 
that  she  has  ever  seen  written  by  a  mathematician.  Mr.  Meilde 
is  too  able  a  man  to  be  wrecked  by  a  little  knowledge  of  matb- 
ematics.  He  is  eminent  as  a  mathematician,  but  still  more  so 
as  a  man.  He  handles  the  whole  subject  without  gloves  and 
shoe's  that  this  undulator>-  theory  of  sound  is  entirely  untenable, 
preposterous,  and  impossible.  The  wonder  is  that  after  such  a 
thorough  and  unanswerable  exposure  the  theor>'  was  not  aban- 
doned, although  of  course  the  vested  interests  in  text  books 
and  of  instructors  stood  tremendously  in  the  way  of  such  aban- 
donment.    Still,  always,  sooner  or  later  the  truth  will  prevail. 

'•  It  seems,  too,  from  a  second  article  by  Mr.  Meikle,  pub- 
lished in  the  same  volume  of  the  *  Quarterly  Journal/  that 
Professor  Leslie  had  previously  made  similar  criticisms  of  this 
theor}'.     Thus  Mr.  Meiklc,  in  this  second  article,  says : 

'In  the  "Philosophical  Magazine"  and  "Annals"  for  November  last, 
Mr.  Ivor>'  has  brought  forward  what  he  calls  an  "Answer"  to  my  article, 
in  No.  VII.  of  the  "Journal  of  Science,"  on  his  doctrines  about  sound 
and  heat.  A  ])rominent,  an»i  i>erhaps  unavoidable,  feature  of  Mr.  Ivor>**s 
answer,  which  cannot  fail  to  strike  the  reader's  attention,  is  the  total 
absen*  e  of  everything  bearing  immediately  on  the  points  in  dispute. 
'Ilie  whole  aftair  is  got  conveniently  over,  by  a  series  ot  excuses  more 
or  less  plau>ible  :  while  ever}-  one  of  my  criticisms  remains  unansTi'ereJ 
in  full  forre. 

'Mr.  Ivory's  first  insinuation  is,  that  my  strictures  are  little  else  than 
taken  from  I'rofe>sor  Leslie's  article  **  Acou>tics.'*  He  takes  good  care 
to  offer  no  eN  iden*  e  of  this.  I  have  only  to  regret,  that,  so  far  from  its 
having  been  the  fijct,  I  had  entirely  fori;otten  that  that  valuable  artic'iC 
f.ontaineri  any  objection  to  the  theory  ot  sound.  I  now  see  that  had  1 
looked   into   it   in   time,  I  might  have  materially  improved   my  paper. 


WHISPERINGS    OF   AN    OlAi    V]SK 

I  presume,  however,  that  by  endea\onng  to  sift  the  analytical  investi- 
gation to  the  bottom,  1  have  distinctly  pointed  out  several  striking 
inconsistencies,  impossibilities,  and  unwarraia table  assumptions,  not 
before  noticed  by  any  one;  and  therefore,  "the  subject  is  not  left,"  as 
Mr.  Ivory  could  wish,  "just  where  I  found  it.** 

*Mr.  Ivory  next  remarks  on  my  article  that  *Svhatever  purposes  such 
discussions  may  serve,  one  is  at  a  loss  to  fiud  out  how  they  can  benefit 
science***  A  very  natural  remark,  to  be  sure,  while  the  tide  of  discus- 
sion tan  against  Mr.  Ivory.  He  might  just  as  well  say,  he  was  at  a  loss 
to  see  how  the  destruction  of  weeds,  and  other  useless  or  noxious  herbs, 
can  benefit  the  produce  of  a  garden.  I'he  removal  of  s]>urious  produc- 
tions, especially  th  ose  wearing  the  garb  of  mathematical  investigation, 
being  as  necessary  and  beneficial  to  the  progress  of  science  as  the 
destruction  of  weeds  in  the  other  case.  I  would  rather  ask — what 
benefit  can  result  to  science  from  an  "Answer,"  which  leaves  unan- 
STift  red  every  thing  it  professed  to  answer?  lu  particular,  it  **  leaves  the 
analytical  theory  of  sound/*  which  I  had  impugned,  **  to  stand  on  its 
own  merits,*'  after  it  had  not  a  foot  left  to  stand  upon,' 

**  Ellen  has  been  unable  to  obtain  the  article  by  Professor 
Leslie  referred  to.  but  she  will  call  especial  attention  to  some 
of  the  unanswerable  objections  to  the  theory  pointed  out  by 
Mr.  Meikle,  showing  that  mathematically  as  well  as  in  fact  it 
has  no  existence : 

*'  First.  The  amplitude  of  the  particle  propagating  sound 
must  be  always  of  the  same  magnitude,  or  else  the  accel- 
crating  force  of  this  particle  must  be  everywhere  inversely 
proportional  to  the  space  passed  over  by  the  particle*  The 
first  could  not  be  true,  as  it  would  necessitate  that  the  intensity 
of  sound  be  always  the  same  in  air  of  like  condition.  And  the 
last   is  distinctly   opposed   to   a   fundamental    principle    upon 


268  ELLEN   OR  THE 

which  the  theory  is  based,  that  the  accelerating  force  must  be 
proportional  to  the  space  passed  over  by  the  particle.  A  prin- 
ciple which  harmonizes  with  Boyle's  law,  that  *  the  temperature 
remaining  the  same,  the  volume  of  a  given  quantity  of  gas  is 
inversely  as  the  pressure  which  it  bears.'  There  is  no  answer 
to  this,  and  it  is  fatal  to  the  theory. 

"Second.  In  the  third  note  Mr.  Meikle  points  out,  what  has 
since  been  demonstrated  by  Regnault,  and  what  is  in  its  nature 
self-evident,  that  the  velocity  of  the  particles,  and  distance 
passed  over  by  them,  in  a  pulse  of  air  must  constantly 
decrease. 

"Third.  By  preserving  so-called  infinitesimals,  that  is  by  an 
accurate  solution,  absurd  results  are  reached,  which  of  itself  is 
a  fatal  objection.  Other  points  are  referred  to  and  the  utterly 
untenable  character  of  the  whole  theory  pointed  out  and 
demonstrated.  So  that  the  existence  of  these  undulatory 
theories  to-day  is  absolutely  without  warrant  or  excuse,  and 
can  only  be  explained  by  the  fact  that  large  property  interests 
are  at  stake  in  the  sale  of  text  books,  and  in  the  profession  of 
teaching. 

"  It  can  be  demonstrated  in  an  open  tube,  as  Ellen  has  said, 
that  when  a  piston  pushes  the  particles  of  air,  not  only  these 
particles  move  the  distance  of  the  piston,  as  they  must,  but 
neglecting  viscosity  and  friction,  all  particles  in  the  tube  for  a 
long  distance  do  the  same,  and  a  number  of  particles,  equal  to 
those  displaced  by  the  piston,  will  go  out  from  the  other  end. 
If,  as  scientists  assert,  unconfined  air  acts  as  confined  air,  all 
the  particles  influenced  by  the  compression  must  move  as  far 
as  those  pushed  by  the  tuning   fork.     The  whole   conceit  of 


WHISPERINGS    OF   AN   OLD    PINE  269 

developing  heat  is  arrant  nonsense;  but  if  it  was  true,  the 
heat  would  be  developed  according  to  the  force  of  the  com- 
pression,— hence  loud  sounds  would  go  much  faster  than  low 
ones,  and,  indeed,  every  sound  on  this  account  would  have  a 
different  speed.  And  thus  again  the  theory  as  now  announced, 
with  the  Laplace  modification,  is  demonstrated  to  be  uttei 
nonsense. 


270  ELLEN   OR  THE 


XVII. 


^  *  C I-I-'*-?^  will   now  return   to  the  review  of   Mr.  Tyndall's 


ELLKNwill  n 
book.     He 


further  says: 


*\Ve  have  already  learned  that  what  is  loudness  in  our  sensations  is 
outside  of  us  nothing  more  than  width  of  swing,  or  amplitude^  of  the 
vibrating  air  particles.  Kvery  other  real  sonorous  impression  of  which 
we  are  conscious  has  its  correlative  without,  as  a  mere  fonn  or  state  of 
the  atmosphere.  Were  our  organs  sharp  enough  to  see  the  motions 
of  the  air  through  which  an  agreeable  voice  is  passing,  we  might  see 
stamped  uix)n  that  air  the  conditions  of  motion  on  which  the  sweetness 
of  the  voice  depends.  In  ordinarj-  conversation,  also,  the  physical 
preceiles  and  arouses  the  psychical ;  the  six)ken  language,  which  is  to 
give  us  jileasure  or  pain,  which  is  to  rouse  us  to  anger  or  soothe  us  to 
I>eace,  existing  for  a  time,  between  us  and  the  speaker,  as  a  purely 
mechanical  condition  of  the  intervening  air.' 

'*  IVrhaps  no  passai^o  in  the  book  sut^i^ests  the  absurdities 
i^f  the  ihovMy  more  vividly  than  this.  Mr.  Tyndall  at  last 
awakes  to  the  perception  that  every  impression  of  which 
we  aic  conscivHis  has  lis  CvMrclativo  without,  and  this 
corrcKuivc.  in  the  case  vM"  sound,  he  would  assume  to  be 
built  ot  air.  and  further  assumes  thai  this  is  accomplished 
by  a  very  slii;hl  mechanical  force,  and  transferred  repeat- 
edly tv^  an  cx.iclly  similar  number  of  air  particles  in  exactly 
siniilar  arranL;cmcnt ;  and  this  process  repeated  in  all  direc- 
tion<  as  Ivmi^;  as  the  souiui  o\i<:s.  an  operation  that  under 
Uv^  conceivable  circumstances  would   be  possible,   but  that,   if 


'%VinsrHRL\GS   UF 


possible,  would  necessitate  all  the  air,  within  the  distance  that 
a  sound  is  heard,  to  be  occupied  exclusively  in  the  propagation 
ol  that  sound  for  a  certain  definite  time.  The  old  Pine  and 
Ellen  would  have  to  stop  breathing  if  they  wished  to  hear 
any  perfect  sounds.  For  breathing  would  disturb  the  air  parti- 
cles about  the  head  and  cars,  and  thus  further  damage  and 
destroy  what  remained  of  every  supposed  correlative.  And 
certainly  Ellen  and  the  old  Pine  wouldn't  want  to  be  uncivil  to 
the  pretty  birds  that  sing  to  them,  or  the  brooks  which  make 
such  beautiful  melody.  And  the  idea  of  such  a  correlative  as 
this,  which  is  simply  the  most  unmitigated  nonsense,  is  called 
science.  As  well  might  scientists  state  that  utensils  are  made 
of  water,  cities  built  of  air;  and  ropes  formed  of  sand,  thrown 
together  by  the  wind.  For  the  one  thing  is  as  sensible  and 
possible  as  the  other.  The  principle  of  a  sufficient  cause 
upon  which  science  is  founded,  though  constantly  over- 
looked by  scientists,  belongs  to  all  nature.  Nothing  takes 
place  without  it  As  Ellen  has  said  before,  insufficient  causes 
will  not  answer;  they  must  be  suflFicient,  Nor  is  it  possible 
that  anything  is  a  cause  which  is  opposed  to  the  laws  of  nature. 
Then  such  a  correlative  as  this,  ragged,  incomplete,  and 
impossible,  which  scientists  offer  for  sound,  can  only  exist  in 
their  imagination,  or  want  of  imagination.  Nature  has  pro- 
vided something  very  different  and  complete,  by  w^hich  the 
dulcet  tones  of  her  harmonfbs,  and  all  her  beautiful  sym* 
phonies,  are  made  possible  to  our  understandings.  Ellen  is 
awfully  glad  that  nature  fixed  up  things  before  the  scientists  got 
along.  It  would  have  been  a  sorry  world  that  we  should  have 
had  if  she  hadn*t. 


272  ELLEN    OR   THE 

"Then  it  is  certain  that  whatever  represents  this  thing  sound 
to  the  senses,  that  is,  whatever  sound  is,  must  be  fashioned  of  such 
material  and  by  such  forces  as  are  adequate  to  make  it,  and  in 
such  manner  that  its  consistency  may  be  maintained  throughout 
its  existence.  And  it  is  also  certain,  as  Ellen  has  said  before, 
that  the  correlative  of  sound  must  be  a  correlative  in  the  fullest 
sense,  just  as  all  things  are  which  are  correlatives  of  sensations. 
The  correlative,  always,  of  anything,  includes  and  must  include 
everything  perceived  by  the  senses.  That  of  the  tree  must 
include  trunk,  bark,  and  flower — each  leaf  and  every  twig, 
and  it  does  include  all  these  and  many  things  besides  that 
Ellen  cannot  enumerate.  For  every  leaf  reflected  in  the  mind 
dwells  on  the  tree.  And  these  leaves  have  notched  shores,  and 
are  divided  into  mountain  ranges  and  valleys.  All  are  formed 
with  the  most  exquisite  care,  and  composed  of  the  choicest 
materials.  There  is  no  fraud  in  them,  nor  in  any  part  of  the 
tree.  And  so  with  a  bush,  or  with  a  flower.  The  workmanship 
in  each  is  of  the  finest,  and  the  material  in  each  of  the 
choicest.  And  it  is  in  this  way  that  nature  builds  up  all 
things.     She  neglects  nothing. 

'Consider  the  lilies  of  the  fieKl,  how  they  grow  ;  they  toil  not,  neither 
do  they  spin.  And  yet  I  say  unto  you,  that  even  Solomon  in  all  his 
glory  was  not  arrayed  like  one  of  these.' 

"But  if  the  correlative  of  all  things  that  we  see  is  thus 
made  so  perfectly,  we  know  that  the  correlative  of  those  things 
which  we  hear  is  made  with  equal  care,  both  in  material  and  in 
form.  And  every  sound  has  its  own  consistency  of  form  and 
character,  and  always  the  same  sound  is  composed  in  the  same 
way.     The  old  Pine  can't  see  the  sound,  can  he?" 


WHISPERINGS    OF  AN   OLD    PINE 


273 


**No,"  I  said,  **  but  he  knows  that  it  includes  all»  even  to  the 
minutest  feature,  that  intelligence  perceives  in  it,  or  gathers 
from  it." 

**  Sensible  old  Tree/'  she  said.  **  How  does  any  one  sup- 
pose that,  even  if  they  existed^  such  conformations  as  those 
of  this  theory  could  be  conveyed  to  the  soul?  Only  by 
vision  might  such  a  feat  be  attempted,  and  they  are  not 
visible.  For  if  they  could  be  made,  the  larger  part  of 
them  could  not  by  any  possibility  reach  the  ear  intact, 
or  in  any  such  shape  as  to  suggest  their  supposed  shape 
when  formed.  For  by  other  sounds  and  other  constantly 
occurring  disturbances  in  the  air,  their  consistency  would 
and  must  be  entirely  destroyed.  The  man  who,  with  arms 
spread,  requested  the  crowd  to  get  out  of  his  way  because 
he  had  the  measure  of  a  door  between  his  hands,  was  a 
marvel  of  wisdom  to  the  scientist  who  believes  that  air 
waves  carry  or  can  carry  the  measure  of  sounds.  Thus  in 
talking,  often  those  that  we  speak  to  arc  many  rods  from 
us,  with  numerous  noises  taking  place,  as  the  rustling  of 
leaves,  the  murmuring  of  streams,  the  singing  of  birds, 
the  barking  of  a  dog,  lowing  of  cows  or  neighing  of 
a  horse,  each  one  of  which,  by  this  theory,  must  o:cupy 
every  particle  of  air  and  keep  it  in  constant  and  different 
vibration,  throughout  the  whole  continuation  o(  its  sound; 
and  always  at  the  same  time,  if  out  of  doors,  there  is 
more  or  less  disturbance  of  the  air  by  w^inds,  which  are 
simply  particles  of  air  moving,  because  of  gravity  and 
elastic  force,  from  the  more  dense  to  the  less  dense. 
The   old    Pine    will   see   how   absolutely  impossible    it  would 


274  ELLEN   OR  THE 

be  for  the  measure  of  the  door  to  be  maintained.  And 
yet,  under  all  such  circumstances,  the  voices  of  those  talking 
to  us,  are  brought  to  our  understanding  in  such  manner,  that 
we  recognize  not  only  the  words,  but  pitch,  tone,  intonation, 
all  the  belongings  of  speech,  which  add  so  much  to  its  beauty 
and  force.  And  not  only  brought  to  us,  but  to  all  others, 
within  hearing.  That  is,  according  to  this  theory,  every  one 
of  the  millions  of  waves,  more  or  less,  or  the  infinite  millions  of 
parts  of  waves  which  are  supposed  to  reach  some  ear,  are 
kept  in  exactly  the  same  condition,  so  as  to  convey  exactly  the 
same  sensation  to  perhaps  a  million  hearers. 

"Concerning  this  correlative  without.  Professor  ChalHs 
remarks : 

*  llie  possibility  of  hearing  distinctly  words  spoken  at  a  distance, 
depends  on  the  faithfulness  with  which  the  air  transmits  the  impressions 
made  on  it  by  the  organ  of  voice.  As  the  difference  between  the 
sound  of  one  letter  and  that  of  another  corresponds  to  a  difTerence  in 
the  form  of  the  curve  representing  the  succession  and  magnitude  of  the 
condensations  impressed,  it  is  necessary  that  the  form  should  remain 
unchanged  by  distance  of  transmission  in  order  that  words  heard  at 
different  distances  may  be  the  same  sounds.  The  law  of  transmission 
expressed  by  the  formula  a  -f  Vy  which  is  the  basis  of  Mr.  Airy's  specu- 
lations, is  opposed  to  this  constancy  of  form.  M.  r>iot,  however,  has 
recorded  an  experiment  made  at  Paris,  according  to  which,  words 
pronounced  at  one  end  of  a  cylindrical  tube  3120  feet  in  length  were 
perfectly  distinct  at  the  other  end. ' 

*'  The  old  Pine  can  be  perfectly  certain  that  for  such  wonder- 
ful results  God  ordered  no  impossible  and  insufficient  method, 
but  instead  created  a  system  abundantly  able   to  perform  all 


WHISPERINGS   OF   AN   OLD   FINE 


275 


'  these  marvelous  things,  and  which  in  its  workings  would  inter- 
fere vvnth  nothing  else  ordered  by  Him, 
*'Mr.  Tyndall  continues: 

'Having  determined  the  rapidity  of  vibration,  the  length  of  the 
corresponding  sonorous  wave  is  found  with  tiie  utmost  facility. 
Imngiue  a  tuning  fork  vibrating  in  free  air.  At  the  end  of  a  second 
fnom  the  time  it  commenced  its  vibrations  the  foremost  wave  would 
have  reached  a  distance  of  1,090  feet;  in  air  of  the  freezing  tempera- 
ture of  about  1^0  c.,  it  would  reach  a  distance  of  1,120  in  a  second. 
In  this  distance,  therefore,  are  embraced  384  sonorous  waves.  Divid- 
ing 1,120  by  3S4,  we  find  the  length  of  each  wave  to  be  nearly  three 
feet.  Determining  in  this  way  the  rates  of  vibration  of  the  four  tuning 
forks  now  before  you,  we  find  them  to  be  256,  320,  384,  and  512; 
these  numbers  corresixtoding  to  wave  lengths  of  four  feet  four  inches, 
two  feet  eleven  inches,  and  two  feet  two  inches,  respectively.  The 
waves  generated  by  a  luan's  voice  in  common  conversation  are  from 
eight  to  twelve  feet,  those  of  a  woman's  voice  are  from  two  to  four  feet 
in  length.  Hence  a  woman's  ordinary  pitch  in  the  lower  sounds  of 
conversation  is  more  than  an  octave  abfjve  a  man*s ;  in  the  higher 
sounds  it  is  two  octaves, 

'And  here  it  is  important  to  note  that  l>y  the  term  vibrations  are 
meant  complete  ones  ;  and  by  the  term  sonorous  wave  are  meant  a  con- 
densation and  its  associated  rarefaction.  By  a  vibration  iin  excursion 
/*;  and  fro  of  the  vibrating  body  is  to  be  understood.  Ivvery  wave  gen- 
erated by  stich  a  vibration  Iteiuls  the  tympanic  inembnme  onre  in  and 
once  out* 

*  During  the  time  refjuired  by  each  of  those  sonorous  waves  to  pass 
entirely  over  a  particle  of  air,  that  particle  accomplishes  one  complete 
vibration.  It  is  at  one  moment  pushed  forward  into  the  condensation, 
while  at  the  next  moment  it  is  urge*!  back  into  the  rarefaction.  The 
time  required  by  the  particle  to   execute  a  complete  oscillation   is, 


2^fi  ELLEN   OR   THE 

therefore,  that  required  by  the  sonorous  wave  to  move  through  a  dis» 
tance  equal  to  its  07un  length.  Supposing  the  length  of  the  wave  to  be 
eight  feet,  and  the  velocity  of  sound  in  air  of  our  present  temperature 
to  be  1,1 20  feet  a  second,  the  wave  in  question  will  pass  over  its  own 
length  of  air  in  i -140th  of  a  second  :  this  is  the  time  required  by  every 
air  particle  that  it  passes  to  complete  an  oscillation.' 

**  This,  too,  is  as  ineffable  a  lot  of  nonsense  as  it  would 
be  possible  to  conceive.  There  are  here  two  known 
facts,  and  only  two;  namely,  that  the  C  fork  vibrates 
256  times  per  second  and  that  sound  goes  1090  feet  per 
second.  From  these  it  is  possible  to  deduce  the  single  addi- 
tional fact  that  in  ^^^  of  a  second  sound  will  go  about  four 
feet  four  inches,  supposing  it  to  proceed  at  uniform  rate,  as  it 
is  generally  supposed  to  do.  This  is  the  limit  of  knowledge. 
Like  a  true  scientist,  Mr.  Tyndall  immediately  crosses  it  and 
states  a  number  of  other  things  to  be  true  about  which  he  has 
no  knov.'ledgc  whatever.  Ellen  has  already  called  attention  to 
the  difficulty  of  a  wave  passing  over  a  particle  of  air  supposed 
to  be  a  component  part  of  itself.  The  statement  that  the  time 
required  for  a  particle  to  execute  a  complete  oscillation  is  that 
required  by  the  sonorous  wave  to  move  through  a  distance 
equal  to  its  own  length,  is  one  of  the  fundamental  conditions  of 
this  theory,  but  is  without  proof;  and  taken  in  connection  with 
other  parts  of  the  hypothesis,  is  impossible.  For  one 
part  of  the  theory  requires  that  the  waves  should  all  be 
of  equal  length,  and  claims,  as  Mr.  Tyndall  does,  that  they 
are.  But  another  part  of  the  same  theory  makes  it  neces- 
sary that  these  waves  should  vary  in  length,  constantly  dimin- 
ishing.    Thus  the  oscillation,  or  half  oscillation,  of  the  particle 


WHISPERINGS    OF   AN   OLD    PINE 


279 


is  known  as  the  ainplitiide  of  the  vibration.  But  the  intensity 
of  sound  by  the  theory  is  proportional  to  the  square  of  this 
amphtude.  This  intensity  also  varies  inversely  as  the  square 
of  the  distance  from  the  Sounding  body;  therefore  the  ampli- 
tude of  oscillation  must  vary  inversely  as  the  distance  from  the 
source  of  soundi  and  the  velocity  of  sound  must  vary  through- 
out its  course.  For  as  the  particles  all  vibrate  in  equal  times 
and  move  through  a  constantly  decreasing  amplitude,  their  ve- 
locity will  decrease  as  the  distance  from  the  sounding  body  in- 
creases. But  the  velocity'  of  sound  depends  upon  the  velocity 
of  the  particles,  and  therefore  must  decrease  constantly  as  the 
distance  from  the  sounding  body  increases." 

"But  would  not  the  scientists  claim/'  I  asked,  "that  this 
amplitude  is  an  infinitesimal  which  can  be  neglected?'* 

**  Ellen  knows  not  what  they  might  claim,**  she  replied  ;  "but 
it  is  not  an  infinitesimal  which  under  any  circumstances  can  be 
neglected.  For  the  velocity  of  sound  is  proportional  to  the 
velocity  of  the  particles,  and  therefore  when  their  velocity  has 
decreased  one-half,  the  velocity  of  sound  by  this  theory  must 
have  decreased  one-half.  It  follows,  too»  that  if  there  was  any 
such  system  vi  waves,  these  waves  would  all  be  of  different 
length,  each  one  being  shorter  than  the  one  preceding. 

**This  is  under  the  supposition  that  the  medium  is  of  uni- 
form density.  But  supposing  that  the  density  diminishes,  it 
is  claimed  that  there  is  no  variation  in  the  velocity  of 
;  propagation,  or  in  the  intensity  of  the  sound,  over  what  it 
would  be  if  the  medium  was  uniform.  But  by  the  theory 
the  intensit>'  depends  upon  the  vis  vit^t  which  equals  half 
the  mass  times  the  square   of    the  velocity.      Then,    because 


280  ELLEN   OR  THE 

of  the  fact  that  if  the  product  of  two  factors  is  constant 
and  one  of  the  factors  diminishes  the  other  must  increase, 
if  the  intensity  is  not  diminished  when  sound  goes  from 
dense  air  to  less  dense,  the  square  of  the  velocity,  and  hence 
the  velocity  of  the  particles,  must  increase.  Therefore  the 
velocity  of  propagation  as  well  as  the  wave  length  must  increase. 
Both  of  which  conclusions  are  contrary  to  the  theory.  Hence 
again,  if  there  was  any  such  system  of  waves  in  a  medium  of 
varying  density,  these  waves  would  all  be  of  different  length. 
And  therefore  it  would  be  impossible  for  different  partidles 
to  be  in  same  phase,  and  hence  the  intonations  of  sound,  the 
clang  tint,  or  acoustic  color,  could  not  possibly  be  formed 
according  to  the  theory  as  now  maintained,  and  conveyed 
from  the  vibrating  body  to  the  ears  of  those  within  hearing,  by 
such  a  system  of  waves. 

**  Again,  supposing  it  possible  for  these  waves  to  be  thus 
composed  exactly  alike  in  a  medium  of  uniform  density,  then, 
as  Ellen  has  said,  the  theory  demands  that,  first,  they  should 
continue  of  the  same  length,  and  second,  that  the  particles  of 
which  they  are  composed  should  be  constantly  decreasing  in 
their  movement  inversely  as  the  square  of  their  distance  from 
the  sounding  body. 

"  Such  a  wave,  if  existing,  must  be  composed  of  a  certain 
number  of  particles.  It  may  be  any  number — a  billion  or  a 
hundred  billions  We  will  assume  it  is  twelve  particles.  It 
has,  too,  by  the  theory,  as  all  waves  have,  a  certain  definite 
length.  We  will  suppose  this  to  be  one  foot.  Then  each  par- 
ticle must  move  one  inch  before  it  delivers  up  its  motion, 
minus  the  very  small  diameter  or  thickness  of  the  particles. 


WHISPERINGS   OF  AN   OLD    PINE  28 1 

We  will  suppose  that  the  motion  of  this  wave  is  transferred  to 
another  exactly  similar  number  of  particles, — for  by  the  theory 
it  is  the  correlative  of  sound,  carrying  not  only  pitch  and 
intensity,  but  all  the  intonations  of  tone,  —  and  again,  to 
another  set,  and  thus  continuously  until  the  sound  has  reached 
every  ear  through  which  it  is  supposed  to  make  a  sensation. 
It  will  of  course  be  a  dilapidated  correlative  unless  all  of  these 
transfers  are  made  with  perfect  accuracy,  a  thing  that  could 
never  happen,  and  this  again  exposes  the  idiotic,  because 
impossible,  character  of  the  theory. 

*'But  supposing  all  this  to  happen,  or  after  all  this  has  hap- 
pened, two  things  arc  demanded  by  this  theory.  P'irst,  that 
the  wave  after  the  transition  of  its  motion  to  an  equal  number 
of  particles,  should  be  not  only  of  the  same  length  that  it  was 
when  made,  and  hence,  that  the  particles  to  which  it  is  trans- 
ferred should  vibrate  precisely  as  the  first  particles  composing 
the  wave :  but  also  that  they  should  vibrate  with  an  amplitude 
diminished  as  the  square  of  the  distance  increases. 

•'And  thus  again  we  sec  the  theory  is  full  of  folly  and  non- 
sense anywhere  we  touch  it.  ICllcn  gets  awfully  ashamed  in 
discussing  it." 

**Thc  old  Pine  doesn't  blame  Ellen,"  I  said,  **and  he  won't 
ask  her  to  discuss  it  much  longer,  but  wishes  she  would  finish 
her  review  of  Mr.  Tvndall's  book." 


282  ELLEN    OR  THE 


XVIII. 
*^  T  ¥  ryii^^  Ellen  will  try  once  more  to  please  the  old  Pine. 


V  V      Mr.  T 


Tyndall  continues: 

'The  difference  of  velocity  in  iron  and  in  air  may  be  illustrated  by 
the  following  instructive  experiment :  Choose  one  of  the  longest  hori- 
zontal bars  employed  for  fencing  in  Hyde  Park ;  and  let  an  assistant 
strike  the  bar  at  one  end  while  the  ear  of  the  observer  is  held  close  to 
the  bar  at  a  considerable  distance  from  the  point  struck.  Two  sounds 
will  reach  the  ear  in  succession ;  the  first  being  transmitted  through  the 
iron  and  the  second  through  the  air.  This  efTcct  was  obtained  by  M. 
Biot,  in  his  experiments  on  the  iron  water  pipes  in  Paris. 

'The  transmission  of  sound  through  a  solid  depends  on  the  manner 
in  which  the  molecules  of  the  solid  are  arranged.  If  the  body  be 
homogeneous  and  without  structure,  sound  is  transmitted  through  it 
equally  well  in  all  directions.  But  this  is  not  the  case  when  the  body, 
whether  inorganic  like  a  crystal  or  organic  like  a  tree,  possesses  a 
definite  structure.  This  is  also  true  of  other  things  than  sound.  Sub- 
jecting, for  example,  a  sphere  of  wood  to  the  action  of  a  magnet,  it  is 
not  equally  affected  in  all  directions.  It  is  repelled  by  the  pole  of  the 
magnet,  but  it  is  most  strongly  repelled  when  the  force  acts  along  the 
fibre.  Heat  also  is  conducted  with  different  facilities  in  different 
directions  through  wood.  It  is  most  freely  conducted  along  the  fibre> 
and  it  passes  more  freely  across  the  ligneous  layers  than  along  them. 
Wood,  then,  possesses  //tree  unequal  axes  of  calorific  conduction. 

*  When  the  tuning  fork  is  first  excited  the  sound  issues  from  it  with 
maximum  loudness,  becoming  gradually  feebler  as  the  fork  continues  to 


WHISPERINGS    OF    AN    ULI)    PINE  2^^ 

vibrate.  A  person  close  to  the  fork  can  notice  ai  the  same  time  thai 
the  amplituile,  or  space  ihrough  which  the  prongs  oscillate,  becomes 
gradually  less  and  less.  But  the  most  expert  ear  in  this  assembly  can 
detect  no  change  in  the  pitch  of  the  note.  The  lowering  of  the 
intensity  of  a  note  does  not  therefore  imply  the  lowering  of  its  pitch. 
In  fact,  though  the  amplilnde  changes,  the  rate  of  vibration  remains  the 
same.  Pitch  and  intensity  must  therefore  be  held  distinctly  apart  j  the 
latter  depends  solely  upon  the  amplitude,  the  former  solely  upon  the 
rapidity  of  vibration, 

'When  two.  notes  from  two  distinct  sources  are  of  the  same  pitch, 
their  rates  of  vibration  are  the  same.  If,  for  example,  a  string  yield  the 
same  note  as  a  tuning  fork,  it  is  because  they  vibrate  with  the  same 
rapidity ;  and  if  a  fork  yield  the  same  note  as  the  pipe  of  an  organ  or 
the  tongue  of  a  concertina,  it  is  because  the  vibrations  of  the  fork  in  the 
one  case  are  executed  in  precisely  the  same  time  as  the  vibrations  of 
the  cohnnn  of  air,  or  of  the  tongue,  in  the  other.  The  same  holds  good 
for  the  human  voice.  If  a  string  and  a  voice  yield  the  same  note,  it  is 
because  the  vocal  chords  of  the  singer  vibrate  in  the  same  time  as  the 
string  vibrates. 


'Opening  the  innermost  and  outermost  series  of  the  orifices  of  our 
siren,  ajid  sounding  both  of  them,  either  together  or  in  succession,  the 
musical  ears  present  at  once  detect  the  relationship  of  the  two  sounds. 
*rhey  notice  immediately  that  the  sound  which  issues  from  the  circle  of 
sixteen  orifices  is  the  octave  of  that  w^hicji  issues  from  the  circle  of 
eight.  In  this  way  we  prove  that  the  physical  meaning  of  the  term 
"octave"  is,  that  it  is  a  note  produced  by  double  the  numljcr  of 
vibrations  of  its  fundamental  By  multiplying  the  vibrations  of  the 
octave  by  two,  we  obtain  t'/s  octave,  and  by  a  continued  m ill li plica- 
tion of  this  kind  we  obtain  a  series  of  numbers  answering  to  a  series  of 


284  ELLEN   OR   THE 

octaves.  Starting,  for  example,  from  a  fundamental  note  of  100  vibra- 
tions, we  should  find,  by  this  continual  multiplication,  that  a  note  five 
octaves  above  it  would  be  produced  by  3,200  vibrations. 

*The  ear's  range  of  hearing  is  limited  in  both  directions.  Savart 
fixed  the  lower  limit  at  eight  complete  vibrations  a  second;  and  to 
cause  these  slowly  recurring  vibrations  to  link  themselves  together,  he 
was  obliged  to  employ  shocks  of  great  power.  By  means  of  a  toothed 
wheel  and  an  associated  counter,  he  fixed  the  upper  limit  of  hearing  at 
24,000  vibrations  a  second.  Helmholtz  has  recently  fixed  the  lower 
limit  at  sixteen  vibrations,  and  the  higher  at  38,000  vibrations  a  second. 
By  employing  very  small  tuning  forks,  the  late  M.  Depretz  showed  that 
a  sound  corresponding  to  38,000  vibrations  is  audible.  Starting  from 
the  note  16,  and  multiplying  by  2,  or  more  compendiously  raising  2  to 
the  nth  ix)wer,  and  multiplying  this  by  16,  we  should  find  that  at  ii 
octaves  above  the  fundamental  note  the  number  of  vibrations  would  be 
32,768.  Taking,  therefore,  the  limits  assigned  by  Helmholtz,  the  entire 
range  of  the  human  ear  embraces  about  eleven  octaves.  But  all  the 
notes  com[)rised  within  these  limits  cannot  be  em])]oyed  in  music.  The 
practical  range  of  musical  sounds  is  comprised  between  40  and  4,000 
vibrations  a  second,  which  amounts,  in  round  numbers,  to  seven 
octaves.' 

•Tt  will  be  seen  from  Mr.  Tyndall's  statements,  that  sound 
is  conducted  in  wood  very  similarly  to  electricity. 

"This  statement  that  the  intensity  depends  solely  upon  the 
amplitude  of  a  hypothetical  wave  is  not  correct.  Mr.  Ganot 
says: 

'Many  causes  modify  the  force  or  the  intensity  of  sound.  'J'hese  are 
the  distanc  e  of  the  sounding  body,  the  am])litude  of  the  vibrations,  the 
density  of  the  air   at   the    place   where   the  sound   is   produced,   the 


\VHISI'EKIX(;S    OF   AN    OLD    PINE 


585 


direction  of  the  currents  of  air,  and,  lastly,  the  neighborhood  of  other 
sounding  bodies.' 

'*But  all  the  other  statements  are  both  interesting  and 
instructive.  Indeed,  outside  of  the  wonderfully  silly  mistake 
as  to  airwaves  and  a  failure  to  perceive  that  sound  like  any- 
thing else  must  be  an  entity,  the  scientists  have  done  much 
good  work  in  elucidating  and  explaining  sound. 

"Ellen  will  introduce  here  the  following  quotation  from  the 
*Philosophjca]  Magazine/  vol.  6,  page  245,  concerning  the 
intensity  and  propagation  of  sound  in  gases  and  other  bodies: 

*  Perolle  has  made  experiments  on  the  intensity  of  sound  in  different 
gases,  which  seem  to  give  a  result  contrary  to  those  of  Priestley, 
Chladni,  and  Jacquin  jun,  Maunoir  and  Paul,  of  Geneva,  having 
inspired  hydrogen  gas  without  being  incommoded  by  it,  were  much 
surprised,  when  they  attempted  to  speak,  to  find  that  their  voices  had 
become  tihrill  and  squeaking. 

M*erolle  has  given  experiments  also  respecting  the  propagation  of 
sound,  by  which  he  shows  that  arr  is  not  the  best  medium  for  conveying 
it.  He  stopped  his  ears  with  bits  of  chewed  paper,  and,  having  applied 
his  watch  to  them,  could  not  hear  the  noise  of  its  heating.  He 
removed  the  watch,  and  placed  it  in  contact  with  a  small  cyliudrk 
piece  of  wood,  the  other  extremity  of  which  touched  one  of  those 
external  parts  of  the  head  that  propagate  sound  ;  such,  for  example,  as 
the  cartibginonsi  parts  of  the  ear;  and  he  then  heard  the  beating  of  the 
watch. 

*  He  suspended  the  watch  in  the  middle  of  a  glass  jar,  and  found 
that  the  sound  reached  him  ;  but  having  filled  the  jar  with  water,  the 
sound  was  much  stronger.     The  joints  of  the  watch   had  been  luted. 

He  placed  the  watch  on  different  bodies,  such  as  wood,  a  marble  table 
etc.,  and  found  that  the  latter  transmitted  the  sound  faintly,  while  the 


286  ELLEN   OR  THE 

former  transmitted  it  with  greater  or  less  force.  He  thence  concludes 
that  the  sound  of  musical  instruments,  such  as  violins,  harps,  harpsi- 
chords, etc.,  depends  on  the  property  which  wood  has  of  transmitting 
sounds ;  and  that  houses  built  of  marble  or  stone  are  less  sonorous, 
because  these  bodies  are  worse  conductors  of  sound.* 

**In  'Nicholson's  Journal,'  vol.  2  (1805),  the  following  state- 
ment is  made  by  M.  Hassenfratz  in  regard  to  the  propagation 
of  sound : 

*  By  the  side  of  the  high  road  that  leads  from  the  Place  de  la  Con- 
corde to  Chaillot  along  the  bank  of  the  Seine,  on  the  stone  wharf  of  St. 
Leir,  opposite  the  steam  engine  of  Gras-Caillon,  is  placed  a  railing  210 
paces  in  length,  formed  of  31  pieces  of  timber  separated  by  four  large 
IX)sts.  The  blow  of  a  hammer  at  one  extremity  of  this  railing  was 
heard  distinctly  at  the  other,  though  through  the  air  it  was  audible  only 
1 20  paces.  At  the  distance  at  which  both  the  sounds  were  audible, 
that  through  the  w^ood  was  heard  long  before  the  other ;  and  when 
standing  at  the  greatest  distance  from  the  place  of  the  blow,  I  heard 
the  sound  transmitted  through  the  timber,  the  velocity  of  its  transmis- 
sion was  so  great  that  it  was  ditBcuIt  to  distinguish  any  interval 
between  the  perception  of  the  sound  by  the  ear  and  the  motion  of  the 
hammer  by  the  eye.'  " 

"But  what  docs  it  all  mean.  Kllcn,"  I  asked,  "that  an 
increased  number  of  vibrations  varies  the  pitch?  The  old  Pine 
would  suppose  that  if  vibration  makes  sound,  more  vibrations 
would  make  more  sound." 

"And  so  it  would,"  she  answered,  "and  that  it  docs  not 
shows  that  it  docs  not  make  sound.  It  can  no  more  make 
sound  than  the  saw  can  the  lumber  whose  shape  it  defines. 
But  there  arc  different  kinds  of  sound,  just  as  there  are  of  other 


WHISPERINC^S    or   AN    uLh    I'lNE 


287 


"things.  Thus  vvc  have  not  only  the  different  kinds  of  trees 
or  plants  which  are  made  at  different  mills;  but  also  the 
different  species  of  the  same  genus  made  at  the  same  mills. 
That  is,  the  mills  are  similar,  with  the  machinery  slightly 
changed,  by  which  different  kinds  of  the  same  tiling  are  pro- 
duced. This,  too,  is  one  of  nature's  fundamental  and  universal 
laws.  And  so  there  is  an  infinite  variety  of  sounds,  to  make 
which  there  has  to  be  the  machinery.  And  this  machinery 
consists,  in  part  certainly  and  perhaps  entirely,  in  the  vibration 
of  elastic  bodies. 

"Ami  thus  bv  appropriate  machinery  nature  makes  all 
things;  and  Hllen  thinks  it  is  a  most  marvelously  complete  and 
excellent  system.  The  law  governing  it  ts  precisely  the  same  in 
the  things  made  by  man.  There  isn't  the  slightest  difference^ 
nor  is  there  anywhere  in  the  great  laws  of  nature.  Their 
operation  is  continuous  and  universal,  and  dips  down  into  the 
domain  of  man  as  gracefully  and  as  easily  as  a  fwan  rides  upon 
the  waves,  h^llen  has  referred  to  this  before.  Thus  a  chair 
factory,  by  adding  a  little  machinery,  makes  different  kinds  of 
chairs,  and  piano  factories  different  pianos.  By  these  we  can 
see  exactly  the  principle  that  works  and  how  it  works. 

**Thus  nature  does  with  sounds.  And  so  she  does  with  the 
pattering  rain  drops,  for  they  are  of  very  different  sizes  and 
character,  though  they  are  all  rain-drops.  Sometimes  they  are 
awfully  big  and  sometimes  they  are  awfully  small,  little  bits  of 
tiny  ones,  so  fine  that  they  almost  frighten  Ellen,  for  they  get 
all  over  her  clothes  and  into  her  hair.  And  it's  just  the  same 
with  the  snow.  The  flakes  are  of  many  sizes  and  descriptions. 
There  is  the   snow  sifted  by  the  wind,  caught  in  its  embrace 


•  r 

s 


r-i-   TJ 


:_--     -1-=.     jv: 


w-1 


•^TiiruT:*? 


288  ELLEN   OR  THE 

and  whirled  over  the  drifts ;  and  then  there  are  the  great  white 
snow-flakes  that  balance  themselves  so  daintily,  and  act  as  if 
they  were  sure  that  they  were  the  most  graceful  thing  in 
existence." 

"But  they  are  not,"  I  said;  **in  gracefulness  and  in  beauty 
Ellen  will  give  them  points  and  beat  them  all ;  for  her  step  is 
as  light  as  the  zephyrs  that  caress  her  feet,  nor  is  the  dawn  ol 
the  morning  more  beautiful." 

**The  old  Pine  is  always  flattering  Ellen,"  she  answered,  "as 
the  sunlight  flatters  the  hillside.  And  Ellen  has  to  get  along 
the  best  she  can  with  all  this  flattery.  But  the  old  Pine  will 
see  that  sounds  are  varied,  as  all  things  else,  by  addition 
or  changes  in  the  machinery  that  makes  them.  And  none  of 
them  or  anything  else  is  ever  made  without  machinery,  though 
often  the  machinery  is  very  simple." 

"  But  often,"  I  said,  "  the  different  kinds  of  things  come  from 
different  materials  used,  do  they  not,  Ellen?" 

"Yes,"  she  said.  "These  are  the  two  great  laws  by  which 
things  may  be  varied  —  a  change  in  the  machinery  that  makes 
them,  or  in  the  material  of  which  they  arc  made.  The  two  laws 
are  universal,  and,  as  Ellen  thinks,  apply  to  all  things.  And 
thus  the  pitch  of  sounds  is  altered  by  an  increase  in  the  number 
of  vibrations.  But  the  quantity,  which  represents  the  intensity, 
follows  the  universal  law.  If  there  are  several  sources  of 
sound,  there  is  more  sound;  and  the  whole  amount  is  always 
exactly  the  sum  of  the  different  amounts  produced.  It  also 
diminishes  with  the  wear  that  comes  from  time." 

**But,  Ellen,"  I  said,  "the  text  books  and  scientists  are  con- 
stantly speaking  of  pitch  being  due  to  the  number  of  vibrations 


1 

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THF  HEW  YORK 
PUBLIC  LIBRARY  1 

Abroa.  LtH9A  AH* 
9^                             t 

^ 

WHISPERTNGS    OF  AN   OLD    PINE 


291 


tn  a   second.     Is  it    necessary  that  a    body  should    vibrate  a 
second  in  order  to  be  heard?  *' 

*'  Ellen  thinks  not,**  she  answered  ;  '*  sound  should  be  thrown 
off  by  the  first  vibration,  though  it  is  quite  possible  there  might 
not  be  enough  for  us  to  hear.  For»  as  Ellen  has  before  said, 
we  hear  by  an  aggregate  of  sound,  just  as  we  see  by  an  aggre- 
gate of  light.  *' 

***Then  Ellen  thinks  vibration  shapes  and  throws  off  sound?" 

**  Ellen  thinks  this/'  she  answered,  *' that  the  sounds  of  the 
world  are  made  by  the  elastic  bodies  of  the  world,  the  process 
being  first,  shock  or  disturbance  of  an  elastic  body,  which  creates 
sound;  that  this  sound  consists  of  electrical  matter;  that  all 
elastic  bodies  are  so  constituted  that  this  matter  which  has  a 
power  of  motion  will  circulate  in,  or  through  them,  thus  pro- 
ducmg  vibration  of  the  body,  the  nature  of  which  depends 
upon  its  construction.  The  pitch  of  the  sound  at  least  is 
determined  by  the  vibration.  The  sounds  are  then  thrown  off 
by  the  sounding  body,  generally  into  the  air»  whence  they  enter 
animal  bodies  by  the  different  way.,  provided  for  this  purpose 
and  form  a  system  of  signals  that  convey  information  to  the  in- 
telligence dwelling  in  such  body  whether  that  of  man  or  beast. 

"  Sound  is  endowed  in  some  way  with  a  principle  of  move- 
ment. Thus  water  is  endowed  by  gravitation,  but  the  action  of 
this  force  is  only  in  one  direction,  whilst  sound  goes  with  equal 
facility  in  all  directions;  as  do  also  light  or  electricity.  They 
are  therefore  not  under  the  control  of  gravitation. 

*'  Rain  is  another  thing  that  moves,  carried  in  the  clouds, 
and  these  are  borne  by  the  air  whose  motion  is  the  result  of 
elastic  force.     Nor.  if  the  speed  of  sound  is  due  to  the  elastic 


292  ELLEN   OR  THE 

force  of  the  air,  is  there  any  possible  reason  for  sound  going 
faster  than  clouds;  and  therefore  the  speed  of  sound  is  not  due 
to  the  elastic  force  of  the  air.  The  assertion  that  the  velocity 
of  sound  is  due  to  the  elastic  force  of  the  air,  when  it  is  per- 
fectly evident  that  it  is  not.  is  one  of  the  many  inexplicable 
features  of  this  theory,  which  at  all  points  reminds  one  of  the 
remarkable  experiences  of  Baron  Munchausen: 

*  The  only  circumstance/  says  the  Baron,  '  which  happened  on  our 
voyage  worth  relating  was  the  wonderful  effects  of  a  storm,  which  had 
torn  up  by  the  roots  a  great  number  of  trees  of  enormous  bulk  and 
height,  in  an  island  where  we  lay  at  anchor  to  take  in  wood  and  water; 
some  of  these  trees  weighed  many  tons,  yet  they  were  carried  by  the 
wind  so  amazingly  high  that  they  appeared  like  the  feathers  of  small 
birds  floating  in  the  air,  for  they  were  at  least  five  miles  above  the  earth  ; 
however,  as  soon  as  the  storm  subsided  they  all  fell  perpendicularly  into 
their  respective  places,  and  took  root  again,  except  the  largest,  which 
happened,  when  it  was  blown  into  the  air,  to  have  a  man  and  his  wife,  a 
very  honest  old  couple,  upon  its  branches,  gathering  cucumbers  (  in 
this  part  of  the  globe  that  useful  vegetable  grows  upon  trees )  :  the 
weight  of  this  couple,  as  the  tree  descended,  overbalanced  the  trunk, 
and  brought  it  down  in  a  horizontal  position  :  it  fell  upon  the  chief 
man  of  the  island,  and  killed  him  on  the  spot.' 

"Sound  spreads  in  all  directions,  so  that  as  Lord  Bacon  ex- 
pressed it,  it  is  in  every  part  of  the  air,  as  well  as  in  all  the  air. 
That  it  should  thus  spread  is  most  natural  because  it  can  then 
better  perform  the  purposes  for  which  it  exists.  Thus  mist  or 
fog  may  be  in  every  part  of  the  air,  as  well  as  in  all  the  air. 

"Sound  is  produced  in  elastic  bodies  and  may  be  conducted 
from  them   by   other   bodies   which  arc    in    contact,   the  chief 


WHISPERINGS   OF  AN   OLD    PINE  293 

of  which.  SO  far  as  man  is  interested,  is  air.  But  sound 
may  also  be  conducted  from  the  producing  bodies  to 
solid  bodies  whose  action  can  be  partially  observed.  Thus» 
if  the  handle  of  a  tuning  fork  is  placed  against  a  wooden 
rod  the  sound  may  be  conveyed  through  the  rod  to  the  brain, 
and  we  can  feel  the  tremor  of  the  rod  as  the  sound  goes 
through  it  This  tremor  appears  to  be  precisely  the  same 
as  that  which  occurs  in  a  sounding  board,  and  presumably 
sound  is  conducted  through  the  air,  or  other  gas,  in  similar 
manner.  This  tremor  in  the  sounding  board  or  rod  is  gener- 
ally called  a  vibration,  but  Ellen  notices  it  is  very  different 
from  the  vibration  of  the  prongs  of  the  tuning  fork  or  any 
body  that  is  in  what  is  called  normal  vibration.  Try  it ;  take 
a  tuning  fork,  vibrate  it,  and  hold  the  stem  on  a  table;  then, 
with  the  same  fork,  strike  the  table  and  thus  throw  it  into  normal 
vibration*  The  difference  in  the  action  of  the  table  is  as  wide 
as  that  between  noonday  and  darkness,  and  it  would  be  impos- 
sible to  suppose  that  the  two  results  were  produced  by  the 
same  conditions.  In  a  fork  and  string  the  vibrations  are 
reciprocal  and  very  nearly  equal,  like  those  of  an  oscillating 
pendulum.  And,  as  Ellen  thinks,  this  is  the  case  with  all 
bodies  in  normal  vibration.  But  when  sound  is  constantly 
advancing  it  is  very  ccrum  tliat  it  docs  not  vibrate  to  and 
fro." 

*'And  how,**  I  asked,  '*  is  sound  so  much  increased  by  sound- 
ing boards,  as  that  of  the  tuning  fork  by  the  table?  " 

*'The  whole  subject  of  the  machinery  for  the  production  of 
sound,  and  its  manner  of  operation.  Ellen  will  discuss  in  connec- 
tion   with    the    telephone    and    graphophone.     It   is    certain 


294  ELLEN   OR  THE 

that  the  sound  ceases  when  the  original  vibrating  body 
ceases  to  vibrate.  It  is  certain,  too,  that  the  prongs  of  a  tuning 
fork  stop  vibrating  more  quickly  when  the  stem  of  the  fork 
comes  in  contact  with  a  solid  body.  And  experiment 
shows  that  the  fork  ceases  to  vibrate  sooner  when  the  stem 
is  placed  upon  wood  than  when  it  is  placed  upon  stone, 
suggesting  that  the  result  does  not  come  from  resistance,  but, 
as  will  be  shown  later,  from  the  conducting  power  of  the  body 
on  which  it  is  placed." 

"And  what  is  the  cause  of  sympathetic  vibration?" 
"  The  character  of  the  shores  and  bed  of  the  channels  through 
which  sound  passes.  Ellen  will  make  this  very  plain  later. 
Thus  usually  a  stream  of  water  flows  in  straight  course,  but 
entering  such  a  conformation  as  produces  an  eddy,  a  part  of  the 
water  moves  in  a  circle,  whilst  a  part  continues  in  its  course. 
And  thus  streams  of  sound  usually  flow  in  straight  lines,  but 
entering  certain  bodies  whose  bed  and  shores  are  similar  to  those 
of  the  body  by  whose  vibration  the  sound  is  made,  a  part  of  the 
sound  is  reflected  back  and  forth,  thus  causing  what  is  called 
sympathetic  vibration.  Fluids  act  that  way  just  as  dogs  bark 
and  bite,  because  it's  their  nature  to.  And  they  never  consult 
scientists.  They  don't  care  anything  about  scientists.  Awfully 
funny  things,  fluids  are.  They  arc  not  a  bit  polite;  just  as 
soon  run  over  Ellen's  feet  as  anywhere  else.  And  the  fluid  of 
electricity  is  as  wavering  in  its  course  as  the  roots  of  a  tree, 
moving  where  there's  the  least  resistance; — thus  the  lightning. 
And  all  fluids  do  the  same  thing;  for  that  is  the  way  they 
are  made. 

'*  Surely  the  old  Pine  doesn't  suppose  that  either  eddies  or 


WtllSPEHINGS   OF   AN   OLD    PINE 


295 


sympathetic  vibration  take  place  without  cause,  does  he, 
or  that  the  cause  has  something  to  do  with  the  rings  of  Saturn, 
or  the  hiding  of  Moses  in  the  bulrushes?  Or  does  he  think 
with  the  scientists  that  the  cause  is  the  hitting  of  these  bodies 
by  air  waves  that  never  had  existence,  or»  if  they  did  exist» 
would  be  entirely  unable  to  make  such  bodies  vibrate?" 

**0h*  no/*  1  said;  *' the  old  Pine  knows  that  nothing  takes 
place  without  a  cause,  and  that  all  causes  must  be  sufficient 
and  closely  connected  with  their  phenomena.  And  he  sees 
that  the  cause  of  an  eddy  is  the  nature  of  its  bed  and  shores. 
And  he  sees,  too,  that  the  cause  of  sympathetic  vibration  must 
be,  as  Ellen  says,  in  the  nature  of  the  channels  of  the  body  in 
which  it  takes  place." 

"Sensible  old  Pine,"  she  said*  '*In  a  somewhat  similar 
manner  the  flowing  of  streams  In^  pools  or  basins  of  lower 
level  is  explained.  And  thus  electricity  flows  from  a  higher 
to  a  lower  potential ;  nor  docs  Ellen  see  why  such  a  feature 
with  streams  of  sound  need  be  more  remarkable  than  the 
similar  action  of  other  streams. 

**For  within  certain  limits  sound,  like  light  or  heat  or  elec- 
tricity, is  distributed  evenly  through  the  atmosphere  and  all 
bodies  conducting  it*  Nor  is  it  controlled  by  the  laws  of 
gravitation.  And  this  is  one  of  the  remarkable  things  con- 
nected with  that  division  of  matter  which  we  arc  now  con- 
sidering, that  it  appears  to  be  outside  of  the  action  of 
gravitation*  Nor  can  Ellen  see  anything  remarkable  in  this; 
for  gravitation,  in  whatever  it  consists,  exists  for  certain 
purposes.  Nor  is  there  any  reason  to  suppose  that  its  action 
extends  beyond  these  purposes.     But  Ellen  does  not  think  at 


296  ELLEN   OR  THE 

all  that  the  laws  of  the  universe  are  coincident  with  those  of 
gravitation.  For  gravitation,  as  Ellen  thinks,  is  but  the  flowing 
of  streams  of  subtle  matter,  whose  function  is  to  hold  in  their 
places  certain  other  portions  of  matter,  which,  especially,  include 
the  heavenly  spheres,  and  all  material  things  perceivable  by  us. 
It  is  ponderable  bodies,  and  those  only,  which  come  under 
the  influence  of  gravitation.  They  include  all  those  things 
which  are  most  intimately  known  to  us,  but,  as  Ellen  thinks, 
they  include  a  very  small  part  of  the  immensity  of  the 
universe.  For  it  is  not  reasonable  to  think  that  more  than  a 
small  part  should  be  revealed  to  an  understanding  hampered 
as  ours  is,  and  limited  to  a  duration  so  brief. 

"Ellen  now  approaches  a  chapter  in  Mr.  Tyndall's  book  that 
for  ways  that  are  dark  and  tricks  that  are  vain  is  peculiar.  It 
is  the  chapter  on  resonance,  the  principal  statement  in  which 
is  essentially  false,  and,  as  would  appear,  intentionally  mis- 
leading.    Ellen  will  quote : 

*The  series  of  timing  forks  now  before  you  have  had  their  rates  of 
vibration  determined  by  the  siren.  One,  you  will  remember,  vibrates 
256  times  in  a  second,  the  length  of  its  sonorous  wave  being  four  feet 
four  inches.  It  is  detached  from  its  case,  so  that  when  struck  against 
a  pad  you  hardly  hear  it.  When  held  over  this  glass  jar,  a  u,  fig.  14, 
18  inches  deep,  you  still  fail  to  hear  the  sound  of  the  fork.  Preserving 
the  fork  in  its  position,  I  pour  water  with  the  least  possible  noise  into 
the  jar.  The  column  of  air  underneath  the  fork  shortens,  the  sound 
augments  in  intensity,  and  when  the  water  has  reached  a  certain  level 
it  bursts  forth  with  extraordinary  power.  A  greater  quantity  of  water 
causes  the  soimd  to  sink,  and  become  finally  inaudible,  as  at  first.  By 
pouring  the  water  carefully  out  a  point  is  reached  where  the  reenforce- 
ment  of  the  sound  again  occurs.     Experimenting  thus,  we  learn  that 


WH1S!'ERINGS   OF   AX   OIJ)    PINE 


297 


there  is  one  particular  length  of  the  column  of  air  which,  when  the  fork 
h  placed  above  it,  produces  a  maximum  augmentation  of  the  sound* 
This  reenforcement  of  the  sound  is  named  resonance. 

'Ofierating  in  the  same  way  with  ail  the  forks  in  succession,  a  column 
of  air  is  found  for  each,  which  yields  a  maximum  resonance.  These 
columns  become  shorter  as  the  rapidity  of  vibration  increases. 

'What  is  the  physical  meaning  of  this  very  wonderful  effect?  To 
!4olve  this  question  we  must  revive  our  knowledge  of  the  relation  of  the 
motion  of  the  fork  itself  to  the  motion  *'f  the  sonorous  wave  produced 


Kig.  14. 

by  ihe  fork.  Supposing  a  prong  of  this  fork,  which  executes  256  vibra- 
tions in  a  second,  to  vibrate  between  the  points  a  and  A,  fig.  15,  in  its 
motion  from  r^  to  ^  the  fork  generates  half  a  sonorous  wave,  and  as  the 
length  of  the  whole  wave  emitted  by  this  fork  is  four  feet  four  inches, 
at  the  moment  the  prong  reaches  ^  the  foremost  point  of  the  sonorous 
wave  will  be  at  c,  two  feet  two  inches  distant  from  the  fork.     The 


298  ELLEN   OR   THE 

motion  of  the  wave,  then,  is  vastly  greater  than  that  of  the  fork.  In 
fact,  the  distance  a  b  is,  in  this  case,  not  more  than  one-twentieth  of  an 
inch,  while  the  wave  has  passed  over  a  distance  of  twenty-six  inches. 
With  forks  of  lower  pitch  the  difference  would  be  still  greater. 

*  Our  next  question  is,  what  is  the  length  of  the  column  of  air  which 
resounds  to  this  fork  ?  By  measurement  with  a  two-foot  rule  it  is  found 
to  be  thirteen  inches.  But  the  length  of  the  wave  emitted  by  the  fork 
is  fifty- two  inches ;  hence  the  length  of  the  column  of  air  which 
resounds  to  the  fork  is  equal  to  one-fourth  of  the  length  of  the  sound 
wave  produced  by  the  fork.  This  rule  is  general,  and  might  be  illus- 
trated by  any  other  of  the  forks  instead  of  this  one. 

'  Reflecting  on  what  we  have  now  learned,  you  would  have  little  diffi- 
culty in  solving  the  following  beautiful  problem  :  You  are  provided  with 
a  B 


-ze  inches >c 


V 


Fig.  15. 
a  tuning  fork  and  a  siren,  and  are  required  by  means  of  these  two 
instruments  to  determine  the  velocity  of  sound  in  air.  1\)  solve  this 
jnoblem  you  lack,  if  anything,  the  mere  power  o{  manipulation  which 
practice  imparts.  You  would  first  determine,  by  means  of  tlie  siren» 
the  number  of  vibrations  executed  by  the  tuning  fork  in  a  second  ;  you 
would  then  determine  the  length  of  the  column  of  air  which  resounds 
to  the  fork.  This  length  multiplied  by  four  would  give  you,  approxi- 
mately, the  wave  length  of  the  fork,  and  the  wave  length  multiplied  by 
the  number  of  vibrations  in  a  second  would  give  you  the  velocity  in  a 
second.     Without  quitting  your  private  room,  therefore,  you  could  solve 


WHISPERINGS    OF   AN    OLD    PINE 


299 


this  important  problem.     We  will  go  on,  if  you  please,  in  this  fashion, 
making  our  footing  sure  as  we  advance/ 

** These  conclusions  are  entirely  false»  because  they  teach  that 
resonance  is  due  to  a  certain  length  of  jar.  and  that  this  length 
is  proportional  to  that  of  the  hypothetical  air  waves,  and  for 
a  perfect  result  is  exactly  one-quarter  of  their  length;  the  truth 
being,  as  is  self-evident,  that  the}-  hav^e  no  relation  whatever, 
not  the  slightest,  with  the  supposed  lengtli  of  these  hypo- 
thetical air  waves. 

**The  effect  of  resonance  does  not  necessarily  depend  upon 
the  height  of   the   jar  above  which  the  fork   is   sounded.     It 


depends  upon  the  general  shape  of  the  jar.  With  a  fork  of 
256  vibrations  Ellen  obtained  the  greatest  resonance  from  a 
glass  pitcher  with  handsome  swelling  form  of  eight  and  one- 
half  inches  in  height,  (fig.  16)  ;  the  next  best  resonance  was 
from  a  pitcher  of  different  shape  and  somewhat  lower.  Good 
results  were  got  all  the  way  from  one-half  inch  to  nineteen 
inches  from  the  same  tin  tube.  With  a  regulation  cylinder 
(of    brass)    having    a    diameter    of    two    and    seven-eighths 


300  ELLEN   OR   THE 

inches  and  eighteen  inches  long,  furnished  by  instrument 
makers,  the  greatest  reinforcement  was  at  twelve  inches 
instead  of  the  theoretical  height  of  thirteen  inches.  Prob- 
ably a  cylinder  could  be  made  that  would  fit  the  theory, 
but  this  would  mean  that  the  resonance  jar  might  be  of  any 
height.  It  follows  as  regards  the  speed  of  sound  in  different 
bodies,  that  the  estimates  depending  upon  the  supposition  that 
the  best  effects  of  resonance  come  from  a  jar  one  quarter  of 
the  length  of  these  hypothetical  air  waves  are  wholly  worthless. 

"The  word  resonance  as  applied  to  sound  has  two  mean- 
ings. It  may  come  from  the  reflection  of  sounds  as  in  rooms, 
or,  as  in  these  experiments,  it  may  be  the  result  of  an  increased 
amount  of  vibration.  It  is  the  air  that  vibrates  in  jars,  and  it  is 
essential  that  the  jar  should  be  of  such  shape  that  the*  air  within 
it  may  vibrate  synchronously  with  the  sounding  body.  Ellen's 
experiments  proved  that  the  air  in  jars  of  very  different  shapes 
would  thus  vibrate,  and  that  the  greatest  resonance  is  obtained, 
not  from  any  particular  length,  but  from  certain  conformations. 

"In  the  last  chapter  Mr.  Tyndall  refers  to  what  is  called 
interference  of  sound,  or  the  supposed  coincidence  of  air  waves. 
It  is  stated  that  sound  is  thus  increased  in  intensity  or 
destroyed;  and  that  always  similar  instruments  of  the  same 
pitch,  if  placed  a  wave's  length  apart,  will  reinforce,  and,  if  half 
a  wave  length,  will  destroy  sound. 

"These  statements  are  not  true;  but  when  a  vibrating 
tuning  fork,  held  near  the  ear  or  near  a  resounding  vessel,  is 
turned  around,  a  marked  difference  in  the  sound  takes  place. 
It  is  also  in  evidence  that  the  diminution  of  sound  connects 
with   the  vibration  of  the   two   prongs.     For  if  something  is 


WiilSPEKlNGS    OF  AN   OLD    PINE 


30t 


placed  bctw^een  the  prongs  of  the  fork,  the  sound  is  immediately 
increased. 

•*The  two  iUustrations  given  are  of  sound  acting  in  two  very 
different  positions.  For  entering  the  ear  it  finds  its  way  to 
the  auditory  nen^c  and  is  so  conveyed  to  the  soul ;  but  enter- 
ing the  resonant  vessel  it  causes  the  air  within  this  vessel  to 
vibrate  synchronously  with  the  sounding  body,  and  so  to  pro- 
duce more  sound.  But  in  this  they  are  alike,  that  in  each  case 
it  is  a  question  of  sound  entering  or  not  entering  the  ear  or 
resounding  vessel/* 

"And  what  is  the  explanation  of  the  diminution  m  sound, 
Ellen?*'  I  asked. 

**This  is  owing  to  the  fork  being  inclined  differently  to  the 
opening  of  the  ear.  Of  course  the  corners  could  throw  off 
but  comparatively  little  sound,  and  of  course,  too,  the  most 
sound  enters  the  car  when  the  flat  part  of  the  fork  is  towards 
its  opening,  thus  throwing  the  sound  directly  into  the  car. 
When  something  is  placed  bet%veen  the  prongs,  the  sound  is 
immediately  increased,  evidently  because  the  paper  guides  the 
sound  thrown  off  by  the  fork  towards  and  into  the  ear. 

"This  is  the  favorite  experiment  used  to  illustrate  so-called 
wave  interference,  although  there  is  no  separation  by  a  half 
wave  or  a  whole  wave,  but,  instead,  by  a  distance  varying  with 
different  forks  and  generally  quite  small  As  every  one  can 
sec,  it  is  completely  and  far  mdre  accurately  explained  by  the 
corpuscular  theory. 


302  ELLEN   OR    THE 


XIX. 


^^DUT,  Ellen,"  I  said,  "do  not  some  scientists  claim  that 
*--^     the  velocity  of  sound  constantly  varies  ?  '* 
"The  different  experiments  to  test  the  velocity  of   sound," 
she  answered,  **  which  Ellen  has  been  able  to  find,  are  as  fol- 
lows.    Ganot  says : 

'Since  the  propagation  of  sound  waves  is  gradual,  sound  requires  a 
certain  time  for  its  transmission  from  one  place  to  another,  as  is  seen 
in  numerous  phenomena.  For  example,  the  sound  of  thunder  is  only 
heard  some  time  after  the  flash  of  lightning  has  been  seen,  although 
both  the  sound  and  the  light  are  produced  simultaneously ;  and  in  like 
manner  we  see  a  mason  at  a  distance  in  the  act  of  striking  a  stone 
before  hearing  the  sound. 

'The  velocity  of  sound  in  air  has  often  been  the  subject  of  experi- 
mental determination.  The  most  accurate  of  the  direct  measurements 
was  made  by  Moll  and  Van  Beck  in  1823.  Two  hills,  near  Amsterdam, 
Kooltjesberg  and  Zevenboomen,  were  chosen  as  stations :  their  dis- 
tance from  each  other  as  determined  trigonometrically  was  57,971  feet, 
or  nearly  eleven  miles.  Cannons  were  fired  at  stated  intervals  simul- 
taneously at  each  station,  and  the  time  which  elapsed  between  seeing 
the  flash  and  hearing  the  sound  was  noted  by  chronometers.  This 
time  could  be  taken  as  that  which  the  sound  required  to  travel  between 
the  two  stations ;  for  it  will  be  subsequently  seen  that  light  takes  an 
inappreciable  time  to  traverse  the  above  distance.  Introducing  cor- 
rections for  the  barometric  pressure,  temperature,  and  hygrometric 
state,  and  eliminating  the  influence  of  the  wind,  Moll  and  Van  Beck's 


■ 

THE  (lEW  YORK 
PUBLIC  LIBRARY 

titDKH  rouNeAti#ift 

r^H 

ULD  Vim 


results  as  recalculated  by  Schroder  van  der  Kolk  gave  1,092^78  feet  as 
the  velocity  of  sound  in  one  second  in  dr}'  air  at  o''  C.  and  under  a 
pressure  of  760  mm.  Kendall,  in  a  North  Pole  expedition,  found  that 
the  velocity  of  sound  at  a  temperature  of-40**  was  314  metres,  or  1050  4 
feet.  Stone's  determinations,  made  at  the  Cape  of  Good  Hope  with 
very  great  care,  gave  1090*57  feet,  or  332*4  metres,  as  the  velocity  of 
sound  at  o**, 

'The  velocity  of  sound  at  zero  may  be  taken  at  1,093  fc^*»  or  333 
metres.  This  velocity  increases  with  the  increase  of  temperature  and 
may  be  calculated  for  a  temperature  /°  from  the  formula 

v^  i,o93v'( I +0-0036 65/) 

where  1,093  is  the  velocity  In  feet  at  0°  C,  and  0-003665  the  coefficient 
of  expansion  for  1**  C.  This  amounts  to  an  increase  of  nearly  two  feet 
for  every  degree  Centigrade  For  the  same  temperature  it  ts  inde- 
pendent of  the  density  of  the  air,  and  consequently  of  the  pressure. 
It  is  the  same  for  the  same  temperature  with  all  sounds,  whether  they 
be  strong  or  weak,  deep  or  acute.  Biot  found,  in  his  experiments  on 
the  conductivity  of  sound  in  tubes,  that  when  a  well-known  air  was 
played  on  a  flute  at  one  end  of  a  tube  1,040  yards  long,  it  was  heard 
without  alteration  at  the  other  end,  from  which  he  concluded  that  the 
velocity  of  different  sounds  is  the  same.  For  the  same  reason  the  tune 
played  by  a  band  is  heard  at  a  great  distance  without  alteration,  except 
in  loudness,  which  could  not  be  the  case  if  sounds  differing  in  pitch 
and  intensity  travelled  with  different  velocities. 

'This  cannot,  however,  be  admitted  as  universally  true.  Earnshaw, 
by  a  mathematical  investigation  of  the  laws  of  the  propagation  of  sound, 
concludes  that  the  velocity  of  a  sound  depends  on  its  strength;  and, 
accordingly,  that  a  violent  sound  oufjht  to  be  propagated  with  greater 
velocity  than  a  gentler  one.  This  conclusion  is  confirmed  by  an 
observation  made  by  Captain  Parr>^  on  his  Arctic  expedition.  During 
artillery  practice  it  was  found,  by  persons  stationed  at  a  considerable 


306  ELLEN   OR   THE 

distance  from  the  guns,  that  the  report  of  the  cannon  was  heard  before 
the  command  to  fire  given  by  the  officer.  And,  more  recently,  MaUet 
made  a  series  of  experiments  on  the  velocity  with  which  sound  is  propa- 
gated in  rocks,  by  observing  the  times  which  elapsed  before  blastings, 
made  at  Holyhead,  were  heard  at  a  distance.  He  found  that  the  larger 
the  charge  of  gunpowder,  and  therefore  the  louder  the  report,  the 
more  rapid  was  the  transmission.  With  a  charge  of  2,000  pounds  of 
gunpowder  the  velocity  was  967  feet  in  a  second,  while  with  a  charge 
of  12,000  it  was  1,210  feet  in  the  same  time. 

'Jacques  made  a  series  of  experiments  by  firing  different  weights  of 
powder  from  a  cannon,  and  determining  the  velocity  of  the  report  at 
different  distances  from  the  gun  by  means  of  an  electrical  arrangement. 
He  thus  found  that,  close  to  the  gun,  the  velocity  is  least,  increasing  to 
a  certain  maximum  which  is  considerably  greater  than  the  average 
velocity.  The  velocity  is  also  greater  with  the  heavier  charge.  Thus 
wiih  a  charge  of  ij4  pounds  the  velocity  was  1,187,  ^^^  with  a  charge 
of  J4  pound  it  was  1,032  at  a  distance  of  from  30  to  50  feet;  while  at 
a  distance  of  70  to  §0  it  was  1,267  ^^^  1,120 ;  and  at  90  to  100  feet  it 
was  1,262  and  1,114  respectively. 

'Bravais  and  Martins  found,  in  1844,  that  sound  traveled  with  the 
same  velocity  from  the  base  to  the  summit  of  the  Faulhorn  as  from  the 
summit  to  the  base.' 

"  It  will  be  seen  that  in  this  matter  of  the  speed  of  sound, 
the  scientists  do  not  know  whether  they  are  on  foot  or  horse- 
back.    They  seem  to  be  a  very  ignorant  kind  of  people." 

"Yes,"  I  said,  "some  go  one  road  and  some  go  another,  led 
by  theory  and  experiment." 

"And  ICllcn  notices,"  she  said,  "that  they  don't  lack  long  for 
an  experiment  to  match  a  theory.  So  that,  if  they  can  decide 
what  theory  they  want,  they  will  soon  be  ready  for  the  journey. 


WHISPERINGS    OF    AN    OLD    PINE 


307 


"The  statement  made  by  M,  Ganot  that  *this  cannot  be 
admitted  as  universally  true/  is  unusually  stupid.  It  is  like 
saying  that  water  is  influenced  by  the  action  of  gravity,  but 
that  this  cannot  be  admitted  as  universally  true.  The  mathe- 
matical investig^ation  by  Earnshaw,  showing  that  sounds  of  dif- 
ferent intensity  have  different  velocities,  assumes  Lapface*s 
explanation  of  the  difference  between  theory  and  experiment 
in  the  velocity  of  sound  to  be  correct;  but  in  truth  proves,  as 
must  be  evident  to  an\-  one  with  good  sense,  that  it  is  incorrect. 

'*The  experiments  by  Jacques,  barring  errors,  give  the 
velocity  of  d  pulse.  The  assumption  that  this  is  the  same  as 
that  of  sound  is  another  illustration  of  the  frequent  inability 
of  scientists  to  correctly  interpret  phenomena. 

**The  experiments  of  M.  Jacques  are  thus  described  in  the 
*  American  Journal  of  Science,'  vol.  117: 

*In  the  midst  of  a  large  level  field  was  placed  a  six-]>uund  brass 
field-piece.  In  the  rear  of  this,  at  distances  of  10,  30,  50,  70,  90  and 
110  feet  from  mouth  of  cannon,  were  placed  the  membranes  elevated 
about  5  feet  alwve  the  groimtl.  These  membranes  consisted  of  a  hoop 
c^"  in  diameter  over  which  was  stretched  a  sheet  of  thin  riibben  To 
the  center  of  the  membranes  and  on  the  side  toward  the  cannon  was 
attached  a  very  small  shelf  of  polished  brass.  Upon  this  rested  one 
end  of  a  delicate  steel  spring,  the  other  end  being  fixed  to  an  inde- 
pendent support. 

•The  wire  that  brought  the  current  of  electricity  from  the  chrono- 
graph house  was  connected  with  the  spring,  and  from  the  shelf  a  second 
wire  relumed  to  the  chronograph.  When  the  spring  rested  upon  the 
shelf|  the  circuit  was  closed.  The  passage  of  the  sound  wave,  how- 
ever, would  move  the  membrane  and  break  the  circuit,  causing  a  regis- 
ter on  the  chronograph.     When  the  spring  fell  it  rested  upon   the 


3o8 


ELLEN    OR   THE 


contact  point  from  which  a  wire  ran  to  the  next  membrane  of  the 
series,  so  that  the  circuit,  immediately  after  being  broken  at  the  first 
membrane,  was  made  again  through  the  second  before  the  sound  wave 
reached  it.  In  this  way  the  current  could  be  transferred  to  all  the 
membranes  of  the  series  and  the  successive  breakings  and  makings  of 
contact,  as  the  sound  wave  passed  each  one,  could  be  registered  on  a 
chronograph  placed  at  a  distance. 

TABLE   OF   RESULTS,    WITH   VELOCITY    REDUCED   TO   0°   C. 


Rear  of  Cannon. 

Distance  from 

Side 

of  C^annon. 

Mouth  of  Cannon. 

Charge,  i^^o  lbs. 

Charge,  }.»  lb. 

10-30  feet. 

1076 

30-  50  " 

1 187 

1032 

1067 

50-  70   ** 

1240 

1091 

1162 

70-  90    " 

1267 

1 1 20 

I20I 

90-110     " 

1262 

1114 

1 188 

*  Had  the  cannon  been  turned  in  the  direction  of  the  line  of  mem- 
branes, the  retardation  would  i)robably  have  become  an  acceleration. 
The  experiment  was  of  course  impracticable.  The  conclusions  are 
from  these  experiments :  i.  That  the  velocity  of  sound  is  a  function  of 
its  intensity.  2.  That  experiments  upon  the  velocity  of  sound  in  which 
a  cannon  is  used  contain  an  error,  probably  due  to  the  bodily  motion 
of  the  air  near  the  cannon.  Evidently  a  musical  sound  of  low  intensity 
must  be  used  to  obtain  the  correct  velocity  of  sound.' 

"The  conclusions  are  of  course  utter  nonsense,  and  arise 
from  confusing  a  pulse  of  air  with  sound. 

**Prof.  David  Thompson,  in  his  article  on  'Acoustics/  in  the 
Encyclopaedia  Britannica  says: 

*The  experimental  determination  of  the  velocity  of  sound  in  air 
has  been  carried  out  by  ascertaining  accurately  the  time  intervening 


WIIISFERIXGS    OF   AN   OLD    PINK 


309 


between  the  flash  and  report  of  a  gun  as  observed  at  a  given  distance, 
and  dividing  the  distance  by  the  lime.  A  discussion  ot  the  many 
experiments  conducted  on  this  principle  in  various  coimtries  and  at 
various  periods,  by  Van  Der  Kolk  {LontL  a$uf  Edin,  P/tiL  Ma^,,  July , 
1865),  assigns  to  the  velocity  of  sound  in  dry  air  at  32**  Fahr.,  1091 
feet  S  inches  per  second,  with  a  probable  error  of  i  3*7  feet ;  ami  still 
more  recently  (in  1871)  Mr,  Stone,  the  Astronomer  Royal  at  the  Cape 
of  Good  Hope,  has  found  1,090*6  as  the  result  of  careful  experiments 
by  himself  there.  The  coincidence  of  these  numbers  with  that  we  have 
already  obtained  theoretically  sufFicienlly  establishes  the  general  accu- 
racy of  the  theory. 

'Still  it  cannot  be  overlooked  that  the  formula  for  V  is  founded  on 
assumptions  which,  though  approximately,  are  not  strictly  correct. 
Thus,  the  air  is  not  a  perfect  gas,  nor  is  the  varialiou  of  elastic  force 
caused  by  the  i>assage  through  it  of  a  wave  of  <listurbanre  always  very 
small  in  comparison  with  the  elastic  force  of  the  undisturbed  air. 
Earnshaw  {1S5S)  first  drew  attention  to  these  points,  and  came  to  the 
conclusion  that  the  velocity  of  sound  increases  with  its  luudness,  that  is, 
with  the  violence  of  the  disturbance.  In  confirmation  of  this  statement 
he  appeals  to  a  singular  fact,  viz.,  that,  during  experiments  raade  by 
Captain  Parry,  in  the  North  Polar  Regions,  for  determining  the  velocity 
of  sound,  it  was  invariably  found  that  the  report  of  the  discharge  of 
cannon  was  heard,  at  a  distance  of  2}4  miles^  perceptibly  earlier  than 
the  sound  of  the  word  Jirf,  which,  of  course,  preceded  the  discharge.* 


•*The  facts  in  regard  to  the  expcrinicnts  made  by  Cii plain 
Parry  arc  thus  reported  by  Rev.  George  Fisher,  the  astronomer 
of  the  expedition  (Appendix  to  *Farry*s  Second  Voyage/ 
page  239): 

•The  experiments  on  the  9th  of  Febryary,  1822,  were  attended  with 
a  singular  circumstance,  which  was,   the  officer's  word  nf  command 


3IQ  ELLEN   OR  THE 

"  Fire  I  '*  was  several  times  distinctly  heard  by  Captain  Parry  and  myself, 
about  one  beat  of  the  chronometer  (nearly  half  a  second)  after  the 
report  of  the  gun ;  from  which  it  would  appear  that  the  velocity  of 
sound  depended,  in  some  measure,  upon  its  intensity.  The  word  "  fire  " 
was  never  heard  during  any  of  the  other  experiments.  Upon  this  occa- 
sion the  night  was  calm  and  clear,  the  thermometer  250  below  zero, 
the  barometer  28.84  inches,  which  was  lower  than  it  had  ever  been 
observed  before  at  Winter  Island.' 

*'Thc  statement  of  Mr.  Thompson  that  the  word  'fire'  of 
course  preceded  the  discharge  is  unwarranted.  The  occur- 
rence referred  to  was  noticed  on  but  one  occasion,  and  might 
most  naturally  be  accounted  for  on  the  supposition  that  the 
cannon  was  inadvertently  fired  before  the  word  was  given. 
In  the  nature  of  the  case,  as  there  would  be  several  warnings, 
the  gunner  would  know  about  the  time  the  word  was  to  be 
spoken,  and  might  naturally  anticipate  it. 

**  In  the*  Royal  Transactions,'  vol.  20»  Mr.  Walker  says: 

*  The  Academy  del  Cimcnta  caused  six  aniuehiises  and  six  cham- 
bers to  be  fired  one  after  another  at  the  distance  of  5739  English  feet, 
and  from  the  flash  to  the  arrival  of  the  report  of  each  was  five  seconds. 
And  repeating  the  experiment  at  the  midway,  the  motion  was  in 
exactly  half  the  time. 

*  Mersennus  and  the  Academy  liel  Cimenia  conclude  that  sounds  are 
all  of  the  same  quickness,  whether  they  be  great  or  small.  But  Kircher 
from  several  experiments  infers  that  loud  sounds  are  quicker  than  little 
ones.  Kircher  says  that  an  echo  which  repeated  14  syllables  at  night, 
repeated  but  seven  in  the  day,  which  seems  very  odd. 

*  Because  there  seems  to  be  so  great  affinity  betwixt  the  undulation 
of  water  and  the  propagation  of  sound,  therefore  the  Academy  del 
Cimenia  tried  some  experiments  about  the  first :  and  they  tell  us  that 


WHISPERINGS  OF  AN  OLD   PINE 


;i  T 


the  larger  the  stone  is,  which  is  thrown  into  the  water,  and  the  greater 
the  force,  by  so  much  is  the  undulation  swifter;  though  Gassendus  had 
before  affirmed  that  the  nndnlations  of  water  are  equally  swift/ 

**Mr  Geo,  B.  Air\',  in  his  book  'On  Sound/  says: 

'The  firet  of  the  obvious  laws  of  sound  in  general  is,  that  it  dimin- 
ishes with  the  distance.  The  accurate  law  of  diminution  will  be  con- 
sidered hereafter  when  we  have  applied  mathematical  investigation  to 
the  theory*  The  second  law,  which  is  less  obvious,  but  which  is  suffi- 
ciently well  known,  and  has  been  remarked  by  observant  persons  in  all 
ages  (see,  for  instance,  Lucretius,  VL  169,  etc.)  is,  that  the  propaga- 
tion of  sound  to  a  distance  occupies  time,  and  that  the  lime  required  is 
sensibly  proportional  to  the  distance  to  be  traversed.  It  is  also 
well  known  that  sounds  of  different  pitch  antl  of  difTerent  loudness 
travel  with  sensibly  the  same  speed  :  the  soumls  of  a  ring  of  bells,  at 
whatever  distance  they  are  heard,  fall  on  the  ear  in  the  same  order. 
ll\e  velocity  may  be  stated  roughly  to  lie  between  looo  feet  and  1200 
feet  per  second.  The  numbers,  and  their  variation  under  certain  cir- 
cumstances, will  be  given  with  greater  accuracy  when  we  treat  of  the 
theoretical  investigation.' 

"Mr,  W.  M,  [fifjgins.  in  'Philosophy  of  Sound/  says: 

*  The  whole  science  of  music  may  in  one  sense  be  said  to  depend  on 
the  fact  that  all  sounds  have  the  same  velocity.  If  the  velocity  of 
sound  changed  with  the  pitch,  nothing  but  discord  would  be  heard  by 
one  who  listened  to  music  at  a  distance.  On  a  still  night  music  may 
be  heard  far  away,  and  especially  if  the  performers  and  listeners  ht 
separated  by  water,  and  yet  the  harmony  is  preserved.  The  timt 
required  for  conduction  is  altogether  independent  of  the  pitch. 
Imagine  it  to  be  otherwise  ;  suppose  the  high  notes  to  move  fastei 
than  the  lower  ones,  and  w^hat  a  chaos  of  sound  would  be  produced  bi 


312  ELLEN   OR  THE 

the  performance  of  a  large  band.  We  may,  however,  stand  at  any  dis- 
tance and  can  discover  no  want  of  harmony  from  this  cause ;  there  are 
no  notes  which  are  running  before,  and  none  that  are  lagging  behind  ; 
they  are  all  of  the  same  relative  duration,  and  separated  by  the  same 
interval  of  time,  at  a  distance  where  they  can  be  only  just  heard,  and 
on  the  spot  where  drawn  from  the  instruments  that  gave  them  birth.' 

"  In  vol.  27  of  the  *  London,  Edinburgh  and  Dublin  Philo- 
sophical Magazine,'  Professor  J.  LcConte  says : 

'On  a  fine  and  still  evening  of  June,  1858,  the  Messiah  was  per- 
formed in  a  tent^  and  the  Hallelujah  Chorus  was  distinctly  heard,  without 
loss  of  harmony^  at  a  distance  of  two  English  miles.  As  it  is  well 
known  that  the  human  ear  appreciates,  with  the  greatest  nicety,  the 
slightest  differences  in  musical  intervals,  these  facts  may  be  considered 
as  establishing  the  absolute  consistency  of  the  velocity  of  all  sounds  em- 
braced within  the  musical  scale.' 

"Sir  J.  F.  Herschel,  in  an  article  on  *  Sound'  in  the  Ency- 
clopa,^dia  Metropolitana,  says : 

'  In  a  paper  communicated  to  the  Royal  Society  in  1708  by  Dr.  Dur- 
ham, the  subject  of  the  velocity  of  sound  is  investigated  more  fully  and 
distinctly  than  had  J)efore  been  done,  and  with  some  degree  of  attention 
to  a  variety  of  circumstances,  such  as  :  i.  The  direction  and  velocity  of 
the  wind  ;  2,  Amount  of  barometric  pressure  ;  3,  Temperature  of  the 
air;  4,  State  of  moisture  and  dryness;  5,  Weather,  whether  fog,  rain, 
snow,  etc. ;  6,  Nature  of  sound,  how  produced,  by  blow,  quaintest 
voice,  or  musical  instrument ;  its  pitch,  quality  and  intensity ;  7,  Orig- 
inal direction  impressed  on  the  sound  by  turning,  for  instance^  the 
muzzle  of  a  gun  one  way  or  the  other ;  8,  Nature  and  position  of  surface 
over  which  sound  is  conveyed. 

*  To  all  these  circumstances,  except  the  wind,  Durham  attributes  no 


1 

■ 

PUHLIC  LIBRARY 

M                              k 

^^B 

1 

WHISPKRINGS   OF  AN 


nf 


effect  on  the  velcx:ity,  though  many,  indeed  all,  have  a  powerful  effect 
upon  its  intensity  or  loudness. 


'  The  cannonade  of  a  sea  fight  between  the  English  and  Uutch  in 
1672  was  heard  across  Englanrl  as  far  as  Shrewsbury,  and  even  in 
Wales,  upwards  of  200  miles, 

'That  sounds  of  all  pitches  and  every  quality,  travel  with  equal  s])eed, 
we  have  a  convincing  proof  in  the  performance  of  a  rapid  piece  of  music 
by  a  band  at  a  distance.  Were  there  the  slightest  difference  of  velocity 
in  the  different  notes>  they  could  not  reach  our  ears  in  the  same  precise 
fsrder,  and  at  the  exact  intervals  of  time  in  which  they  are  played  \  nor 
would  the  component  notes  of  a  harmony,  in  which  several  sounds  of 
fkfTerent  pitch  concur,  arrive  at  once.  M.  Biot  caused  several  airs  to 
be  played  on  a  flute  at  the  end  of  a  pipe  3,120  feet  long,  which  w^ere 
distinctly  heard  by  him  at  the  other  end,  without  the  slightest  disar- 
rangement in  the  order  or  intervals  of  the  high  and  low  notes. 

'A  very  material  difference,  however,  is  obsen'ed  in  the  intensity 
with  which  sounds  are  propagated,  or  the  ilistances  to  which  they  may 
he  heard  with  equal  distinctness  according  to  a  great  variety  of  circum* 
stances.  Thus,  if  a  sountl  l>e  prevented  from  spreading  and  losing 
itself  in  the  air,  whether  by  a  pipe,  or  wall,  or  otherwise,  it  may  he  con* 
veyed  to  very  great  distances  with  little  diminution  of  force/ 

"  Hutton'*^  Mathematical  Dictionary.  1795,  f>ays: 

'By  the  accounts  published  by  M.  Cassini  de  Thury,  in  ihe 
"Memoirs  of  the  Royal  Academy  of  Sciences  at  Paris,"  173S,  where 
cannon  were  fired  at  various  as  well  as  great  distances,  under  many 
varieties  of  weather,  wind,  and  other  circumstances,  and  where  the 
measures  of  the  different  places  had  been  settled  with  the  utmost 
exactness,  it  was  found  that  sound  was  propagated,  on  a  medium,  at 
the  rate  of  1,038  French  feet  in  a  second  of  time*     But  1,038  French 


3l6  ELLEN    OR   THE 

feet  are  equal  to  1,107  English  feet.  Therefore  the  difference  of  the 
measures  of  Derham  and  Cassini  is  35  English  feet,  or  33  French  feet, 
in  a  second.' 

*'  In  the  *  Proceedings  of  the  Royal  Society  of  London,'  vol. 
113,  page  96  (1823),  an  article  by  John  Goldingham  says: 

'A  scientific  writer  (Robertson)  in  a  standard  work,  states  that 
some  of  the  most  eminent  philosophers,  judging  that  the  knowledge  of 
the  flight  of  sound  might  be  of  use  on  various  occasions,  have  been  at 
extraordinary  pains  and  expense  to  measure  the  rate  at  which  it  moved  ; 
and  the  result  of  their  experiments,  particularly  of  those  which  were 
best  conducted,  is  as  follows  : 

'  I.  That  the  velocity  of  sound  is  the  same,  whether  by  sea  or  by 
land,  in  dry  or  in  rainy  weather,  by  day  or  by  night,  in  winter  or 
summer. 

'  2.  That  sound,  whether  more  or  less  strong,  flies  with  the  same 
swiftness.  For  by  experiments  a  cannon  fired  with  a  half-pound  charge 
of  powder,  was  heard  at  about  the  distance  of  17I2  miles  in  the  same 
time  after  the  flash  was  seen  as  it  was  when  fired  with  a  charge  of  six 
pounds. 

'3.  That  the  times  in  which  sound  is  heard  are  pr()i)ortional  to  the 
distance  ;  that  is,  at  a  double  distance  it  is  heard  in  twice  the  time  ;  at 
a  triple  distance,  in  thrice  the  time,  etc. 

'This,  however,  is  not  supported  at  a//  points  by  the  experiments  I 
am  about  to  detail ;  nor  indeed  could  we  expect  it  would  be,  from  the 
manner  in  which  sound  is  conveyed ;  as  this  leads  us  to  the  conclusion, 
that  the  more  dense  and  less  elastic  the  atmosphere,  the  slower  sound 
would  travel.* 

"  D.  G.  Gregory,  in  '  Economy  of  Nature,'  says: 

*  Some  curious  experiments  were  made  relative  to  sound  by  MM. 
de  Thury  Maraldi  and  de  la  Caille  upon  a  line  14,636  fathoms  in  length. 


WHISPERINGS    OF   AN   OLD    HNE  317 

having  the  tower  of  Mount  Liberi  at  one  end  anil  the  pyramid  of  Mont- 
martre  at  the  other.  Their  observatory  was  placeil  between  the  two 
objects.  The  results  of  their  observations  were  :  i.  That  sound  moves 
173  French  fathoms  (1,106^  English  feet)  in  a  second  when  the  air  is 
calm.  2.  That  sound  moves  with  the  same  degree  of  swiftness, 
whether  it  be  strong  or  weak.  An  explosion  of  half  a  pound  of  ix)wder, 
discharged  in  a  lx)x,  having  been  heard  in  the  same  space  of  time  as 
the  report  of  a  great  gun  charged  with  nearly  six  poimds  of  jKJwder. 
3.  That  the  motion  of  sound  is  uniform,  its  velocity  neither  accelerating 
nor  diminishing  through  the  whole  course  of  its  progress.  4.  That 
sound  traveled  at  the  same  rate  whether  the  gun  be  pointed  perpen- 
dicular to  the  horizon,  or  towards  the  person  who  hears  the  report,  or 
from  him.  By  other  experiments,  however,  the  progress  of  sound 
appeared  to  be  impeded  by  a  strong  wind.* 

**  These  statements  are  quite  complete  and  specific  that 
sounds  of  different  intensities  travel  at  the  same  speed,  and  that 
this  speed  is  independent  of  distance,  nor  do  there  appear  to 
have  been  any  well  authenticated  experiments  to  disprove  this." 


3l8  ELLEN   OR  THE 


XX. 

^^T^HIS  theory  of  sound  seems  to  be  very  stupid,"  I 
^      said. 

" Awfully  stupid,"  she  replied;  ** and  it's  everywhere  stupid. 
The  only  merit  Ellen  ever  found  in  it  was  its  consistency  in 
stupidity.  Without  exception  the  evidence  is  against  it 
wherever  examined,  so  that  to  believe  it  to  be  true,  one  has  to 
believe  something  true  which  every  particle  of  evidence  contra- 
dicts;  and  that,  of  course,  no  person  with  any  sense  would  do. 

**The  theory  is  a  crude  one,  built  on  the  fact  that  sounds  are 
generally  hcan^  in  air.  It  is  said  to  have  been  handed  down 
from  the  time  of  Pythagoras,  the  great  Greek  philosopher, 
or  before ;  and  if  so,  hails  from  the  same  quarter  and  time  as 
the  Ptolemaic  system  of  astronomy,  which  held  that  the  sun 
went  around  the  earth,  and  for  2000  years  or  more  was  univer- 
sally taught. 

**More  accurately,  this  theory  in  its  present  form  teaches 
that  sound  is  propagated  through  the  air  from  the  center  of 
disturbance  or  sounding  body,  by  a  so-called  wave  motion — 
that  is,  a  motion  similar  to  that  which  takes  place  in  still  water, 
when  a  stone  or  other  body  is  thrown  into  it. 

"This  introduces  a  subject  of  great  beauty,  both  of  vision 
and  melody, — that  of  waves.  In  the  article  on  waves  Chambers' 
Encyclop.iedia  says : 

'We  next  come  to  what  are  called  oscillatory  waves  in  water 
or  other  liquids.     To  this  class  belong  all  waves  whose  length  from 


WHISl'ERINGS   OF  AN   OLD   I'lNE 


319 


crest  to  crest  is  small  compared  with  lUe  depth  of  the  liquid ; 
from  ripples  on  a  pool  to  the  long  roll  of  the  Atlantic,  They  are  never 
observed  as  solitary'  waves,  their  general  characteristic  being  their  peri- 
odical recurrence.  And,  by  watching  a  piece  of  cork  floating  on  the 
surface,  we  see  that  it  moves  forwards  when  at  the  crest  of  the  wave, 
and  backwards  through  an  equal  amount  when  in  the  trough.  Also  it 
rises  while  passing  from  trough  to  crest,  and  sinks  from  crest  to  trough. 
Mathematical  investigation,  confirmed  by  experiments  with  floats  at  sea, 
and  with  short  waves  in  the  glazed  box  before  described,  shows  that 
each  particle  of  the  water  describes  a  drcie  about  its  position  of  rest 
in  the  vertical  plane  in  which  the  wave  is  advancing.  Particles  at 
greater  and  greater  depths  describe  smaller  and  smaller  circles.  The 
diameters  of  these  circles  diminish  with  extreme  rapidity.  At  a  ilepth 
equal  to  the  distance  from  crest  to  crest  (i.  e.,  the  length  of  the  wave), 
the  displacement  of  the  water  is  already  only  1-5 35th  of  that  at  the 
surface.  At  the  depth  of  two  wave-lengths,  it  is  about  i -300,000th  of 
that  at  the  surface.  Thus  we  may  see  to  how  small  a  depth  the  ocean 
is  agitated  even  by  the  most  tremendous  wind- waves  ;  for,  according 
to  Scoresby,  43  feet  is  about  the  utmost  diflference  of  level  between 
crest  and  trough  in  ocean- waves.  If  the  wave-length  be  300  feet 
(which  is  a  large  estimate),  then  at  a  depth  of  300  feet  the  water- par  tide* 
describe  circles  whose  radii  are  only  the  2i.5*535th  of  a  foot,  or  about 
four-tenths  of  an  inch;  and  at  600  feet  this  is  reduced  to  i-i 200th  of 
an  inch  ;  while  the  depth  of  the  Atlantic  is  in  many  parts  more  than 
three  or  fotir  miles.  In  this  case,  the  velocity  of  propagation  of  the 
wave  has  been  shown  to  be 


where  ^  is  32*2  feet ;  /  is  the  wave-length  in  feet ;  and  ir  is  the  ratio 
of  the  circumference  of  a  circle  to  its  diameter.  Thus,  the  velocity  of 
an  oscillatory  wave  in  deep  water  is  proportional  to  the  square  root  of 
its  length.    •     •     • 


320  ELLEN    OR   THE 

'  When  the  depth  is  not  infinitely  great  compared  with  the  length  of 
a  wave,  theory  and  experiment  agree  in  showing  that  the  motion  of 
each  particle  takes  place  in  an  ellipse  whose  major  axis  is  horizontal. 
These  ellipses  diminish  rapidly  in  length  as  we  descend  in  the  liquid, 
but  still  more  rapidly  in  breadth ;  so  that,  as  was  to  be  expected,  the 
particles  at  the  bottom  oscillate  in  horizontal  straight  lines.  The  ex- 
pression for  the  velocity  of  propagation  is  now  by  no  means  so  simple 
as  in  the  previous  cases — but  it  is  easily  shown  to  include  the  valuer 
already  given. 

*  So  far,  the  first  approximation.  A  section  of  the  surface  made  by  a 
vertical  plane  in  the  direction  of  the  wave*s  motion,  is  shown  to  be 
bounded  by  the  Harmonic  Curve,  or  Curve  of  Sines^  the  form  assumed 
by  a  vibrating  string ;  from  which  it  follows  that  the  crests  are 
similar  to  the  troughs.  The  second  approximation  makes  the  troughs 
flatter,  and  the  crests  steeper,  and  also  shows  that  the  particles 
are,  on  the  whole,  carried  forward  by  each  successive  wave.  The 
amount  of  this  progression  diminishes  rapidly  with  the  depth  below  the 
surface.  A  third  approximation  shows  that  the  velocity  is,  ceteris  pari- 
busy  greater  the  greater  is  the  height  of  the  waves. 

'When  waves  advance  toward  the  shore,  their  circumstances  change 
in  general  gradually,  from  those  of  oscillatory  waves  to  those  of  waves 
of  translation,  as  the  depth  of  the  water  becomes  less  and  less  consid- 
erable in  comparison  with  the  length  of  the  wave  ;  and  it  is  found  by 
experiment  that  they  "break,"  as  it  is  railed,  when  the  depth  of  the 
water  is  about  equal  to  the  height  of  the  crest  above  the  undisturbed 
level.  All  the  curious  phenomena  of  breakers  are  thus  easily  explained 
by  the  results  we  have  already  given,  when  they  are  considered  with 
reference  to  the  gradual  alteration  of  the  depth  of  the  water. 

'Finally,  we  must  notice  a  singular  phenomenon  often  observed,  viz., 
that  of  a  series  of  waves  breaking  on  the  coast,  every  eighth,  or  ninth, 
or  tenth,  etc.,  is  seen  to  be  higher  than  its  predecessors  or  successors. 


WHfSPERINGS   OF   AN   OLD    PINE 

The  explanation  is  simple  enough,  and  points  to  the  siraultiineous  exist- , 
ence  of  two  or  more  sets  of  oscillatory  waves  of  different  lengths,  due 
in  general  to  quite  distinct  causes,  which  reach  the  shore  together.* 

"The  assumption  of  scientists  is  that  sound  is  carried  in  the 
air  by  air  waves,  resembling  water  waves.  Thus  l*rofessor 
Hehiiholtz,  the  highest  scientific  authority,  says: 

'Suppose  a  stone  to  be  thrown  into  a  piece  of  calm  water.  Round 
the  spot  struck  there  forms  a  little  ring  of  wave,  which,  ail%'ancing 
equally  in  all  directions,  expands  lo  a  constantly  increasing  circle^ 
Corresponding  to  this  ring  of  wave  sotmd  also  proceeds  in  the  air  from 
the  excited  point,  and  advances  in  all  directions  as  far  as  the  limits  of 
the  mass  of  air  extend.  The  process  in  the  air  is  essentially  identical 
with  that  on  the  surface  of  water.  ♦  •  •  phe  ]>rocess  which  goes 
on  in  the  atmospheric  ocean  about  us  is  of  a  precisely  similar  nature, 
•  *  •  The  waves  of  air  ♦  •  *  transport  the  tremor  to  the 
human  car  exactly  in  the  same  way.* — Setisaiion\'  of  7)>ne^  pages  14,  15. 

**Thc  popular  acceptance  of  the  undulatory  theories  has 
unquestionably  been  largely  due  to  this  comparison  with  water 
waves,  and  the  inference  that  the  waves  considered,  whether  of 
sound  or  light,  are  essentially  the  same.  It  reduced  the 
theory  to  a  practical  condition,  and  was  especially  satisfactory, 
because  the  manner  in  which  water  waves  apparently  pass  each 
other,  was  supposed  to  represent  the  manner  in  which  sounds 
pass  each  other.  To  further  illustrate  this  fact,  Ellen  will  quote 
as  follows ; 

"First,  from  the  '  Circle  of  Sciences,'  vol.  i,  pages  13,  14,  52: 

'  Quitting  the  material  theory  of  heat,  or,  as  it  has  been  sometimes 
called,  the  "  corpuscular/'  because  corpuscles,  or  small  particles,  of 


322  ELLEN   OR   THE 

this  quasi- material  were  supposed  to  emanate  from  heated  bodies — we 
now  proceed  to  investigate  what  has  been  termed  the  "undulatory 
theory/*  or  that  which  explains  the  production  and  effects  of  Heat, 
Light,  etc.,  on  the  supposition  that  an  "^-///^r,"  by  its  wave-like  or 
undulatory  motion,  is  their  mutual  cause. 

'The  term  undulatory  has  been  derived  from  the  Latin  word  unda^  a 
wave ;  and  the  reader  will  understand  the  nature  of  the  whole  undu- 
latory theory  by  performing  what  at  first  sight  may  seem  a  most  childish 
experiment ;  but  which  has,  in  its  application,  as  much  effect  on  the 
scientific  theories  of  the  present  day,  as  had  the  notable  one  observed 
by  Newton — namely,  the  falling  of  an  apple. 

'  On  casting  a  pebble  into  a  still  pond,  it  will  be  observed  that  the 
water  forms  a  series  of  circles,  all  of  which  have  the  point  where  the 
stone  first  touched  the  water  as  their  common  centre.  These  waves,  or 
undulations,  thus  created,  continue  to  be  produced,  until  the  edge  or 
bank  of  the  pond  prevents  their  further  propagation.  At  first  sight  it 
would  seem  that  the  water  really  moved  in  a  horizontal  direction  from 
the  center :  but,  on  a  careful  examination,  such  will  not  be  found  to 
be  the  case.  Each  particle  of  water  communicates  its  motion  to  that 
next  to  it ;  and  thus  each  particle  is  scarcely  disturbed  horizontally  : 
the  action  rather  raises  the  particles  in  an  upright  or  vertical  posi- 
tion ;  and  thus  the  apparent  and  actual  motion  afford  a  i)aradox,  and 
also  a  refutation  to  the  general  idea  "that  seeing  is  believing." 

'A  very  familiar  illustration  of  the  fact,  that  the  body  or  mass  of  the 
water  does  not  move,  is  found  in  the  case  of  a  swan  or  other  bird  float- 
ing on  ruflled  water.  Instead  of  the  bird  moving  in  the  apparent 
direction  of  the  waves,  in  the  absence  of  li.le  or  current,  its  body  will 
retain  its  horizontal^  although  its  vertical  or  perpendicular  position  will 
undergo  continual  change. 

'  By  refining  the  ideas  or  imagination,  and  supposing  the  existence  of 
an  extremely  rare  substance,  which  has  been  called  "^///<fr,"   undula- 


WHISPRRI? 


OX 


32i 


lions  in  this  material  have  been  suggested  as  the  cause  of  the  forces  of 
which  we  have  now  to  speak  ;  and,  as  we  shall  presently  show,  that 
although  the  idea  or  theory  has  no  exact  foundalion,  still  it  has  the 
inestimable  advantage  of  explaining  a  variety  of  phenomena  for  which 
we  have  no  equally  suitable  expression. 

•Taking as  a  postulate  the  existence  of  an  ether,  we  proceed  to  speak 
of  its  motion  as  the  cause  of  forces;  and  we  may  here  remark,  that 
whilst  the  undulations  of  the  ether  may  be  proximate  causes^  wc 
assume  the  existence  of  some  unknown  force,  the  action  or  suspension 
of  which  is  the  uUimatt  cause  of  the  proximate.  Of  the  ultimate  cause 
we  are  ignorant ;  we  can  only  assign  its  origin  to  the  First  Cause,  of 
whom  it  has  been  recorded  ^ — 

**Go(l  said,  Let  there  be  light,  and  there  was  light." 

'When  two  pebbles  arc  cast  into  the  same  still  sheet  of  water,  it  will 
be  found  that  the  waves  produced  destroy  each  other  when  they  come 
in  contact  in  certain  positions.  Transferring  our  attention  to  the 
undulations  of  ether  in  a  binary  or  two- fold  form,  we  can  thus  explain 
the  cause  of  interference  and  polarization ;  and  assuming  that  any 
number  of  undulations  may  be  produced  by  a  similar  number  of 
initiative  motions,  we  can,  by  applying  the  doctrine,  explain  a  vast 
variety  of  the  phenomena  of  the  forces  now  under  discussion.  The 
reader  will  do  well  to  study  the  eflfects  produced  by  casting  stones  into 
still  water,  and  by  watching  the  results  afforded  when  the  radial  waves 
intersect  each  other.  Indeed,  we  cannot  recommend  any  plan  so 
effective  for  inducing  an  appreciative  idea  of  the  various  laws  to  which 
the  undulations  of  a  fluid  are  subject.' 

"Seconds  from  Professor  TyndalFs  Book  •  On  Sound/  pages 
3S4-3S7: 

*  From  a  boat  in  Cowes  Harbor,  in  moderate  weather,  I  have  often 
watched  the  masts  and  ropes  of  the  ships,  as  mirrored  in  the  water. 


324  ELLEN   OR  THE 

The  images  of  the  ropes  revealed  the  condition  of  the  surface,  indi*- 
eating  by  long  and  wide  protuberances  the  passage  of  the  larger  rollers, 
and,  by  smaller  indentations,  the  ripples  which  crept  like  parasites  over 
the  sides  of  the  larger  waves.  The  sea  was  able  to  accommodate  itself 
to  the  requirements  of  all  its  undulations,  great  and  small.  When  the 
surface  was  touched  with  an  oar,  or  when  drops  were  permitted  to  fall 
from  the  oar  into  the  water,  there  was  also  room  for  the  tiny  wavelets 
thus  generated.  This  carving  of  the  surface  by  waves  and  ripples  had 
its  limit  only  in  my  powers  of  observation  ;  every  wave  and  every  ripple 
asserted  its  right  of  place,  and  retained  its  individual  existence,  amid 
the  crowd  of  other  motions  which  agitated  the  water. 

*The  law  that  rules  this  chasing  of  the  sea,  this  crossing  and  inter- 
mingling of  innumerable  small  waves,  is  that  the  resultant  motion  of 
every  particle  of  7uater  is  the  sum  of  the  ituUvidual  motions  imparted 
to  it.  If  a  particle  be  acted  on  at  the  same  moment  by  two  impulses, 
both  of  which  tend  to  raise  it,  it  will  be  lifted  by  a  force  equal  to  the 
sum  of  both.  If  acted  upon  by  two  impulses,  one  of  which  tends  to 
raise  it,  and  the  other  to  depress  it,  it  will  be  acted  upon  by  a  force 
equal  to  the  ditlerence  of  both.  When,  therefore,  the  sum  of  the 
motions  is  spoken  of,  the  algebraic  sum  is  meant — the  motions  whiih 
tend  to  raise  the  particle  being  regarded  as  positive,  and  those  which 
tend  to  depress  it  as  negative. 

*  When  two  stones  are  cast  into  smooth  water,  20  or  ^^o  feet  apart 
round  each  stone  is  formed  a  series  of  expanding  circular  waves,  every 
one  of  which  consists  of  a  ridge  and  a  furrow.  The  waves  touch,  cross 
each  other,  and  carve  the  surface  into  little  eminences  and  depressions. 
Where  ridge  coincides  with  ridge,  we  have  the  water  raised  to  a  double 
height ;  where  furrow  coincides  with  furrow,  we  have  it  depressed  to  a 
double  depth  ;  where  ridge  coincides  with  furrow,  we  have  the  water 
reduced  to  its  average  level.  The  resultant  motion  of  the  water  at 
every  point  is,  as  above  stated,  the  algebraic  sum  of  the  motions  im- 


THF  NFW  YCRK 
piU-iU:  LIBRARY 

-      .  e  >  ■'.;  I  A  N  L 


WinsrEKIXCJS    OF   A3Sr   OLD    TINE 


1^7 


pressed  ujioii  that  i>oiiU.  And  if,  instead  of  two  sowrces  of  disturbance, 
we  had  leii,  or  a  hundred,  or  a  thousand,  the  ronse([uence  would  be  the 
same  ;  the  actual  result  might  transrend  out  powers  of  observation^  but 
the  law  above  enunriated  would  still  hold  good* 

•  Instead  of  the  intersection  of  waves  from  two  distinct  centres  of  dis- 
liirbame,  we  may  cause  direct  and  reflected  waves,  from  the  same 
centre,  to  cross  each  other.  Many  of  you  know  the  beauty  of  the 
effects  produced  when  light  is  reflected  from  np[»les  of  water.  When 
mercur>^  is  employed  the  effect  is  more  brilliant  stilt.  Here,  by  a 
proper  mode  of  agitation,  direct  and  reflected  waves  may  be  caused  to 
cross  and  interlace,  and  by  the  most  wonderful  self-analysis  to  untie 
their  knotted  scrolls. 

'This  power  of  water  to  accept  and  transmit  uuiltitudinous  impulses  is 
shared  by  air,  which  concedes  the  right  of  space  and  motion  to  any 
number  of  sonorous  waves.  The  same  air  is  competent  to  accept  and 
transmit  the  vibrations  of  a  thousand  instmments  at  the  same  time. 
When  we  try  to  visualize  the  motion  of  that  air — ^to  present  to  the  eye 
of  the  min  I  the  battling  of  the  pulses  direct  and  reverberated — the 
imaginjlion  retires  ba*Tled  from  the  attempt.  Still,  amid  all  the  com- 
plexity, the  lav¥  ab3ve  enunciated  /holiis  good,  every  particle  of  air 
being  animated  by  a  resultant  motion,  which  is  the  algebraic  sum  of  all 
the  individual  motions  imparted  to  it.  And  the  most  wonderful  thing 
of  all  is,  that  the  human  ear,  though  acted  on  only  by  a  cylinder  of  that 
air,  which  does  not  exceed  the  thickness  of  a  quill,  can  detect  the  com- 
ponents of  the  motion,  and,  by  an  act  of  attention,  can  even  isolate 
from  the  aerial  entanglement  any  particular  sound*' 

**The  trouble  with  this  law  of  resultant  motions,  given  as  the 
explanation  ol  the  action  of  these  waves,  is  that  the  thing  to  be 
explained  is  two  or  more  systems  of  waves  passing  each  other, 
while  a  resultant  motion  would  only  at  the  best  explain  a  single 
system.     For  a  resultant  motion  is  but  one  motion,  and  if  the 


328  ELLEN   OK  THE 

motions  of  all  the  particles  are  reduced  to  resultant  motions^ 
there  could  be  but  one  system  of  waves  instead  of  two  or  more. 
Evidently,  then,  although  there  may  be  resultant  motions 
among  the  particles,  as  in  those  which  rise  to  double  height, 
and  others,  this  does  not  explain  the  progression  of  the  waves. 

"With  the  multitude  the  effect  of  this  legerdemain  of  waves, 
so  long  as  it  is  not  understood,  is  very  great.  The  boy,  greatly 
frightened  by  a  barking  dog,  replied,  when  his  mother  asked  if 
he  did  not  know  that  barking  dogs  never  bite,  *  Yes,  he  knew, 
but  he  was  afraid  the  dog  didn't  know.'  And  so  the  spectator 
watching  water  waves  knows  that  no  particle  can  go  two  dif- 
ferent ways  at  the  same  time ;  but  he  is  afraid  that  the  particles 
don't  know  it. 

"  But  as  those  who  have  claimed  this  similarity  between 
water  waves  and  hypothetical  air  waves,  not  to  mention 
assumed  sound  waves  in  earth,  iron,  steel,  and  other  solid 
bodies,  are  of  that  class  of  men  known  as  scientists,  that  Ellen 
has  so  often  warned  the  old  Pine  against,  who  arc  very  reckless 
in  statement,  often  asserting  things  that  arc  not  only  not  true, 
but  impossible,  it  will  be  necessary  to  examine  and  find  out 
whctlicr  it  is  possible  for  such  similarity  to  exist,  as  this  which 
has  been  universally  proclaimed  by  physicists,  both  in  text 
books  and  lectures,  to  exist  between  water  waves  and  ima^nnary 
air  waves. 

"The  claim  that  sound  proceeds  by  waves  from  the  excited 
point,  in  a  manner  essentially  identical  with  waves  on  the 
surface  of  water,  may  be  tested  in  water  itself.  P\)r  water 
is  one  of  the  mediums  in  which  sound  moves,  and  with 
a   rate   of  speed    about  three    and    one-half  times   that  in   air. 


WHISPERINGS   OF   AN   OLD    PINK 


329 


If,  then,  sound  is  carried  by  waves  essentially  identical  to  water 
waves,  that  fact  should  be  and  must  be  illustrated  in  water 
itself.  And  if  this  was  a  fact,  we  would  suppose  that  a  sound 
caused  by  a  stone  falling  into  the  water  would  be  carried  by  the 
waves  produced  at  the  same  moment  and  by  the  same  cause. 
But  nothing  of  this  sort  happens;  for  whilst  the  water  waves 
are  circling  at  the  slow  rate  of  six  or  eight  feet  in  a  second,  the 
sound  is  propagated  by  the  water  in  all  directions^  by  some 
method  entirely  invisible  to  the  human  eye^  at  a  rate  of  about 
4,000  feet.  This  would  seem  to  be  sufficient  proof  that  waves 
similar  to  water  waves  have  nothing  whatever  to  do  with  sound ; 
for  if  sound  does  not  make  or  use  this  kind  of  wave  in  water,  it 
certainly  does  not  anywhere  else.  It  also  becomes  manifest  that 
if  sound  is  propagated  by  waves,  there  are  two  entirely  distinct 
systems  in  water — the  ordinary  surface  wave  with  which  air 
waves  have  been  compared,  and  another  entirely  invisible  in 
regard  to  which  nothing  whatever  is  known. 

"Mr*  TyndalFs  last  statement  that  *this  power  of  water  to 
accept  and  transmit  multitudinous  impulses  is  shared  by  air, 
which  concedes  the  right  of  space  and  motion  to  any  number 
of  sonorous  waves,*  is  as  purely  imaginary  as  the  explana- 
tion of  the  water  waves.  Air  does  nothing  of  the  kind,  and 
has  nothing  whatever  to  do  with  sonorous  waves.  The 
conception  that  the  car  could  detect  the  components  of 
the  extraordinary  and  complicated  motion  supposed,  is 
an  illustration  of  the  possible  conceptions  of  folly.  It 
could  no  more  do  it  than,  by  the  undulations  of  the  sup- 
posed ether,  it  could  understand  conversation  going  on  in 
the  fixed  stars, 


330  ELLEN   OR   THE 

"Again,  all  water  waves  have  a  depth,  which  is  called 
their  amplitude,  from  crest  to  sinus  (hollow),  or  sinus  to 
crest,  of  about  one  to  ten  as  compared  with  their  length. 
This  is  an  indispensable  characteristic  of  water  waves,  as  much 
as  sphericity  is  of  a  sphere,  or  roundness  of  a  circle.  The 
old  Pine  will  see,  then,  that  if  any  waves  whatever  are  possible 
in  connection  with  sound  they  are  essentially  dissimilar  to 
water  waves.  Indeed  he  will  see  that  waves  similar  to  water 
waves  cannot  possibly  be  used  in  the  propagation  of  sound,  for 
if  they  were  their  action  would  be  perceived  in  water,  iron,  steel, 
and  many  other  solids  through  which  sound  is  conveyed. 
But  this  is  not  the  case. 

*' Disturbances  made  in  the  water  below  the  surface  spread 
but  a  little  way  toward  the  top.  The  disturbance  made  by  a 
fish  is  seen  only  when  the  fish  is  near  the  surface,  and  good- 
sized  stones  or  other  bodies  which,  thrown  into  a  pond, 
would  cause  a  system  of  waves  that  would  extend  many  rods 
will,  when  dragged  upon  the  bottom  at  four  to  six  feet  of 
depth,  cause  no  waves  upon  its  surface. 

'*The  water  waves  arc  all  right.  Ellen  has  had  lots  of  fun  in 
throwing  stones  into  a  pond  and  watching  the  rings  of  waves 
circle  on  every  side,  and  especially  in  watching  different  rings 
apparently  pass  through  each  other.  The  water  is  pressed 
downwards  and  laterally  by  the  stone,  which  thus  starts  the  first 
ring  of  waves.  In  this  ring  there  is  quite  a  movement  of  the 
water  thrown  up  by  the  stone.  This  is  illustrated  in  throwing 
a  stone  beyond  a  chip  or  other  article  floating  on  the  water,  to 
bring  it  shoreward.  Immediately,  because  of  gravity,  the 
water  rushes    in   to    fill    the   space   through  which    the    stone 


WHISPERINGS   OF  AN   OLD   PINE 


33t 


passed.  In  doing  this  it  rises  above  the  normal  level,  thus 
startinf^  the  second  ring  of  waves.  The  water  is  again 
drawn  down  by  gravity  and  between  the  two  forces  (the  motion 
first  caused  by  th^  pushing  of  the  stone,  and  gravity)  oscillates 
a  number  of  times^  forming  each  time  a  ring  of  waves,  whose 
height  decreases  as  the  rings  enlarge. 

**  But  the  motion  of  water  waves  is  not  chiefly  accomplished 
by  one  particle  pushing  another.  Nor  is  any  continuous 
motion  thus  accomphshed.  The  water  is  started  b\'  the 
pressure  of  the  stone,  and  so  forced  above  the  level 
and  onto  a  ridge  or  crest.  From  this  crest  it  is 
pulled  back  by  gravity  into  a  maelstrom  of  agitated 
water.  Gravity  pulls  down  another  particle  on  the  other  or 
advanced  side  of  this  first  formed  ridge,  and  this  particle 
by  its  momentum  and  the  action  of  other  particles,  is  carried 
up  and  helps  form  another  ridge,  when  gravity  pulls  It  back 
into  the  first  trough  following  that  made  by  the  stone.  In 
the  meantime  a  second  inner  ridge  is  formed  by  the  same 
forces»  when  immediately  and  of  necessity  gravity  again  begins 
its  work.  And  so  the  different  ridges  are  formed,  and  by 
the  nature  of  tlie  conditions  each  one  is  carried  outward  with 
a  widening  circle.  And  so  another  and  another  particle  of 
water  is  caught  by  gravity  and  pulled  down  in  front  of  each 
advanced  ridge,  then  urged  by  momentum  to  help  form  another 
ridge.  And  thus  the  circle  of  waves  is  continued,  only,  of 
course,  it  is  not  made  by  single  particles  of  water,  but  by 
millions  of  them,  all  moved  in  a  similar  manner.  The  whole 
operation  is  as  deceptive  as  a  mirage.  It*s  a  chopped-up 
performance,   in  which  the   star  performers    are    gravity  and 


332  ELLEN   OR  THE 

momentum,  with  the  water  particles  as  puppets.  Nor  could  it 
be  continued  at  all  except  for  the  action  of  gravity." 

"Then/*  I  said,  **the  different  systems  of  waves  do  not  pass 
through  each  other?" 

"Not  at  all,"  she  said;  "the  whole  thing  is  a  delusion, 
or  illusion.  Different  circles  may  meet  each  other,  and 
thus  the  particles  of  colliding  circles  hit,  when  they  will 
obey  the  laws  of  all  colliding  bodies,  stopping,  reflecting, 
or  assisting  each  other  according  to  the  conditions  under 
which  they  meet.  But  gravity  doesn't  care  how  the  ridges 
from  which  it  pulls  the  water  drops  are  formed,  whether  by 
the  performances  of  one  ring  of  waves,  or  two,  or  more;  the 
higher  its  ridges  the  better  its  pull.  So  it  continues  its  part 
of  the  work,  and  now  the  particles  which  advancing  were  carry- 
ing on  one  system,  receding  are  sustaining  the  other.  This  is 
practically  true  from  the  start.  The  whole  performance  is  a  dis- 
connected one,  but  in  which  the  different  parts  fit  so  perfectly, 
that  its  discontinuity  is  not  apparent.  In  time  the  ridges 
and  the  surface  of  the  water  coincide,  or  the  rings  arc  dashed 
upon  the  shore,  when  all  the  pull  which  gravity  has  is  that 
back  into  the  water.  Reflected  waves  arc  made  and  continued 
in  the  same  manner. 

'*  The  old  Pine  will  sec  how  utterly  erroneous  it  is  to  com- 
pare a  system  of  waves  like  these  with  that  of  the  hypothetical 
sound  waves.  With  the  nature  of  water  waves  understood,  no 
one  with  good  sense  would  attempt  it.  Certainly,  with  their 
nature  understood,  no  one  would  be  deceived  by  any  such 
comparison. 

"This  ends  the  theory  of  sound;   destroys  the   illusion,  and 


WHISPERINGS   OF  AN   OLD    PINE  333 

shows  people  how  they  have  been  deceived.  For  with  the 
manner  in  which  water  waves  are  made  understood,  they  have 
no  more  resemblance  to  the  hypothetical  air  waves,  than  a 
squash  vine  has  to  the  north  star.  For  in  not  a  single 
feature  is  there  any  similarity.  The  one  takes  place  upon  the 
surface  of  a  fluid,  the  other  in  the  body  of  a  fluid.  The  fluids 
are  entirely  different.  Water  waves  are  the  result  of  conditions 
which  take  place  nowhere  else.  Their  only  possible  signifi- 
cance in  this  connection  is  in  their  illusory  or  deceptive  char- 
acter. That  is,  so  long  as  the  world  is  ignorant  of  the  manner 
in  which  they  are  made,  it  can  be  deceived  in  regard  to  them, 
and  made  to  think  that  they  constitute  a  new  system  for  the 
propagation  of  motion  that  might  be  used  in  the  propagation 
of  sound.  With  their  true  character  understood,  and  the 
impossibility  oi  sound  or  light  being  propagated  by  similar 
motion,  the  undulatory  theories  as  now  taught,  disappear. 
For,  in  the  popular  estimation  or  in  fact,  all  the  foundation 
these  theories  ever  had  was  in  their  supposed  resemblance  to 
water  waves." 


334  ELLEN  OR  TUB 


XXI. 

^^OUT  why,  Ellen/'  I  asked,  "should  the  scientists  deceiye 

'^  the  world  in  such  a  matter,  leading  them  to  bdieVe 
what  is  entirely  false?  Do  they  not  profess  above  all  otheiB 
to  be  seekers  after  truth,  following  the  most  exact  methods?** 

"Yes,"  she  said,  "Ellen  has  thought  that  sometimes  thcgr 
do  profess  too  much.  But  largely  it  is  because  of  their  own 
ignorance.  They  are  themselves  deceived.  Certain  it  is  that 
no  text  book  or  writer  in  physics,  so  far  as  Ellen  knows,  has 
ever  explained  the  nature  of  water  waves,  so  that  it  might  be 
generally  understood.  This  explained,  as  Ellen  has  said,  the 
undulatory  theories  are  gone.  The  old  Pine  will  see  that  it  is 
impossible  for  waves  like  water  waves  to  exist  in  air." 

"But  the  old  Pine  has  noticed  pictures  of  them  in  books  on 
sound,"  I  said. 

"Oh,  yes,"  she  answered;  "the  physicists  draw  a  very  per- 
fectly undulating  line,  embellish  it  with  ordinates,  and  an  axis 
of  abscissas,  and  call  it  a  sound  wave.  It  is  very  amusing  to 
Ellen  to  see  them  spend  so  much  time  describing  something 
that  not  only  doesn't  exist,  but  can't  exist,  although  they  seem 
to  be  as  well  satisfied  in  discussing  it,  as  though  it  really 
existed.  And  then  those  of  them  that  have  a  smattering  of 
mathematics  will  undertake  to  show  how  such  a  wave  might  be 
propagated." 


WHISPERINGS    OK   AN    OLl>   VWE 


337 


"And  tlic  old  Pine  also  saw  recently,"  I  said,  **an  account  of 
the  photography  of  sound  wavesj  assuming  to  give  both,  illus- 
trations of  these  waves  and  of  their  reflection/* 

**Yes/'  she  answered,  '*  Ellen  saw  the  article,  in  which  dis- 
turbances made  by  explosions  and  by  electricity  are  supposed 
to  be  sound  waves.  Ellen  has  already  exposed  the  erroneous 
character  of  the  assumption  that  disturbances  in  air  made  by 
explosions  are  sound.  The  supposition  that  those  made  by 
electricity  are  sound  is  substantially  another  phase  of  the  same 
delusion.  The  gentleman  furnishing  the  article  in  question 
claims  to  have  photographed  the  sound  wave  caused  by  the 
crack  of  an  electric  spark,  by  the  hght  of  another  spark.  An 
electric  spark  on  a  small  scale  is  precisely  similar  to  a  flash 
of  lightning,  and  its  crack  to  a  thunderbolt.  It  is  in  the  nature 
of  electricity  to  violently  disturb  the  particles  of  matter  intt^ 
which  it  enters.  This  is  illustrated  in  the  rending  of  any  body 
struck  by  lightning*  The  following  quotation  from  Ganot 
refers  to  this  propcrt>\  and  demonstrates  how  the  same  result 
takes  place  when  electricity  enters  a  gas : 

*The  mechanical  effects  are  the  violent  lacerations,  fractures,  and 
sudden  expansions  whit  h  ensue  when  a  powerful  discharge  is  passed 
through  a  badly  conducting  substance.  Glass  is  perforated,  wood  and 
stones  are  fractured,  and  gases  an<l  liquids  are  violenlly  disturbed. 
The  mechanical  effects  of  the  electric  spark  may  be  demonstrated  by  a 
variety  of  experiments.  Thus  the  perturbation  and  sudden  expansion 
which  the  discharge  produces  may  be  illustrated  by  means  of  what  is 
known  as  Kinntrsk/s  thtrmomckr.  This  consists  of  two  glass  lubes 
which  fit  into  metallic  caps  and  communicate  with  each  other.  At  the 
top  of  the  large  tube  is  a  rod  terminating  in  a  knob,  and  moving  in 
a  sniffing' box,  and  at  the  bottom  there  is  a  similar  rod  with  a  knob. 


338  ELLEN   OR  THE 

The  apparatus  contains  water  up  to  the  level  of  the  lower  knob.  When 
the  electric  discharge  passes  between  the  two  knobs,  the  water  is  driven 
out  of  the  larger  tube  and  rises  to  a  slight  extent  in  the  small  one. 
The  level  is  immediately  re-established,  and  therefore  the  phenomenon 
is  not  due  to  a  rise  of  temperature.* 

**It  would  appear  by  the  illustrations  in  the  article,  that  the 
gentleman  furnishing  it  very  ingeniously  succeeded  in  photo- 
graphing the  disturbance  thus  made  among  the  particles  of 
air  by  the  passage  of  an  electric  spark.  The  radiant  quality  of 
such  particles  would  appear  to  be  very  fully  illustrated  in  these 
photographs;  and  in  the  action  of  these  particles  we  may  also 
see  illustrated  that  of  the  very  much  more  subtle  particles 
which  compose  sound.  Whether  by  improved  methods  of 
photography  it  may  yet  be  possible  to  photograph  a  sound 
mist,  spreading  in  air,  as  it  unquestionably  does,  in  all  directions 
from  the  sounding  body,  and  reflecting  after  the  wonderful 
character  of  radiant  matter,  as  is  fully  illustrated  by  echoes, 
Ellen  will  not  undertake  to  say ;  but  the  air  particles  pushed 
by  explosive  gases,  or  excited  into  activity  by  electricity,  are 
no  more  sound  than  a  ball  is  sound  that  comes  back  from  a 
barn  against  which  it  is  thrown. 

**  Ellen  is  very  much  obliged  to  the  professor  who  made  these 
experiments,  for  the  very  beautiful  illustrations  he  has  given  of 
the  reflecting  qualities  of  particles  of  air,  and  hopes  that  he  may 
yet  be  successful  in  photographing  sound,  although,  should 
that  be  accomplished,  it  would  be  as  superfluous  to  call  it 
sound  waves  as  it  would  be  to  refer  to  mist,  or  fog,  or  clouds, 
as  mist  waves,  or  fog  waves,  or  cloud  waves.  The  word  wave 
pertains  to  a  surface,  and  has  no  legitimate  use  anywhere  else." 


\VHISrERINX.S    OF  AN    OLD    IMNE 


339 


**Thcn  there  are  no  waves  in  air?" 

•'Not  similar  to  water  waves;   the  thing  is  impossible/' 

*•  Hut  there  are  differences  of  condensation?" 

*' Constantly,  and  in  every  conceivable  form  and  place. 
And  therefore  the  air  would  be  entirely  ynsuitcd  to  the  carry- 
ing of  symbols.  Rut  the  physicists^  not  being  at  all  respon- 
!^ible  for  results,  assume  and  teach  that  it  is  so  used;  that  by 
sin  arrangement  of  its  molecules  all  the  beauties  of  sound^ 
including  its  innumerable  differences  of  tone  and  inflection,  are 
conveyed,  often  fur  miles,  through  wind  and  rain,  and  the 
thousands  of  different  interferences  that  they  must  constantly 
meet.  Otherwise  all  this  happens  without  cause.  Mr.  Tyndall 
admits  that  the  mind  retires  baOled  from  the  attempt  to  con- 
ceive how  air  waves  could  do  this.  And  w^ell  it  may.  for  it 
would  be  impossible  for  them  to  do  it.  But  all  this  happens; 
and  it  certainly  does  not  take  place  without  a  cause,  and  a 
sufficient  cause,  And  thus,  as  needed,  the  forces  of  radiant 
matter  enter  into  the  economy  of  nature,  easily  accomplishing 
the  phenomena  to  which  they  are  adapted.  New  forces,  then, 
arc  introduced ;  but  man,  not  being  able  to  see  them,  plays  the 
fool,  and  imagines  that  things  are  accomplished  without  an 
adequate  cause — something  that  never  happens  in  all  this 
great  universe. 

'*  Al!  of  this  is  very  wonderful ;  but  it  is  possible.  Ellen  can 
well  believe  the  wonderful,  but  she  refuses  to  believe  the 
impossible.  It  is  indeed  very  wonderful  that  by  such  in  fin- 
itesimal  particles  can  be  carried  all  the  harmonics  and  inflec- 
tions of  sound,  but  Ellen  hardly  believes  that  this  is  any  more 
wonderful  than  are  all  the  phenomena  of  nature;   certainly  not 


340  ELLEN   OR   THE 

SO  wonderful  as  that  the  old  Pine  and  Ellen  can  think,  nor  any- 
more wonderful  to  Ellen  than  the  beauties  that  gaze  out  upon 
her  from  a  flower." 

"But  why  does  Ellen  say  that  anything  is  impossible?  " 

**  Because  with  her  mind  she  perceives  it  to  be  so.  For  mind 
can  easily  distinguish  the  possible  from  the  impossible  in 
nature.  And  there  is  no  part  of  nature,  so  Ellen  thinks, 
nothing  in  this  material  universe,  which  it  is  not  able  to  com- 
prehend." 

**But  it  might  be  mistaken,  might  it  not?" 

"Ellen  doesn't  think  that  in  its  higher  perception  it  can  be 
mistaken.  From  this  it  looks  off  upon  all  material  existence 
and  sees  it  plainly  and  truly.  But  it  is  demonstrable  that  the 
sort  of  result  supposed  by  this  theory  to  be  accomplished, 
cannot  take  place  in  unconfincd  air.  The  claim  is  that  the 
vibration  of  a  tuning  fork,  or  the  motion  of  anything,  whether 
in  vibration  or  otherwise,  in  unconfincd  air,  will  condense 
this  air,  as  the  air  in  a  tube  is  condensed  by  the  shoving 
in  of  a  tightly  fitting  piston.  And  the  further  claim  is 
made  that  the  pulse  thus  formed  in  unconfincd  air  will  be 
propagated  by  clastic  force  the  same  as  a  pulse  made  in  the 
tube.  This  is  the  contention,  and  to  fortify  this  position  the 
scientists  claim  that  the  speed  of  a  pulse  in  a  tube  is  the  same 
as  that  of  sound.  They  also  claim  that  the  speed  of  all  pulses 
is  the  same,  whatever  the  force  making  them,  and  that  they 
will  be  transmitted  with  uniform  velocity.  Thus  Thomas 
Young,  who  with  Huyghens  invented  the  undulatory  theory  of 
light,  says  ('Miscellaneous  Works,'  edited  by  George  Peacock, 
vol.  I ,  page  79)  : 


WHISPERINGS    OF    AN    OLD    PINE  34 1 

*The  uniformity  of  the  motion  of  light  in  the  same  metlium^  which  is 
a  difficulty  in  the  Newtonian  theory,  favors  the  atlmission  of  the  ITuy- 
ghenians ;  as  all  impressions  are  known  to  be  transmitted  through  an 
elastic  fluid  with  the  same  velocity,* 

*'  And  again : 

'  It  has  been  demonstrated  by  M,  De  la  Grange  and  others  that  any 
impression  whatever  communicated  to  one  particle  of  an  elastic  fluid 
will  be  transmitted  through  that  fluid  with  an  uniform  velocity,  depend- 
ing on  the  constitution  of  the  fluid,  without  reference  to  any  supposed 
laws  of  the  continuation  of  that  impression/*' 

"And  docs  not  Ellen  think  that  all  of  this  is  true?" 

"Ellen  knows  that  it  is  not  true.  In  the  first  place  sound 
has  nothing  in  common  with  a  pulse  in  a  tube.  It  rs  some- 
thing entirely  distinct  and  governed  by  wholly  different  laws. 
The  pulse  in  a  tube,  by  whatever  force  started,  will  go  with 
varying  velocity  throughout  its  course,  the  velocity  at  first 
depending  upon  the  manner  in  which  it  is  made.  In  this 
respect  it  is  precisely  opposite  to  what  the  scientists  and 
mathematicians  have  for  over  a  century  asserted  to  be  a  fact." 

**But/*  I  said,  "are  not  the  velocities  of  the  different  pulses 
uniform,  as  Mr,  Young  claimed?'* 

"Not  at  all,"  she  answered.  "Instead  of  being  uniform, 
every  one  varies  according  to  the  intensity  of  the  force  which 
makes  it." 

"But  why,"  I  asked,  "should  so  eminent  a  scientist  and 
mathematician  as  Dr,  Young  blunder  so  badly?" 

"  It  is  precisely  such  that  make  the  trouble,"  she  replied, 
"Ellen  has  quoted  before  that  famous  remark  attributed  to 
Socrates  by  Plato  that  it  is  not  those  who  do  not  know,  and 


342  ELLEN    OR  THE 

know  that  they  do  not  know,  who  make  the  trouble,  but  those 
who  do  not  know  and  think  they  do." 

**  And  Ellen  thinks  that  a  pulse  started  in  unconfined  air  will 
not  act  like  a  pulse  in  a  tube?*' 

"She  is  sure  that  it  will  not." 

"But,"  I  said,  "is  not  the  undulatory  theory  of  sound 
founded  upon  the  supposition  that  it  will  and  does?" 

** Certainly,"  she  answered,  "this  is  its  whole  and  only  basis, 
though  it  is  inconceivable  how  any  sensible  person  could  sup- 
pose it.  For  it  is  as  open  as  the  day  that  a  pulse  in  a  tube 
behaves  as  it  does,  because  of  the  tube.  The  tube  operates  to 
take  away  from  the  air  its  mobility,  giving  to  it  a  certain 
solidity. 

**  Wc  know  how  a  pulse  of  air  acts,  confined  in  a  tube. 
Thus,  suppose  a  long  tube  and  a  piston,  tightly  fitted,  shoved 
in  at  one  end.  The  pulse  will  pass  very  quickly  through  the 
tube,  and  exactly  as  much  air  come  out  of  the  further  end  as 
was  pushed  in  by  the  piston.  So  through  the  whole  length  of 
the  tube,  all  the  particles  of  air  are  shoved  along  this  distance. 
In  this  case  the  air  acts  as  a  stick,  one  end  of  which  would  go 
out  of  the  tube  as  far  as  the  other  end  was  pushed  in,  and 
nearly  at  the  same  moment;  and  so  the  whole  stick  would  be 
advanced  through  the  tube.  The  action  of  the  air  in  the  tube 
is  evidently  produced  by  motion  going  through  the  tube, 
just  as  motion  goes  through  the  stick. 

"  For  in  some  way  motion  enters  into  the  different 
particles  of  a  body,  so  as  to  carry  them,  and  when  it  carries  all 
of  them  it  of  necessity  carries  the  body  which  they  form. 
Thus,    if   all    the    planks    and     timbers    forming    a    ship    are 


WIllSrERlNGS    OV   AN    OLD    I'lNE 


343 


carried,  the  ship  is  carried.  And  if  all  the  particles  forming  a 
stick  are  carried,  the  stick  is  carried.  In  thus  entering  a  body, 
motion  seems  to  act  as  a  fluid.  It  is  stated  that  i(  an  iron  rail 
reached  from  the  earth  to  the  sun,  and  were  pushed  at  one 
end,  it  would  take  1,075    ^^ly^  ^^^  the  other  end  to  move. 

**  Motion  is  divided  into  that  of  translation  when  all  parts  of 
a  body  move  at  once  in  parallel  lines;  motion  of  rotation  when 
the  different  paints  of  the  body  describe  concentnc  circles 
about  its  center;   and  a  combination  of  these  two," 

•*But  what  is  the  motion  called  oscillatory?"  I  asked. 

"Ellen  cannot  see  that  oscillatory  motion  can  exist  anywhere 
excepting  as  there  are  two  reciprocally  operating  forces.  Thus 
a  pendulum  oscillates,  influenced  by  the  two  forces  of  gravity 
and  momentum.  In  water  waves,  gravity  and  momentum  act 
as  in  a  pendulum.  Momentum  is  Mr.  Newton's  principle  of 
inertia  of  motion,  or  supposed  inability  of  a  body  to  alter  the 
condition  in  which  it  exists.  But  this  so-called  inertia  of 
motion,  as  Ellen  thinks,  is  the  result  of  a  moving  sub- 
stance connected  with  the  body  that  moves.  That  is,  it  is  the 
result  of  unbalanced  motion,  motion  itself  being  matter.  When 
this  unbalanced  motion  is  withdrawn  we  have  the  inertia  of  rest* 
Thus  a  ship  moves  because  of  the  motion  imparted  to  it  by  its 
sails.  And  thus  the  ship  acquires  the  inertia  of  motion. 
Withdraw  the  sails  and  it  may  acquire  the  inertia  of  rest.  Thus 
a  chip  upon  a  stream  moves  whilst  the  stream  exists,  but  if  the 
stream  dries  up,  the  chip's  movement  is  stopped.  It  is  not  true 
that  the  chip  has  no  power  of  movement  of  its  own,  for  it  has. 
And  so  everything  has,  but  it  is  a  slow  motion*  and  the  result  of 
disintegration.     So  that,  as  a  chip,  it  may  be  said  to  have  no 


344  ELLEN   OR   THE 

such  motion.  In  its  entirety  it  can  be  moved,  but  cannot  move 
itself.  But  all  motion  is  a  property  of  matter,  the  same  as  exten- 
sion is,  or  mobility,  or  impenetrability,  or  elasticity. 

"There  is  no  question  in  regard  to  the  transmission  of 
motion  through  elastic  bodies.  Take  two  equal  elastic  balls, 
hung  with  threads,  and  let  them  fall  from  equal  heights  in  the 
arc  of  a  pendulum.  Each  bounds  back  equally,  theoretically 
the  distance  that  it  fell,  practically  a  little  less,  some  motion  hav- 
ing been  lost  by  friction.  If  these  balls  fall  in  the  same  arc  from 
unequal  distances,  they  will  apparently  swap  motions  perfectly, 
the  one  falling  in  the  shorter  arc  returning  in  the  arc  of  the 
other,  and  the  one  falling  in  the  longer  arc  returning  in  the 
shorter  one,  thus  apparently  showing  that  what  takes  place  is 
an  interchange  of  motions,  by  which  each  motion  continues 
its  course  unobstructed  by  the  other.  The  same  results  seem 
to  take  place  when  one  ball  is  stationary,  and  single  balls 
of  same  size  arc  let  fall  from  equal  distances  on  each  side. 
And  in  all  cases  where  balls  of  equal  size  arc  dropped  there 
would  appear  to  be  a  transfer  of  motion.  In  all  of  these  cases 
the  motion  is  the  result  of  gravity,  but  it  would  act  the  same, 
however  originating. 

''But  when  balls  of  unequal  sizes  collide,  the  results  appear 
different.  A  small  ball,  thrown  against  a  large  one  at  rest, 
rebounds,  as  a  ball  thrown  against  a  barn  or  wall  rebounds,  only 
not  quite  so  much.  And  by  careful  experiments  with  balls  of 
different  sizes,  and  under  many  different  conditions,  it  appears 
that  in  such  cases  pressure  produces  motion,  and  always  the 
motion  produced  by  a  moving  body  is  in  proportion  to 
momentum,  that  is,  to  the  mass  of  the  body  multiplied  by  the 


WHISPERINGS    OF    .\N    OI.U    PINE 


345 


velocity  with  which  it  is  moving*  And  the  motion  thus  pro- 
duced is  in  the  direction  of  the  moving  body;  or,  if  one  of  tlie 
bodies  is  stationar>%  the  motion  caused  by  the  resistance  of  the 
stationary  body  is  in  opposition  to  that  of  the  body  which 
strikes  it.  This  law  and  the  further  one  that  opposite  motions 
destroy  each  other,  while  partially  opposing  motions  produce 
resuhants,  appear  to  be  the  laws  of  all  motion, 

*'  But  motions  are  substances ;  that  is,  they  are  matter  in  one 
or  more  of  its  phases.  And  therefore,  like  all  matter,  they  arc 
indestructible.  But  motion  is  energy,  and  hence  energy  is 
indestructible  That  it  h  so  is  a  great  truth  which  modern 
science  has  blundered  upon,  though  not  perceiving  that  it  is 
but  another  way  of  proclaiming  the  indestructibility  of 
matter. 

'*The  fundamental  and  universal  law  of  motion  is  that 
it  is  rectilinear;  though  the  old  Pine  mustn't  be  confused 
in  its  possibilities,  as  it  may  be  rectilinear  in  any  direction. 
And  this  with  the  law  of  resultants  provides  for  motion  every- 
where, or  in  any  direction.  Surely  these  are  very  simple  laws 
for  such  wonderful  results.  It  is  these  that  make  the  old  Pine's 
whisperings.  For  his  leaves  are  ever  moving  like  a  restless 
sea.  Thus,  then,  comes  all  motion ;  and  this  includes  that  of 
electricity  and  sound.  For  the  motion  that  passes  through  air 
in  a  tube,  or  the  motion  that  passes  Into  and  through  a  stick, 
when  it  is  pushed,  causing  it  to  move;  or  the  motion  that 
passes  through  a  train  of  cars  when  they  arc  pushed,  causing 
them  to  move, —  all  motion  is  a  result  of  pressure,  and  pressure 
is  a  result  of  contact.  It's  an  awfully  simple  way  to  get  up 
motion,  isn't  it?*' 


346  ELLEN   OR  THE 

"Yes,"  I  replied;  ** there  couldn't  be  any  simpler  method. 
But  when  opposing  motions  meet  and  destroy  each  other,  what 
becomes  of  them?** 

"They  are  changed  into  something  else — probably  heat. 
We  know  that  at  the  same  time  heat  is  produced.  Possibly  a 
certain  part  of  such  motion  is  changed  into  something  besides 
heat.  Ellen  does  not  know,  but  apparently  the  most  of 
it,  if  not  all,  is  changed  into  heat.  And  thus  again  is  evident 
the  transformation  of  matter." 

"But  is  not  the  transformation  too  sudden,"  I  asked,  '•to 
represent  that  of  matter?" 

"Not  at  all.  For  the  transformations  of  matter,  so  far  as 
we  can  perceive,  are  not  limited  in  time.  With  some  things, 
as  rocks,  or  mountains,  or  spheres,  ages  arc  consumed  in 
the  process  of  decay.  With  others,  as  animals  and  plants,  a  few- 
brief  years,  more  or  less.  And  again,  as  soap  bubbles,  or 
gases,  or  in  many  chemical  changes,  that  by  electricity  for 
instance,  or  in  light  or  heat,  the  transformation  may  be  nearly 
instantaneous.  As  the  world  is  full  of  collisions,  there  must  be 
a  constant  supply  of  heat  being  produced." 

**And  what  becomes  of  the  surplus  heat?" 

"Probably  under  pressure  it  is  in  part  drawn  upon  to  form 
motion.  But  it  is  very  evident  that  the  different  changes 
follow,  in  some  form,  nature's  great  system  of  circulatory 
action. 

"  The  destruction  or  partial  destruction  of  one  thing  always 
precedes  the  formation  of  another.  For  it  is  the  same  matter 
that  makes  all ;  nor  can  the  same  matter  make  more  than  one 
thing  at  a  time.      It  cannot  be  in  two  different  places   at  the 


WHISPERINGS   OF   AN   OLD    PINE  347 

same  time.  Ellen  understands  that  the  scientists  do  not  recog- 
nize this  last  law,  as  illustrated  in  the  kinetic  theory  of  gases 
and  their  theories  of  light,  heat,  etc.,  but  that  is  because,  like 
all  those  who  embrace  superstitions,  they  have  entirely  lost 
their  heads." 


34^  ELLEN   OR  THE 


XXII. 


^^IT  is  clastic  force  that  pushes  the  air  in  the  tube,  is  it  not^ 

1     Ellen?" 

**  Call  it  clastic  force,  or  call  it  motion.  It  must  be  similar 
to,  if  not  the  same  as,  that  which  moves  the  stick." 

"Then  Ellen  doesn't  chink  that  the  air  in  a  tube,  influenced 
by  the  shoving  of  a  tight-fitting  piston,  will  act  the  same  as  the 
unconfined  air  under  the  same  influence?" 

**The  old  Pine  ought  not  to  ask  Ellen  so  foolish  a  question." 

**But  Ellen  will  please  tell  the  old  Pine  how  differently  it 
will  act." 

*'The  difference  would  be  like  that  between  darkness  and 
day;  it  would  literally  be  world-wide.  For  in  a  tube,  the  air 
being  confined  would  act  as  ICllcn  has  said ;  but  in  unconfined 
air  from  the  same  force  there  would  be  very  much  less  notice- 
able disturbance,  ^^')r  because  of  the  mobility  of  the  air  the 
pressure  exerted  wtnild  spread  in  all  directions  and  be  soon 
dissipated.  Hy  the  hypothesis  we  have  the  same  force,  and 
the  same  force  will  produce  the  same  momentum ;  but  the 
momentum  is  equal  to  the  mass  into  the  velocity.  Then  if 
the  mass  increases  the  velocity  must  diminish,  or  if  the  mass 
diminishes  the  velocity  will  increase." 

"But  what  becomes  of  the  theory  (^f  sound,  Ellen?" 

"There  isn't  any  theor}',"  she  answered,  "except  the  entity- 
theory.  For  an  intelligent  explanation  of  a  pulse  in  a  tube 
shows  that  the  other  never  had  any  existence. 


"  Ellen  will  quote  to  the  old  Pine  a  very  plain  exposition  of 
the  action  o!  energ)'^  or  force,  something  which  every  scientist 
ought  to  know  as  perfectly  as  a  bright  schoolboy  knows  the 
multiplication  table.  It  is  from  *  Force,'  one  of  the  excellent 
scientific  books  written  especially  for  the  young,  by  Jacob 
Abbott : 


*  Lawrence  went  on  to  say  that  the  principle  which  he  referred  to  was 
this:  that  force  was  an  agency  that  existed  always  in  definite  and 
measurable  quantities,  such  that,  though  it  might  be  transferred  from 
one  place  of  deposit  to  another,  and  so  be  accumulated  or  dispersed,  it 
could  not  in  any  way  be  increased  or  diminished. 

'"Yes/*  said  John,  "it  can  be  increased;  for  when  your  grindstone 
was  spinning  round  very  fast,  it  exerted  a  great  deal  more  force  than 
Rick  did  by  the  power  of  his  foot." 

'"It  exerted  more  force  in  any  one  instant*'  said  Lawrence,  "than 
Rick  could  exert  in  that  instant;  but  the  whole  amount  of  all  the  im- 
pulses that  Rick  gave  to  it  was  equal  to  all  that  the  grindstone  could 
exert ;  that  is,  there  was  in  the  stone  an  accumulation  of  a  great  many 
small  forces,  and  not  any  increase  of  the  whole  amount. 

*'*  It  was  like  filling  a  pail  with  water  by  pouring  in  a  great  many 
mugsful  from  a  spring,"  continued  lawrence.  "  It  is  true,  you  may 
increase  the  quantity  that  is  in  the  pail^  and  in  that  sense  we  may  say 
there  is  an  increase;  but  there  is  no  actual  increase  on  the  whole,  for 
the  amount  that  is  in  the  pail,  when  it  is  full,  is  only  made  up  of  the 
separate  amounts  of  all  the  dipperfuls*  There  can  not  be,  absokitely, 
in  the  whole  amount,  any  increase  or  diminution/* 

*  "There  might  be  a  diminution,*'  said  John,  "for  some  of  the  water 
might  be  spilled." 

'"True,"  replied  lawrence,  "a  part  might  be  spilled,  and  a  part 
might  dry  up;  but  none  of  it  would  cease  to  exist  on  that  account. 


352  ELLEN   OR   THE 

Wherever  it  went  when  it  was  spilled,  or  wherever  the  vapor  went  of 
that  which  was  turned  into  vapor,  there  it  would  be.  There  might  be  a 
diminution  of  the  quantity  in  the  pail,  but  there  could  be  no  diminution 
of  the  actual  amount  of  water  employed  in  the  experiment.  Preciocly 
the  same  amount,  neither  any  more  nor  any  less,  would  exist  somewhere 
at  the  end  of  the  experiment  that  existed  at  the  beginning. 

'"And  it  is  just  so  in  respect  to  force,"  continued  I^wrence.  "Pre- 
cisely the  same  quantity  that  we  have  at  the  commencement  of  any 
process,  or  at  the  entrance,  so  to  speak,  of  any  combination  of  machin- 
ery, exists  somewhere  at  the  end  of  the  process;  or,  in  the  case  of 
machinery,  must  be  stored  in  it,  or  must  issue  from  it  in  some  way. 
There  can  not  possibly  be  any  real  gain  or  loss  of  force  any  more  than 
there  can  be  of  water.  A  great  many  small  or  gentle  forces  may  be 
combined  to  make  a  great  one,  and,  on  the  other  hand,  a  great  one  may 
be  subdivided  into  many  small  ones,  but  there  can  not,  in  either  case, 
be  any  absolute  increase  or  diminution  of  the  amount."  * 

*' Again  it  is  evident  that  this  thing  force  consists,  as  all 
things  else,  of  the  same  wonderful  matter,  of  which  all  things. 
—  force  as  well  as  those  things  which  we  do  not  consider  as 
force, —  are  made.  The  law  of  its  creation  is  the  same  as  that 
of  an  orange,  or  any  other  material  thing.     Faraday  says : 

'I  have  long  held  an  oi)inion,  almost  amounting  to  conviction,  in 
common,  I  believe,  with  m:iny  other  laws  of  natural  knowledge,  that 
the  various  forms  under  which  the  forces  of  matter  are  made  manifest, 
have  one  common  origin  ;  or,  in  other  words,  are  so  directly  related 
and  mutually  dependent,  that  they  are  convertible,  as  it  were,  one  into 
another,  and  possess  equivalents  of  power  in  their  action.' 

"But  this  is  true  of  all  matter  and  is  the  essential  part  of  the 
principle  that  nothing  is  or  can  be  destroyed. 


WHISPERINGS    OF  AN    OLD    PINK 


353 


"And  thus,  too»  thought  and  the  emotions  as  manifested  to 
us  arc  made,  as  Ellen  thinks,  out  of  the  same  matter,  by  the 
same  law  of  combination.  For  they,  too,  must  be  made  of 
something.  But  in  this  material  universe  there  is  nothing  else 
but  matter  to  make  things  of,  hence  they  must  be  made  of 
matter.  Ihat  they  are  is  also  evident,  because,  as  Ellen  has 
said  before,  we  see  them.  They  are  plainly  visible  in  the 
thoughtful  or  emotional  expression.  Nor  do  we  see  such 
expression  except  as  thought  or  emotion  exists.  With  the 
idiotic  all  thoughthil  expression  is  absent,  and  it  is  absent 
because  they  do  not  think. 

*' Again,  all  our  sensations  are  the  result  of  material  condi- 
tions. And  it  Is  equally  true  that  all  material  things  are  the 
possible  source  of  sensations.  And  these  sensations  arc  of 
every  conceivable  variety,  yielding  both  pleasure  and  pain, 
instruction  and  amusement.  But  thought  nnd  the  emotions 
are  sources  of  sensation.  And  this  is  further  evidence  that 
they  arc  material 

**And  thus  all  things  in  this  material  universe  are  made  of 
that  substance  which  we  call  matter.  For  God.  when  lie  made 
the  material,  made  it  sufficient  for  every  purpose. 

"And  all  things  are  made  by  machinery^  constructed  by  mind. 
This  machinery  may  be  ver>'  simple,  or  it  may  be  quite  com- 
plex, but  always  in  some  form  it  exists.  The  machinery  which 
makes  vision  is  quite  complex.  That  which  makes  light  may 
be  more  simple.  That  which  makes  thought,  again,  is  more 
complex,  connected  with  the  gray  matter  of  the  brain.  But 
there  is  or  can  be  no  thought  or  emotion  made  manifest  in 
fnaterial  conditions  without  the  proper  machinery  to  make  it. 


354  ELLEN   OR   THE 

"All  science  which  does  not  recognize  the  distinction 
between  mind  and  matter  is  folly;  else,  as  Ellen  has  said,  the 
spade  could  make  the  man  as  well  as  the  man  the  spade.  All 
science  which  does  not  recognize  the  universality  of  nature's 
laws,  both  of  mind  and  matter,  is  baseless ;  for  science  consists 
alone  in  the  order  made  possible  and  made  certain  because 
of  such  laws.  And  this  is  what  the  Bible  means  nhen  it  says 
that  God  made  man  after  His  own  image.  And  therefore  the 
perception  of  the  manner  in  which  things  are  made  by  us 
permits  us  to  know  how  all  things  are  made.  This  is  the 
knowledge  that  we  have  of  the  creation,  and  all  that  we  have. 
Besides  this  there  are  only  opinions,  which  are  bad,  all. 

**  Is  it  possible  that  scientists  suppose  that  a  great  force,  or  • 
any  force,  subdivided  into  many  small  ones,  produces  the  same 
effects  as  though  it  was  not?  According  to  the  undulatorj" 
theory  of  sound  they  believe  exactly  this.  Wouldn't  it  be 
well  for  any  sensible  man,  whether  scientist  or  not,  to  give  up 
a  theory  which  teaches  so  great  an  absurdity? 

"Take  a  pail  of  water.  Does  any  one  suppose  that  it  will  act 
the  same  if  thrown  upon  a  flat  surface,  as  it  would  if  turned  into 
a  channel?  Will  it  run  as  fast,  or  will  it  go  as  far?  In  think- 
ing of  such  self-evident  propositions,  the  intelligent  answer  to 
which  entirely  does  away  with  all  undulatory  theories,  Ellen  is 
led  again  to  ask,  —  In  order  to  be  a  scientist  is  it  necessary 
that  one  should  be  a  fool? 

**  Eor  scientists  and  the  text  books  base  the  undulator\' 
theory  of  sound  upon  the  action  of  a  pulse  in  a  tube;  and, 
indeed,  have  absolutely  nothing  else  whatever  to  base  it  on. 
Thus  Ganot  says: 


WinsrE RINGS   OF   AN    OLD    PINE  355 

*  In  order  to  sirapllly  the  theory  of  the  propagation  of  sound  in  air, 
we  shall  first  consider  the  case  in  which  it  is  propagated  in  a  cylindrical 
tube  of  indefinite  length.  Let  MN  (fig*  17)  be  a  tube  filled  with  air  at 
a  constant  pressure  and  temperaliire,  and  let  P  be  a  piston  oscillating 
rapidly  from  A  to  a.  When  the  piston  passes  from  A  to  a  it  com- 
presses the  air  in  the  tube*  But  in  consequence  of  the  great  compres- 
sibility, the  condensation  of  the  air  does  not  lake  place  at  once  through- 
out the  whole  length  of  the  tube,  but  solely  within  a  certain  length,  ^H, 
which  is  called  the  contiensfd  wave, 

'If  the  tube  MN  be  supposed  to  be  divided  into  lengths  equal  to  all, 
and  each  of  these  lengths  divided  into  layers  parallel  to  the  piston,  it 


Fig.  17- 
may  be  shown  by  calculation  that,  when  the  first  layer  of  the  wave  ^H 
comes  to  rest,  the  motion  is  communicated  to  the  first  layer  of  the 
second  wave  HH',  and  so  on  from  layer  to  layer  in  all  parts  of  H'H^, 
H^H'",  The  condensed  wave  atlvances  in  the  tube,  each  of  its  parts 
having  successively  the  same  degree  of  velocity  and  condensation.* 

■*Thc  last  statement,  which  in  this  theory  is  the  essential  one, 
is  not  true;  but,  on  the  contrary,  experiment  proves  that  the 
speed  of  this  pulse  diminishes  throughout  its  course,  and  there- 
fore each  of  its  parts  cannot  have  successively  the  same  degree 
of  velocity  and  condensation, 

**  Mr.  Ganot  further  says: 

*  When  the  piston  returns  in  the  direction  of  <j  A,  a  vacuum  is  pro- 
duced behind  it,  which  causes  an  expansion  of  the  air  in  contact  with 
its  postcnor  face*    The  next  layer,  expanding  in  tiirn,  brings  the  first 


356  ELLEN   OR  THE 

to  its  original  state  of  condensation,  and  so  on  from  layer  to  layer. 
Thus  when  the  piston  has  returned  to  A,  an  expanded  wave  is  produced 
of  the  same  length  as  the  condensed  wave,  and  directly  following  it  in 
the  tube  where  they  are  propagated  together,  the  corresponding  layers 
of  the  two  waves  possessing  equal  and  contrary  velocities. 

'The  whole  of  a  condensed  and  expanded  wave  forms  an  undulation; 
that  is,  an  undulation  comprehends  that  part  of  the  column  of  air 
affected  during  the  backward  and  forward  motion  of  the  piston.  The 
length  of  an  undulation  is  the  space  which  sound  traverses  during  a 
complete  vibration  of  the  body  which  produces  it.  This  length  is  less 
in  proportion  as  the  vibrations  are  more  rapid.' 

"These  paragraphs  must  be  both  untrue,  for  when  the 
piston  is  returned,  a  much  greater  rarefaction  is  produced  than 
that  in  advance  of  the  first  pulse  formed,  and  therefore  that 
pulse  will  cease  to  advance,  being  caught  in  its  progress  and 
drawn  back.  There  can  be  no  question  about  this  if  the  tube 
is  long  enough,  for  the  speed  of  the  pulse,  or,  in  this  case,  of 
two  pulses,  will  be  in  proportion  to  the  force  acting.  But  after 
the  return  of  the  piston  the  force  acting  and  the  only  force 
acting  is  the  clastic  force  of  the  air.  And  as  this  will  have  much 
better  opportunity  to  act  on  the  retrogressive  pulse,  the  latter 
must  soon  reach  the  advance  pulse,  when  the  result  spoken  of 
will  take  place,  and  all  the  air  of  the  tube  will  return  to  its 
original  position. 

"  It  follows,  that  if  this  theor>^  is  true,  the  rarefactions  must 
travel  faster  than  the  condensations,  and  therefore  it  would  be 
impossible  for  the  two  to  form  the  so-called  wave  length,  or  to 
have  any  permanent  connection  with  each  other.  Perceiving 
this  fact,  it  has  been  asserted  by  some  physicists,  who  were  not 


WHISPKKINGS    OF   AN    OLD    lUNE 


357 


clear-headed  enough  to  perceive  that  the  whole  thing  is  a 
humbug,  that  sound  is  accomphshed  alone  by  the  condensa- 
tions. And  the  fact  that  ear  drums  are  concave  ^^thhi,  so  that 
they  could  not  bend  in  without  stretching,  has  been  offered  as 
further  proof  of  this. 

"Mr.  Robert  Moon  demonstrates  mathematically  that  rare- 
factions would  go  faster  than  condensations,  as  reported  in  the 
•Proceedings  ol  the  Royal  Society  of  London,"  vol  9,  which 
says : 

'Reverting  to  the  equation  of  sound,  which  (neglecting  terms  of  the 
second  order)  may  be  put  under  the  form 

dt-'  dx"'  dxut 

the  author  next  shows  that  if  the  initial,  disturbance  consist  of  a  con- 
densation  alone,  it  will  be  transmitted  with  the  velocity  a  (/— r)  the 
direction  in  which  its  particles  are  moving ;  and  that  if  it  consists  of  a 
rarefaction  alone,  it  will  be  transmitted  with  the  velocity  a  (/-f^)  in  the 
direction  contrary  to  that  in  which  its  particles  are  moving.  It  is  here 
shown  also  incidentally,  that  whether  the  resistance  be  taken  into 
account  or  not,  the  particles  of  a  wave  of  condensation  must  all  move 
in  the  same  direction,  which  will  be  the  direction  of  transmission ;  and 
the  particles  of  a  wave  of  rarefaction  will  all  move  in  the  same  direc- 
tion, which  will  be  contrary  lo  that  of  transmission, 

*In  confirmation  of  the  conclusion  that  waves  of  rarefaction  arc 
transmitted  more  rapidly  than  waves  of  condensation,  the  author 
adduces  the  fart,  that  when  explosions  of  gunpowder  have  taken  place, 
the  glass  in  wimlows  has  been  observed  to  break  outwards  rather  than 
inwards, 

*It  is  then  suggested,  that,  as  when  sound  is  produced,  a  condensa- 
tion and  rarefaction  of  air  usually  occur  in  immediate  succession,  if 


358  ELLEN    OR   THE 

both  kinds  of  disturbance  were  capable  of  affecting  the  human  ear,  we 
should  hear  sounds  double ;  and  as  we  know  practically  that  this  is  not 
the  case,  it  is  contended  that  only  one  kind  of  disturbance,  i.  e.,  either 
rarefaction  alone,  or  else  condensation  alone,  can  stimulate  the  ear. 

'It  is  shown  to  be  a  priori  probable,  that  if  one  of  the  two  classes  of 
aerial  disturbances  is  suppressed  by  the  ear,  that  one  would  be  disturb- 
ance by  condensation,  inasmuch  as  waves  of  rarefaction  being  swifter, 
would  better  perform  the  duty  entrusted  to  them :  and  it  is  pointed  out 
that  if  the  sensation  of  sound  is  produced  by  aerial  rarefactions  alone,  a 
difficulty  attending  the  received  theory  will  be  obviated,  by  reason  of 
the  velocity  deduced  upon  that  theory  being  too  small.' 

**Mr.  Ganot  continues : 

*It  is  important  to  remark  that  if  we  consider  a  single  row  of  par- 
ticles, which  when  at  rest  occupy  a  line  parallel  to  the  axis  of  the  cyl- 
inder—  for  instance,  those  along  AH"  (fig.  17) — we  shall  find  they 
will  have  respectively  at  tlie  same  instant  all  the  various  velocities  which 
the  piston  has  had  successively  while  oscillating  from  A  to  a  and  back 


l-ig.  18. 

to  A.  So  that  if  in  fipj.  iS  AH'  represents  the  length  of  one  undula- 
tion, the  curved  line  H'PQA  will  rei)rcsent  the  various  velocities  which 
all  the  jjoints  in  the  line  AH'  have  simultaneously ;  for  instance,  at  the 
instant  the  piston  has  returned  to  A,  the  particle  at  M  will  be  moving  to 
the  right  with  a  velocity  represented  by  QM  ;  the  particle  at  N  will  be 
moving  to  the  left  with  a  velocity  represented  by  PX,  and  so  on  of  the 
other  particles.' 

**  There  is  no  truth  whatever  in  any  of  this,  as  the  experi- 
ments of  M.  Rcgnault  and  others,  which  Ellen  will   give  further 


WHISPERINGS    OF   iVN    OLD    PINE 

oti.  have  demonstrated.     Since,  as  proven,  the  line  AH*  does 
not  represent  the  length  of  one  undulation,  it  is  not  necessary 
to  consider  the  imaginar)^  undulatory  line. 
"Again  Ganot  says: 

*  When  an  undulatory  motion  is  transmitted  through  a  medium,  the 
motions  of  any  two  particles  are  saitl  to  be  in  the  same  phase  when 
those  particles  move  with  equal  velocities  in  the  same  direction ;  the 
motions  are  said  to  be  in  opposife  phases  when  the  particles  move  with 
the  same  velocities  in  opposite  directions.  It  is  plain  from  an  inspec- 
tion of  fig.  1 8  that  when  any  two  particles  are  separated  by  a  distance 
equal  to  half  an  undulation,  iheir  motions  are  always  in  opposite  phases^ 
but  if  their  distance  equals  the  length  of  a  complete  undulation  their 
motions  are  in  the  same  phase,  A  little  consideration  will  show  that  in 
the  condemed  wave  the  condensation  will  be  greatest  at  the  middle  of 
the  wave,  and  likewise  that  the  expanded  wave  will  be  most  rarefied  at 
its  middle.' 

•*  Under  no  circumstances  do  particles  of  a  pulse  in  a  tube 
move  with  equal  velocities ;  and  therefore  it  would  be  impos- 
sible for  them  to  be  in  the  same  phase  according  to  this  defini- 
tion. Nor.  the  unequal  oscillations  and  consequently  unequal 
velocities  of  these  particles  being  admitted,  can  the  last  part  of 
the  statement  be  true, 

*'Mr.  Ganot  continues: 

It  is  an  easy  transition  from  the  explanation  of  the  motion  of  sound 
waves  in  a  cylinder  to  that  of  their  motion  in  an  unenclosed  medium. 
It  is  simply  necessary  to  apply  in  all  directions  to  each  molecule  of  the 
\ibrating  body  what  has  been  said  about  a  piston  movable  in  a  tube. 
A  scries  of  sphencal  waves  alternately  condensed  and  rarefied  is  pro- 
dnced  around  each  center  of  disturbance.     As  these  waves  are  coii' 


36o  ELLEN   OR   THE 

tained  within  two  concentrical  spherical  surfaces,  whose  radii  gradually 
increase,  while  the  length  of  the  undulation  remains  the  same,  their 
mass  increases  with  the  distance  from  the  center  of  disturbance,  so  that 
the  amplitude  of  the  vibration  of  the  molecules  gradually  lessens,  and 
the  intensity  of  the  sound  diminishes.  It  is  these  spherical  waves, 
alternately  condensed  and  expanded,  which  in  being  propagated  trans- 
mit sound.' 

**In  the  above  a  pulse  has  been  exploited  in  a  tube  and 
called  a  sound  wave.  The  whole  conception  is  one  of  the 
grossest  ignorance  and  is  utterly  untrue.  Now,  Mr.  Ganot 
says  that  it  is  an  easy  transition  from  the  explana- 
tion of  a  fictitious  sound  wave  in  a  tube  to  that  of  a 
fictitious  one  in  the  open  air.  This  may  be  true.  Who- 
ever could  talk  of  the  one,  might  readily  of  the  other,  but  any 
one  would  have  to  be  densely  ignorant  of  fundamental 
mechanical  principles  to  suppose  the  action  of  one  similar  to 
that  of  the  other  in  either  velocity  or  distance  passed  over. 

**  There  follows  the  glib  remark  of  one  scientist,  imitating 
other  scientists,  about  spherical  waves,  of  which  Mr.  Challis, 
professor  for  many  years  of  astronomy  in  the  University  of 
Oxford,  England,  and  one  of  the  most  eminent  mathematicians 
of  the  last  century,  and  withal  in  addition,  which  is  of  far  more 
consequence  in  the  discussion,  an  honest  man,  says  ('Philo- 
sophical Magazine,'  vol.  33)  : 

'Before  I  proceed  with  the  inquiry  carried  on  in  several  preceding 
numbers  of  this  joumal,  I  wish  briefly  to  notice  the  views  put  forth  by 
Mr.  Stokes  in  the  November  number,  respecting  a  supposed  remarkable 
difficulty  in  the  Theory  of  Sound  which  he  says  that  I  have  pointed  out. 
What  he  alludes  to  I  have  not  myself  called  a  difficulty,  nor  do  I  so 


VViUSrERLXGS 


)LD    PINE 


regard  it.  By  an  investigation  contained  in  the  '*  Philosophical  Maga- 
rine"  for  last  April,  1  founrl  that  the  general  character  of  aerial  vibrations 
is  non-divergence,  and  that  the  lhto*etical  velocity  of  sound  is  different 
from  that  usually  adopted.  Mr.  Airy  urged  against  these  conclusions, 
that  my  equations  represent  a  particular  case  of  the  propagation  of 
plane  waves :  in  answer  to  which  I  proved,  by  a  nductio  ad  alntirdum^ 
that  plane  waves  are  physically  impossible.  This  proof ,  which  forms  the 
subject  of  Mn  Stokes's  remarks,  is  given  in  the  "  Philosophical  Maga- 
zine," S.  3,  vol.  xxxii.,  from  line  16  of  page  496  to  line  12  of  page  497. 
The  absurdity  to  which  the  hypothesis  of  plane  waves  conducts  is,  that 
the  points  of  maximum  velocity  and  of  no  velocity  in  the  same  wave 
may  be  at  the  same  ijoinl  of  s|iace  at  the  same  time.  Mr.  Airy  did  not 
reply.  Mr.  Stokes,  however,  undertakes  to  maintain  jjlane  waves  by 
the  following  considerations.  He  first  finds  that  11  point  of  maximum 
velocity  of  a  wave  travels  at  a  rate  different  from  that  of  a  point  of 
no  velocity,  and  consequently  that  there  is  at  least  great  danger  of  one 
overtaking  the  nther.  When  this  absurdity  is  on  the  point  of  being 
consummated,  the  wave,  as  he  coficfiv^s  (for  there  is  nothing  in  the 
analysis  to  indicate  such  a  result),  is  converted  into  a  breaker.  What 
the  subsequent  motion  is  Mr,  Stokes  thinks  it  would  not  be  worth  while 
to  inquire,  but  jiroceeds  to  support,  by  considerations  which  it  is  not 
necessary  to  parti<  ularize,  the  possibility  of  the  physical  existence  of  a 
surface  of  discontinuity  at  the  position  where  the  abrupt  alteration  of 
the  character  of  the  wave  takes  place.  How  then  stands  the  question? 
According  to  my  reasoning  plane  waves  are  physically  impossible; 
according  to  Mr.  Stokes's,  plane  waves  are  wholly  ifuompatible  with  the 
transmission  of  articulate  and  musiial  sounds.  The  only  conclusion 
from  either  result  is,  that  the  h>q)othesis  of  plane  waves  is  inadmissible, 
'It  may,  however,  be  urged  that  spherical  waves  are  physically  pos- 
sible \  and  that  as  these  become  plane  waves  at  an  infinite  distance 
from  the  center,  the  latter  are  also  physically  possible.     I  have  already 


364  ELLEN   OR  THE 

met  this  argument  in  the  communication  above  referred  to;  but  as  the 
reasoning  is  given  briefly,  and  may  possibly  have  been  overlooked,  I 
will  repeat  it  here.  I  take  the  results  of  the  hypothesis  of  spherical 
waves  as  they  are  given  in  Poisson's  "Trait  de  M^canique"  (vol.  i, 
page  706,  2d  ed.),  and  as  they  are  commonly  admitted.  The  pressure/ 
being  a^{i  -\-a),  the  following  expression  is  obtained  for  the  condensa- 
tion a  at  the  distance  r  from  the  center  at  the  time  /, 

a  r 

and  it  is  stated  that  there  is  no  condensation  wherever  /•  is  greater  than 
a/-\-€,  and  less  than  a  i—t,  2  c  being  the  breadth  of  the  sonorous  undu- 
lation. Hence,  supposing  2  c  very  small  compared  to  r,  and  putting  for 
r  outside  the  function,  its  value  a  t  corresponding  to  the  middle  of  the 
wave,  the  quantity  of  matter  existing  at  any  time  in  the  wave  beyond 
what  would  occupy  the  same  space  in  the  quiescent  state  of  the  fluid,  is 
very  nearly 

(f{at-r)Ar 
ii  -  / 

the  integral  being  taken  from  rz^a  t—t  to  r^=^ii  t-\-t.  Calling  A  the 
constant  value  of  this  integral,  the  expression  for  the  <iuantity  of  matter 
becomes  47rA/.  Hence  the  matter  increases  in  quantity  7vith  the  time  ! 
Now  the  very  equations  from  which  tliis  result  is  derived  are  founded 
on  the  supposition  that  the  quantity  of  matter  is  constant.  There  is 
consequently  no  difficulty  here  which  any  physical  considerations  can 
explain,  but  strictly  a  redueiio  ad  alnurdiimy  which  necessitates  the 
important  conclusion  that  the  hypothesis  of  spherical  waves  is  inadmis- 
sible. The  physical  impossibility  of  plane  waves  was  proved  by  the 
same  kind  of  reasoning;  and  any  attempt  to  reconcile  the  contradiction 
in  either  case  is  simi)ly  illogical.  As  neither  the  hypothesis  of  plane 
waves  nor  that  of  spherical  waves  is  admissible,  the  theoretical  value  of 


WHISPERINGS   OF   AN   OLD    PINE  365 

sound  which  rests  011  those  hypotheses  necessarily  fails  of  sui>|iort.  I 
return  now  to  the  consideration  of  non-divergent  waves,  or  as  they  may 
also  be  called,  ray  viif rattans,* 

**Mr.  Ganot  further  says: 

'If  many  fKiints  are  disturbed  at  the  same  time,  a  system  of  waves  is 
produced  around  each  point.  But  all  these  waves  are  transmittcil  one 
through  the  other  without  modifying  either  their  lengths  or  their  veloci- 
ties. Sometimes  condensed  or  expanded  waves  coincide  with  others  of 
the  same  nature  to  produce  an  effect  equal  to  their  sum;  sometimes 
they  meet  and  produce  an  effect  equal  to  their  difference.  If  the  sur- 
face of  still  water  is  disturbed  at  two  or  more  points,  the  cO'Cxistence 
of  waves  becomes  sensible  to  the  eye-' 

"And  this  he  says  after  having  distinctly  stated  in  the  open- 
ing chapter  of  his  book  that  the  intimate  character  of  all  these 
agents  is  completely  unknown.  Ellen  will  quote  again  this 
remarkable  statcmcntt  illustrating  how  very  different  a  scientist 
talks  when  telling  the  truth  from  what  he  docs  when  teaching 
science: 

*  In  the  present  state  of  science  we  cannot  say  whether  they  [the  so- 
called  imponderable  agents,  of  which  sound  is  one]  are  properties 
inherent  in  matter,  or  whether  they  result  from  movements  impressed 
on  the  mass  of  subtle  and  imponderable  forms  of  matter  rliffused  through 
the  universe/ 

*'The  statement  that  all  these  waves  are  transmitted  one 
through  the  other  without  modifying  either  their  length  or  their 
velocities  evinces  a  talent  that  Baron  Munchausen  might  well 
have  envied. 


366  ELLEN    OR   THE 

**  As  usual  at  this  emergency,  to  sustain  glaringly  impos- 
sible conditions,  the  narrator  falls  back  upon  the  delusion  of 
water  waves." 

"And  doesn't  Ellen  think  that  the  pulse  in  a  tube  is  moving 
at  the  rate  of  sound  ?  " 

"She  does  not;  for  she  thinks  that  sound  moves  always  at 
the  same  speed  as  far  as  it  can  be  heard,  and  she  knows  that 
the  speed  of  a  pulse  in  a  tube  varies  throughout  its  course.'* 

**  And  doesn't  Ellen  think  the  pulse  in  a  tube  sound?" 

"She  knows  that  it  is  not." 

"And  doesn't  she  think  it  carries  sound?" 

"Not  as  a  pulse.  For  if  it  did  it  would  carry  it  in  uncon- 
fined  air  as  well,  and  there  would  be  a  great  difference  in  the 
speed  of  the  two.  But  there  is  no  such  difference  in  the  speed 
of  sound. 

"But  what  takes  place  always  when  a  piston  or  anything 
else  is  pushed  in  a  tube  or  in  unconfined  air,  is  the  propaga- 
tion of  motion.  And  Ellen  will  repeat:  in  a  tube  this  motion 
may  extend  for  a  lonj^  distance,  in  unconfined  air  but  a  short 
distance,  bcin^:^  dissipated  in  all  directions;  and  in  each  case  the 
velocity  of  the  movement  would  diminish  with  the  distance. 
It  would  hardly  be  possible  to  consider  a  simpler  problem 
than  this." 

"It  seems  to  the  old  Pine,"  I  said,  *'  that  certainly  teachers  of 
science  and  mathematical  principles  should  not  fail  to  see  a 
thing  so  plain." 

"The  failure  is  a  ridiculous  one,"  she  said,  "and  yet  mathe- 
maticians will  spend  much  time  in  ciphering  about  impossible 
wave  motion   and  other  absurd  theories  like  that  of   the  tides. 


VVinSPERlNGS    UV  AX   *H.I)    IMNE 


3^7 


and  publishers  ni  cncyclopaudias  and  text  books  will  allow  them 
to  be  filled  with  the  nonsense.** 

'*And  isn't  Ellen  over  severe,"  I  askcdi  **in  her  criticisms  of 
mathematics  and  mathematicians?'* 

*•  Mathematics  are  a  beautiful  and  delightful  study,"  she 
replied  ;  "  a  Itttle  hard  at  first  to  some,  though  readily  mastered 
by  most  with  proper  application  and  capable  assistance/* 

•'  But  is  not  mathematics  a  singular  noun?'"  1  asked. 

**  It  is  in  German,  French  and  Latin,  being  so  spelled,  and  so 
formerly  the  word  mathematic  was  used  in  Engh'sh,  but  as  now 
in  English  it  has  the  plural  form,  and  as  also  in  its  nature  it  is 
plural,  being  composed  of  several  parts,  Ellen  does  not  care 
to  follow  a  usage  which  would  make  it  singular.  If  it  is 
desired  to  consider  it  singular,  the  spelling  should  conform,  as 
in  other  languages* 

**  A  few  will  learn  them  without  assistance,  and  many  more 
with  but  little.  Once  on  the  road  to  success,  the  whole  of  them, 
so  far  as  they  are  known,  can  be  easily  acquired,  thou3;di  pro- 
ficiency in  their  manipulation,  that  is,  in  the  art  of  performing 
examples,  is  mainly,  like  skill  in  all  things,  a  matter  of  practice. 
It  is  just  as  much  so  in  what  arc  called  the  higher  niathcmatics 
as  in  the  lower;  in  calculus  as  in  arithmetic.  Nor  with  a 
reasonable  amount  of  practice  is  it  any  more  difiicnlt  lu  per- 
form  a  problem  in  algebra,  in  analytical  geometr}%  or  in  cal- 
culus than  in  arithmetic;  to  use  l'aylor*s  theorem  than  to  use 
the  multiplication  table;  the  difference  being  entirely  in  the  fact 
that  many  arc  accustomed  to  add,  subtract,  and  multiply 
figures,  because  of  the  practical  uses  of  such  in  life,  while  few 
have  reason  tu  perform  the  operations  of  the  calculus,  equally 
simple,  when  known. 


368  ELLEN   OR  THE 

"But  there  is  this  difference  between  the  two  branches  of 
mathematics  which  Ellen  has  just  mentioned,  that  the  one  is 
accurate  and  the  other  not.  For  the  fundamental  principle 
of  the  calculus  is  inaccuracy,  in  the  neglect  of  what  are  called 
infinitesimals.  In  many  examples  this  introduces  error,  so  that 
the  results  reached  are  at  the  best  only  approximately  correct, 
and  to  this  circumstance,  and  the  consequent  inability  to  know 
whether  the  work  done  has  any  value  or  not,  is  perhaps  partly 
due  the  perseverance  of  mathematicians  in  so  many  worthless 
theories. 

'*  Ellen  thinks  that  all  mathematical  conditions  can  be  cor- 
rectly instead  of  incorrectly  analyzed,  and  in  time  will  be. 
Thus,  for  example,  much  mathematical  work  is  based  upon 
the  assumption  that  at  their  limits  the  chord  and  arc  of  a  circle 
are  equal.  A  curved  line  is  unquestionably  the  resultant  of 
rectilinear  forces ;  these  forces,  that  is,  the  lines  of  which 
an  arc  or  a  circle  is  the  resultant,  may  be  obtained,  and  the 
mathematics  founded  on  such  results  are  true;  but  it  is  not 
true  that  the  chord  can  ever  be  equal  to  the  arc,  for  in  their 
nature  they  are  essential!}'  different.  It  is  also  true  that  the 
difference  in  length  which  exists  between  them,  which  may 
be  a  very  considerable  amount,  is  composed  of  these  differ- 
ences which,  by  this  system  of  mathematics,  are  considered 
negligible  and  arc  neglected.  In  many  other  ways  possible 
errors  enter  into  such  calculations,  so  that  this  whole  line  of 
mathematical  demonstrations  of  hypotheses,  such  as  those  of 
the  tides,  or  of  undulatory  theories,  are  intrinsically  more  or 
less  worthless,  in  addition  to  the  fact  that  the  assumptions  upon 
which  these  theories  are  based  do  not  exist." 


wnisr'iikixGs  of  an  oij>  vise 


369 


*'But  is  ft  possible/'  I  asked,  **  ihat  ihc  f^rcat  matlicmalicians 
would  spend  quite  a  share  of  their  lives  in  useless  ciphering?** 

*'The  old  Pine  mustn't  be  too  severe,**  she  answered.  **They 
arc  doing  the  best  they  know  how,  Thc>-  are  mathematicians. 
They  are  able  to  do  a  certain  thinjj  and  do  it  well.  Many  of 
them  are  not  able  to  do  anything  else  notable,  or  at  least  not 
equally  well.  Under  such  circumstances  it  would  be  foolish  to 
suj>pose  that  the}^  wauld  stop  ciphering.  Indeed,  this  igm^- 
ranee  itself  is  an  incentive  to  work,  and^  as  Ellen  thinks,  the 
fault  is  not  so  much  with  those  who  [iretend  knowledge,  which 
they  do  not  have,  as  with  those  who  are  foolish  enough  to  be 
deceived  by  such  pretenses.  And  the  moral  is  that  we  must 
accept  nothing  from  human  sources,  no  matter  how  great  or 
long  continued  may  be  the  authority,  unless  it  can  stand  the 
test  of  common  sense. 

*•  All  that  Ellen  is  saying  about  the  limitation  of  present 
knowledge  in  mathematics,  and  consequent  errors  in  results 
obtained  b\-  them,  none  kno^v  better  than  mathematicians 
themselves,  and  those  among  them  who  are  fair  and  honorable, 
and  by  nature  are  seekers  after  truth,  preferring  her  triumph  to 
delusive  positions  and  a  little  vain  authority  for  thcmscK^es, 
will  point  it  out.  Thus  Ellen  has  noticed  the  following  extracts 
from  philosophical  magazines.  Prof,  J,  Le  Conte,  formerly  of 
the  University  of  South  Carolina,  at  Columbia,  thus  writes  in 
the  '  London,  Edinburgh  and  Dublin  Philosophical  Magazine/ 
vol,  27»  pages  6  and  7 ; 

'  The  difficMlties  and  uncertainties  embraceil  under  the  sifprnf  head 
originating  in  the  different  physical  interpretations  of  the  mathematical 
processes  and  their  results^  are  of  a  more  intractable  Lhanuter.      Here 


370  ELLEN   OR  THE 

we  plunge  into  the  quicksands  of  equations  of  partial  differentials^  of 
discontinuous  functions y  and  of  integrals  containing  arbitrary  functions: 
the  arbitrariness  of  which  has  a  signification  in  the  applications  of  the 
functions  to  physical  questions.  Many  of  the  most  interesting  and 
important  dynamical  problems  involve  the  consideration  of  the  true 
signification  of  mathematical  results  which  are  known  to  have  been 
reached  by  processes  which  are  not  rigorously  exact.  Many  of  the 
equations  are  utterly  unmanageable  and  incapable  of  integration  unless 
certain  assumptions  are  made.  Hence  questions  in  relation  to  the 
warrantableness  of  such  assumptions  in  particular  cases  are  perpetually 
arising  among  the  most  eminent  mathematicians.  Such  difficulties  in 
the  mathematical  theory  of  sound  have  been  sources  of  perplexity  and 
controversy  from  the  time  of  Lagrange  and  I^uler  to  the  present  period. 
It  is  very  questionable  whether  the  vast  amount  of  intellectual  energy 
and  analytical  ingenuity  recently  displayed  in  the  discussions  of  the 
various  points  bearing  on  this  problem  by  Challis,  Airy,  Stokes,  Moon, 
Rankin,  Haughton,  Potter,  Earnshaw,  and  others  (however  instructive 
and  important  in  other  respects)  has  made  any  substantial  contribution 
towards  a  clearer  reconciliation  of  the  physical  with  the  mathematical 
aspects  of  the  questions  at  issue.  It  is  not  my  purpose  to  venture  upon 
ground  rendered  historical  by  the  labours  of  the  greatest  geometers  of 
the  i>resent  century.  But  I  must  insist  that  j)urcly  mathematical  ques- 
tions should  be  kept  (juite  distinrt  from  the  physical  considerations, — 
zxi(\  xX^-xX^  in  problcins  of  fJiis  character,  wo  deduction  from  analysis  is 
worthy  of  confidence  icfhich  docs  not  admit  of  a  rational physicial inter- 
pretation, capable  of  bein^  tested  by  observation  or  experiment' 

**  And   James   Clerk   Maxwell,  in    the   'Transactions   of    the 
Royal  Society  of  Edinburgh,'  says: 

*  There  are  few  parts  of  mechani(  s  in  which  theory  has  differed  more 
from  experiment  than  in  the  theory  of  elastic  solids.     Mathematicians, 


WHISPERINGS   OF   AN  OLD    PINE  37 1 

setting  out  from  very  plausible  assumptions  with  respect  to  the  consti- 
tution of  bodies  and  the  laws  of  molecular  action,  came  to  conclusions 
which  were  shown  to  be  erroneous  by  the  observations  of  experimental 
philosophers.  The  experiments  of  Oersted  proved  to  be  at  variance 
with  the  mathematical  theories  of  Navier,  Poisson,  and  Lane  and 
Clapeyron,  and  apparently  deprived  this  practically  important  branch 
of  mechanics  of  all  assistance  from  mathematics.' 


^72  ELLEN    OR   THE 


XXIII. 

^^T^HK  most  accurate  and  complete  experiments  regarding 
^  the  action  of  a  pulse  in  a  tube  were  made  by  the  very 
celebrated  physicist,  M.  Regnault,  of  Paris.  The  following 
resume,  translated  from  the  French,  is  given  in  the  *  London, 
Edinburgh  and  Dublin  Philosophical  Magazine,'  vol.  35: 

*  In  fact,  when  we  assert  that  a  gas  is  perfectly  elastic,  we  assume : — 

*(i)  That  it  exactly  obeys  Mariotte's  law.  Experiment,  however, 
shows  that  all  gases  deviate  more  or  less  from  this  law. 

'(2)  That  its  elasticity  is  not  affected  by  surrounding  objects.  But 
my  experiments  on  the  proi)agation  of  waves  in  tubes  show  that  the 
walls  of  the  tubes  exert  a  very  notable  influence. 

'  (3)  That  the  gas  does  not  oppose  any  inertia  to  the  transmission  of 
the  wave.  Now  my  experiments  show  that  the  emission  of  a  strong 
wave  always  causes  a  true  displacement  {I'criiable  transport)  of  the  first 
gaseous  layers,  which  displacement  considerably  increases  the  velocity 
of  the  wave's  proi)agation,  especially  through  the  first  portion  of  its 
course. 

*(4)  In  order  to  make  allowance  for  the  acceleration  produced  bv 
the  sudden  disengagement  of  heat  which  takes  place  at  the  moment  of 
the  wave's  passage,  Poisson's  law  is  introduced  into  the  calculation. 
But  this  law  is  only  exact  if  the  gas  has  perfect  elasticity,  if  it  obeys 
Mariotte's  law,  etc. 

'  Finally,  the  theoretical  calculation  assumes  that  the  excess  of  com- 
pression which  exists  in  the  wave  is  infinitely  small  compared  with  the 
barometric  pressure  supported  by  the  gas.     But  the  experiments  made 


WHISPERINGS   OF  AN  OLD   PINE 


375 


to  determine  tlie  rate  of  sound  in  free  air  have  been  hitherto  made  by 
meanjs  of  a  cannon,  and  the  wave  has  been  reckoned  from  its  source, 
namely  the  cannon's  mouth*  Now  this  wave  as  it  leaves  the  cannon  is 
under  enormous  compression  —  a  compression,  it  is  true,  which  dimin- 
ishes very  rapidly  as  the  wave  spreads  spherically  through  space  ;  but 
during  the  first  part  of  its  course  it  cannot  be  supposed  that  its  com- 
pression is  infiniuiy  sma/A 

*  When  the  excess  of  compression  in  the  wave  is  a  sensible  fraction  of 
the  compression  of  the  g^aseous  medium  at  rest,  we  can  no  longer 
employ  I^place's  formula,  but  must  have  recourse  to  a  more  complex 
formula  embracing  the  true  elements  of  the  problem.  Even  the 
formula  which  1  have  given  in  my  ^femoir  is  only  an  approximation  j 
for  it  implicitly  admits  Mariotte's  law  and  all  its  consequences. 

'  In  short,  the  mathematical  theory  has  as  yet  only  touched  u|>on  the 
propagation  of  waves  in  a  perffft  gtn —  that  is  to  say,  in  an  tdcai  fluid 
possessing  all  the  properties  which  had  been  introduced  hypotheticaU}' 
into  the  calculation*  It  is  therefore  not  surprising  that  the  results  of 
my  experiments  often  disagree  from  lheor)% 

*  I.  According  to  theory,  a  plane  wave  in  a  straight  cylindrical 
tube  should  advance  to  an  indefinite  distance  with  a  constant  velocity. 
My  experiments  show  that  the  intensity  of  such  a  wave  continually 
diminishes,  and  this  the  more  quickly  the  less  the  section  of  the  tube 
employed, 

*  In  order  to  establish  this  fact  conclusively,  I  created  waves  of  equal 
intensity  by  discharging  one  gramme  of  jxiwder  from  the  same  pistol  at 
the  orifices  of  conducting  tubes  of  very  different  sectional  areas,  and  I 
endeavored  to  ascertain  the  length  necessary  to  be  traversed  for  the 
explosion  to  become  inaudible.  I  have  further  endeavored  to  measure 
the  much  longer  path,  at  the  end  of  which  the  inaudible  wave  ceases  to 
give  any  indication  upon  the  most  sensitive  membranes  which  I  have 
used. 


37^  ELLEN   OR   THE 

*  Thus  the  discharge  in  a  pistol  of  i  gramme  of  powder  gives  a  vibra- 
tion in  the  air  (son)  which  becomes  inaudible  when  it  has  traversed 

1 150  metres  in  a  tube  of  the  diameter  0.108  metre. 
3810  metres  in  a  tube  of  the  diameter  0.300  metre. 
9540  metres  in  a  tube  of  the  diameter  i.ioo  metre. 

*  These  lengths  are  sensibly  proportional  to  the  diameters.  It  is 
nevertheless  probable  that  the  path  would  be  longer  if  the  wave  was 
not  subjected  to  successive  reflections  which  continually  diminish  it. 

*When  the  wave  has  no  longer  sufficient  intensity  to  produce  the 
sensation  of  sound  upon  the  ear,  or  when  it  has  been  so  far  modified  as 
to  be  unable  to  do  so,  it  may  nevertheless,  even  after  a  very  prolonged 
course,  still  mark  its*  arrival  upon  the  membranes. 

'  Thus  when  the  wave  is  produced  by  a  charge  of  i  gramme  of  pow- 
der, it  makes  its  last  impression  upon  a  membrane  when  it  has  passed 
over  the  following  courses  : — 

4056  metres  in  a  tube  of  diameter  0.108  metre. 
1 1430  metres  in  a  tube  of  diameter  0.300  metre. 
19851  metres  in  a  tube  of  diameter  i.ioo  metre. 

'But  in  a  pipe  of  i.ioo  diameter,  which  forms  the  grand  service-pipe 
of  Villemonble,  I  have  observed  paths  of  much  greater  length, — the 
charge  of  powder,  it  is  true,  being  raised  in  this  case  to  2.40  grammes. 
Thus  in  the  table  showing  the  results  of  one  of  the  scries  of  experiments 
made  with  this  large  tube,  the  last  mark  corresponds  to  a  wave  which 
had  traversed  58641  metres;  and  if  the  bands  of  paper  were  allowed  to 
remain,  it  was  easy  to  detect  as  many  as  ten  returns  of  the  wave  to  the 
membrane  A.  This  is,  in  effect,  a  path  equivalent  to  97735  metres,  or 
nearly  100  kilometres ;  but  the  bands  of  blackened  paper  were  then  so 
long  that  I  found  it  impossible  to  collect  the  indications  of  more  than 
six  returns ;  the  band  of  paper  with  this  number  had  already  reached 
the  length  of  2  7  metres. 


^V1IISPERINGS   OF  AX   OLD    PINE 


m 


*  What  are  the  causes  which  thus  weaken  a  plane  wave  when  it  is 
propagated  in  a  straight  cylindrical  tube  ?  They  are  of  several  kinds ; 
but  the  chief  one  undoubtedly  depends  upon  the  continual  loss  by  the 
wave  of  a  part  of  its  xns  viva  by  the  reaction  of  the  elastic  sides  of  the 
tube*  This  is  shown  distinctly  in  the  great  tube  of  the  Saint  Michel 
sewer,  which  is  supported  u|K>n  iron  columns  in  a  large  vaulted  gallery. 
When  the  wave  first  passes,  a  very  loud  noise  is  heard  outside,  in  what- 
ever part  of  the  course  the  observer  is  situated.  Consequently  a  con- 
siderable part  of  the  vis  viva  is  thereby  scattered  abroad.  The  same 
lakes  place  at  the  extremities  and  at  all  the  openings  furnished  with 
membranes.  This  loss  necessarily  continues  after  the  wave  has  ceased 
to  have  sufficient  intensity  to  affect  the  ear;  and  it  is,  strictly  speaking, 
sufficient  to  explain  why  the  sound  becomes  extinguished,  and  how  the 
wave  becomes  so  enfeebled  as  no  longer  to  disturb  the  most  sensitive 
membranes.  But  I  do  not  think  that  this  is  the  only  cause  at  work. 
There  is  another  which  arises  from  an  action  of  the  solid  wall  upon  the 
gas,  whose  elasticity  it  sensibly  diminishes.  I  sliall  give  proof  of  this 
immediately. 

'II.  Laplace's  formula  does  not  contain  the  expression  of  the 
intensity  of  the  wave.  According  to  this  formula  the  rate  of  propaga- 
tion of  a  wave  is  the  same,  whatever  its  intensity  may  be.  But  accord- 
ing to  the  more  general  formula  which  I  have  given,  this  velocity  should 
be  greater  the  greater  the  intensity  of  the  wave. 

*  Now  we  have  just  seen  that  in  a  straight  cylindrical  lube  the 
intensity  of  the  wave  does  not  remain  constant  as  has  been  hitherto 
sup[>osed,  but  that  it  diminishes  continually^  and  this  the  more  rapidly 
the  smaller  is  the  section  of  the  tube.  The  necessary  consequence  of 
this  is  that  the  rale  of  propagation  of  a  wave  in  a  tube  ought  con- 
tinually to  diminish  as  the  wave  advances;  and  this  diminution  should 
be  the  more  rapid  the  smaller  is  the  section  of  the  tube.  This  iS|  in 
fact,  what  occurs  in  all  of  my  experiments.     I  shall  confine  myself  here 


378 


ELLEN    OR   THE 


to  the  discussion  of  the  mean  velocity  of  a  wave  produced  by  the  dis- 
charge of  a  ])istol,  and  which  travels  through  dry  air  at  o®  C,  such 
a  wave  being  measured  from  its  commencement  up  to  the  moment 
when  it  ceases  to  be  of  sufficient  intensity  to  affect  the  membranes.  I 
select  from  experiments  made  upon  tubes  of  the  diameters  o*io8,  0*300 
and  1. 10  metre. 

irnE   OF   DIAMETER   O.I08    METRE    (ROUTE   D*    I\'RV). 


I)ISTANCK„S 
TRAVKRSKI). 

MEAN 
VELOCITIES,  v. 

jwder  0.3  grm. 

DISrANCES 
TRAVERSED. 

MEAN 
VELOCITIES,  v. 

Charge  of  l\ 

Charge  of  Powder  0.4  grm. 

Metres. 

•    566.74 
1133.48 
1700.22 
2266.96 
2833.70 

Metres. 

330.99 
328.77 
328.21 

327.04 
327.52 

Metres. 

1351.95 
2703.00 

4055-85 
5407.80 

Metres. 

329-35 
328.20 

326.77 
323.34 

^The  diminution  of  tlic  mean  velocity  of  one  and  the  same  wave 
reckone<l  from  its  origin,  but  which  is  examined  after  traversing  longer 
and  longer  paths,  is  very  marke<l.* 


**  It  would  seem  as  if  the  fact  that  the  sound  was  heard  at  one 
distance,  and  that  the  action  upon  the  sensitive  membrane  took 
place  at  another  and  very  much  greater  distance,  might  have 
suggested  that  these  were  two  different  things.  And  the  truth 
or  falsity  of  the  undulatury  theory  can  be  tested  right  here. 
For  if  a  pulse  of  air  in  a  tube,  and  sound,  are  two  entirely 
different  things,  a  candle  will  be  quenched  or  duck,  whenever 
by  usual  mechanical  means  a  pulse  is  started,  but  will  not  do  it 
when   no  such  pulse  is  started,  no  matter  what  sound  happens 


WIIISFEKIXGS    OF    AX    OLD    VIXE 


at  one  end  of  the  tube ;  the  only  exception  beinj^  when  the 
candle  has  a  normal  vibration  the  same  as  that  of  the  sound* 
which  would  not  often  occur.  And  therefore  the  experiment 
can  be  easily  and  satisfactorily  made. 

*'ln  Regnault  and  Biot's  experiments,  a  pistol  was  used, 
the  firing  of  which  engenders  gas,  which  of  necessity  starts 
a  pulse  or  the  theoretical  sound  wave.  So,  too,  if  a  piston 
is  pushed  in  the  tube,  a  pulse  will  be  started.  In  the  first 
case,  sound  will  also  take  place.  In  the  latter  It  w^ill  not, 
though  the  pulse  might  be  made  to  go  and  affect  a  sensi- 
tive membrane  placed  in  its  way,  as  far  as  or  further  than  the 
pulse  produced  by  the  pistol  of  MM.  Biot  and  Regnault. 

*'  Mr,  Regnault,  in  the  above  experiments,  found  out  a  num- 
ber of  self-evident  truths,  or  truths  that  should  have  been  self- 
evident  to  any  scientist* — though  they  with  one  accord  have 
refused  to  sec  them  since  they  accepted  the  undulator\'  theories, 
—  and  became  himself  a  wiser  man  ;  although,  again,  with  the 
fatuity  that  follows  believing  by  authority,  he  was  unable  to 
perceive  anything  further  than  was  illustrated  by  his  experi- 
ments. And  his  experiments  stopped  short  of  the  ultimate 
demonstration  that  this  pulse  in  a  tube  acts  as  it  dt^es  because 
uf  the  tube,  and,  if  taking  place  in  the  open  air,  would  go  a 
much  shorter  distance  and  have  a  very  different  speed.  It 
would,  in  other  words,  follow  mechanical  laws  and  be  almost 
immediately  dissipated. 

**ThusW.  K,  Grove,  in  his  celebrated  work  on  *Thc  Cor- 
relation of  Physical  Forces/  says: 

'  If  the  hand  be  moved  in  uncon fined  air>  the  motion  of  the  air  would 
not  be  sensible  to  a  person  at  a  few  feet  distance ;  but  if  a  piston  of  the 


38o  ELLEN   OR   THE 

same  extent  of  surface  as  the  hand  be  moved  with  the  same  rapidity  in 
a  tube,  the  blast  of  air  may  be  distinctly  felt  at  several  yards  distance. 
There  is  no  greater  absolute  amount  of  motion  in  the  air  in  the  second 
than  in  the  first  case,  but  its  direction  is  restrained,  so  as  to  make  its 
means  of  detection  more  facile.  By  carrying  on  this  restraint,  as  in  the 
air  gun,  we  get  a  power  of  directing  the  motion  and  of  moving  other 
bodies  at  far  greater  distances.  The  puff  of  air  which  would  in  the  air 
gun  project  a  bullet  a  quarter  of  a  mile,  if  allowed  to  escape  without  its 
direction  being  restrained,  as  by  the  bursting  of  a  bladder,  would  not  be 
perceptible  at  a  yard  distance,  though  the  same  absolute  amount  of 
motion  be  impressed  on  the  surrounding  air.' 

**  But  M.  Regnault  admits,  first,  that  the  results  of  his  experi- 
ments disagreed  with  theory;  that  is, — with  this  undulatory 
theory  which  Ellen  is  combating;  second,  that  they  so  dis- 
agreed in  the  following  respects : 

"First.  Gases  deviate  from  Mariotte's  law.  But  the  formula 
for  the  speed  of  sound,  as  worked  out  by  Newton  and  certain 
other  later  mathematicians,  rests  entirely  upon  the  assumption 
that  gases  obey  this  law. 

"Second.     Elasticity  is  affected  b)-  surrounding  objects. 

*' Third.  The  gas  itself,  the  air,  for  example,  often  moves 
bodily  at  the  start  instead  of  making  slight  oscillations  as 
assumed  in  the  theory. 

*'  1^'ourth.  The  Laplace  formula  for  the  increase  of  speed 
through  the  action  of  heat  produced  in  the  condensed  waves, 
which  that  class  of  mathematicians  who  uphold  authority  have 
eagerly  adopted,  is  not  correct,  and  will  have  to  be  modified. 

"Fifth.  The  wave,  instead  of  advancing  throughout  its 
course  with  uniform  velocity,  as  has  been  explicitly  taught  in 
text  books,  constanth'  varies  in  its  speed. 


WHISPERINGS    OF   AN    OI,n    PINK 


381 


"Sixth.  Instead  of  pulses  started  by  different  forces  going 
at  the  same  speed,  every  one  of  them  goes  at  different  speed, 
precisely  as  Ellen  has  said  that  they  would  and  must. 

**Such  a  system  of  exposures  of  the  postulates  of  science  in 
one  series  of  experiments  might  well  make  scientists  thoughtful. 
Had  the  experiments  been  continued,  M.  Regnault  would 
have  found,  as  some  one  yet  will  find,  that  sound,  instead  of 
being  made  by  the  pulse,  is  something  entirely  distinct  from  it, 
a  thing  of  itself.  That  the  pulse  is  entirely  disconnected  from 
sound  is  demonstrated  by  the  fact  that  if  made  by  a  piston 
there  is  no  sound,  and  further  by  the  fact  that  when  made  by 
the  explosion  of  a  pistol  it  continues  long  after  the  sound  has 
ceased, 

**  A  somewhat  similar  line  of  experiments  made  by  Jacques. 
Ellen  has  already  given, 

*'  Ellen  has  given  the  results  of  M.  Regnault  s  discoveries, 
from  his  uwn  standpoint  of  small  experiment;  but  rising  above 
this  to  one  of  broad  comprehension,  it  is  clearly  evident  that  the 
experiments,  demonstrating  the  incorrectness  of  the  hypotheses 
upon  which  imdulatory  theories  are  based,  entirely  disprove 
all  such  theories. 


382  ELLEN   OK   THE 


XXIV. 

^^IT  follows,  then,  that  because  of  the  mobility  of  the  air  a 
1  pulse  will  not  behave  at  all  in  unconfined  air  as  in  a  tube. 
A  stick  or  any  solid  body  pushed  would  behave  practically  the 
same  in  a  tube  or  out  of  a  tube.  But  all  those  bodies  whose 
particles  do  not  cohere,  but  are  mobile,  will  behave  very  differ- 
ently. This  is  a  fact  that  no  one  with  common  sense  would 
think  of  overlooking,  although  scientists  care  so  little  for  facts 
that  they  overlook  it  entirely.  There  could  perhaps  be  no 
better  illustration  of  the  utter  worthlessness  of  a  great  part,  if 
not  the  larger  part,  of  the  science  taught  in  our  schools  and 
colleges.  It  is  simply  and  purely  the  vagaries  of  theorists  who 
are  without  common  sense  or  common  honesty. 
'  "Mobility  is  the  great  distinction  between  solids  and  liquids, 

'  and  because  of  it  many  things  can  be  made  out  of  liquids  which 

I  cannot  be  made  out  of  solids.     And  so,  too,  it  is  equally  true 

I  that  many  things  can  be  made  out  of  solids  which  cannot  be 

I  made    out    of    fluids.     Liquids    arc     not    good     for    building 

materials. 

"  Herschel    speaks    of    *  the  extreme  mobility  which  belongs 
I  only  to  the  fluid  state.'     Laplace,  in   his  *  Mecanique   Celeste,' 

vol.   r.,  book  i.,  chap.  4,  says: 

'  To   obtain    the    laws  of  the  equilibrium  of  each  of  the   Darticles 

1  of  a  fluid,  it  would  be  necessary  to  ascertain  their  figure,  which  is  impos- 

sible ;  but  as  these  laws  are  required  only  for  the  fluids  considered  in  a 

I 


/ 


WJIISI-KRINUS    OF    AN    OLT(    I'INE 


385 


mass,  the  knowledge  of  the  ligiire  of  the  ijartieles  becomes  useless. 
Whatever  may  be  these  figures,  and  the  drsj>ositions  which  result  in  the 
separate  particles,  all  fluids,  taken  in  a  mass,  muist  present  the  same 
phenomena,  in  their  equilibrium,  and  in  their  motions;  so  that  the 
observationti  of  these  phenomena  will  not  enable  us  to  iliscover  any- 
thing respecting  the  configuration  of  the  particles  of  the  fluid.  T/t^^r 
generai phenomena  deptnd  on  the  perfect  mohility  of  the  particles^  which 
yield  to  the  least  pressure.  This  mobility  is  the  characteristic  property 
of  fluids  ;  it  distinguishes  them  from  solid  hodies,  and  senses  to  define 
them.  Hence  it  follows,  that  to  maintain  the  equiltbrixmi  of  a  fluid 
mass,  each  particle  ought  to  be  held  in  ef|uilibri\im,  by  means  of  all 
the  forces  acting  on  it,  and  the  pressure  which  it  maintains  ix\\m  the 
surrounding  particles/' 


**  Because  of  this  mobility,  as  Ellen  h*Ls  before  remarked,  the 
mere  blow  of  any  body  moving  at  the  rate  of  ten  feet  per 
second,  or  less,  could  not  affect  the  air  in  front  of  it  except  a 
trifling  way. 

**Of  coarse  a  fan  would  drive  and  condense  the  air  far  more 
than  the  prong  of  a  tuning  fork  or  a  stretched  string,  could; 
and  a  whirlwind  infinitely  more  than  all  of  them,  but  the  last 
can  move  only  150  feet  per  second.  The  old  Pine  mustn*t 
forget  that  m  all  cases  of  sound  the  hypothetical  air  waves  are 
supposed  to  be  started  by  the  air  particles  being  pushed  by 
some  body,  in  exactly  the  same  way  as  they  arc  pushed  by  a 
fan  or  any  other  body  tnoving  in  air,  The  idea  con- 
veyed b\^  Mr.  Tyiidall  and  different  text  books  that  the 
fork  is  swiftly  advancing  is  entirely  untrue.  And  the  sup- 
position held,  perhaps,  In*  triany  that  the  speed  of  hypo- 
thetical   sound  waves    is    in    any    way  connected    with    the 


386  ELLEN    OR   THE 

repeated  vibrations  of  a  fork  or  string  is  entirely  erroneous. 
With  the  string  each  supposed  wave  must  be  caused  by 
a  single  movement  of  the  string.  No  second  movement 
can  in  the  slightest  affect  it.  And  this  would  be  true, 
by  this  theory,  usually  with  sound ;  the  condensed  feature  of 
the  wave  would  be  caused  by  the  movement  of  anything.  One 
movement  of  something  and  return,  by  the  theory,  makes  the 
wave,  and  each  succeeding  movement  and  return  makes  another 
wave;  but  the  first  wave  is  never  overtaken  or  in  any  way 
interfered  with  by  the  second,  or  the  second  by  the  third.  The 
same  would  be  true  of  the  fork,  except  for  the  double 
prong.  The  action  of  cither  prong  might  and  probably  would 
each  time  affect  that  of  the  other. 

**But  this  is  all  different  in  a  tube.  There  by  the  shove  of  a 
piston  a  pulse  is  created  in  the  confined  air  which  is  communi- 
cated through  the  tube,  as  it  seems,  almost  instantly  to  the 
further  end  where,  if  tight,  it  is  reflected ;  but  if  open  it  is 
not  reflected.  Nor  with  an  open  tube  or  one  of  infinite  length 
would  there  be  any  reactionary  movement  unless  the  piston 
was  witlidravvn.  In  a  tube  clastic  force  may  continue  the 
motion  in  advance  for  a  long  distance,  but  in  unconfined 
air  it  cannot  because  of  the  mobility  of  the  air,  which,  as  Ellen 
has  before  remarked,  physicists  rarely  ever  mention  when 
talking  about  sound. 

"If  elastic  force  acted  in  unconfined  air  as  in  air  in  a  tube, 
every  movement  of  air,  with  all  its  amplitude,  would  be  propa- 
gated, with  the  speed  of  elastic  force,  for  great  distances,  in  all 
directions.  And  as  a  pulse  sent  through  a  tube  will  blow  out  a 
light  at  the  further  end,  or,  if  large  enough,  knock  down  a  man, 


WIllSI'ERINGS   OF   AN   OLD    TINE 


387 


SO  there  could  never  be  any  quiet  air,  but  always  pulses  moving 
in  all  directions  sufficient  to  overthrow  everything  existing. 
Ellen  thinks  it  is  pretty  fortunate  that  the  scientists  are  not  per- 
mitted to  run  things.  They  would  destroy  us  all  in  five  minutes. 
For  the  law  of  pulses  in  tubes  is  that  precisely  the  amount 
of  air  shoved  by  the  piston  is  moved  through  the  whole  length 
of  the  tube  and  emitted  at  the  open  end,  If  u  neon  fined  air, 
when  moved,  acted  in  the  same  way,  then  a  whirlwind,  driven 
by  elastic  force,  would  extend  around  the  worlds  destroying 
everything  in  its  path*  Awfully  hicky  the  scientists,  or 
physicists,  or  whatever  they  call  themselves,  don't  run 
things,'* 

**  Why,  yes,"  I  said,  '*it  is  very  fortunate  that  all  they  are 
permitted  to  do  is  to  talk ;  hi  that  way  they  make  trouble 
enough  by  delaying  important  discoveries/' 

"But  if  pulses  in  unconfined  air  do  not  form  and  act  as  in 
tubes,  but  instead  behave  in  a  much  more  civil  and  reasonable 
manner,  because  of  the  mobility  of  the  air, — a  quality  provided 
expressly  to  prevent  destruction  and  allow  things  to  exist, — then 
this  theory  of  sound,  which  has  sur\'ived  the  conflicts  of  more 
than  2CX)0  years,  will  survive  no  longer,  but  at  last  die  and  be 
quietly  buried/' 

'*Ycs/'  I  said,  '*we  will  have  a  great  funeral  and  all  the 
scientists  will  attend  and  be  the  pall  bearers/' 

'*The  old  ViiiQ  will  see  that  the  mobility  of  the  air  prevents 
all  these  accumulated  troubles  which  the  scientists  are  deter- 
mined to  inflict  upon  us,  and  that  it  works  most  admirably, 
allowing  peace,  quiet,  and  tranquility  to  very  generally  pervade 
the  earth,  except  when  storms  are  introduced  for  clearing  up 


3^8  ELLEN    OR   THE 

purposes,  and  these  generally  are  not  severe  enough  to  do  very 
much  damage." 

'*  Yes,"  I  answered,  ''the  old  Pine  does  see  that  everything 
is  very  wisely  ordered ;  that  the  conditions  are  altogether 
delightful,  both  for  beauty  and  for  comfort.  For  quiet  gen- 
erally prevails,  and  all  things  are  at  peace.  The  pumpkins 
and  the  corn  grow  in  the  fields,  and  the  apples  upon  the  trees. 
In  the  universe  there  are  things  innumerable,  but  there  is 
room  for  them  all ;  and,  so  far  as  the  old  Pine  can  see,  room 
for  more." 

"Yes,"  she  said,  ** there  is  plenty  of  room.  And  it  is  upon 
those  lines  that  the  universe  was  built  —  room  enough  for  all. 
For  the  room  is  husbanded ;  it  is  husbanded  so  far  as  this,  that 
a  little  will  answer  when  there  is  not  more.  But  there's  enough 
for  all  practical  purposes.  For  many  things  dwell  in  harmony, 
and  do  not  incommode  each  other.  And  when  they  do,  there 
is  room  enough  for  each,  or  for  enough  of  each  for  the  econ- 
omy of  the  universe.  Thus,  there's  room  enough  for  light,  the 
particles  of  which  arc  darting  everywhere.  But  TZllen  thinks 
they  don't  come  any  faster  than  they  are  wanted ;  and  they 
are  not  wanted  so  very  fast.  For  the  effect  of  light, —  a  ray  of 
light, —  lasts  quite  a  long  time,  if  measured  by  a  short  enough 
standard.  And  Ellen  doesn't  know  why  it  might  not  be  meas- 
ured by  one  standard  as  well  as  by  another.  Light  will  last  and 
perform  its  functions  the  same  as  food  or  drink  will,  that  we 
take  into  the  body.  Ellen  doesn't  think  that  the  rays  of  light, 
or,  more  truthfully,  particles  of  light,  are  at  all  continuous, 
but  that  vast  spaces  intervene  between  those  that  come 
from  the  sun,  or  the  fixed  stars.     Thus,  on  the  cars,  in  passing 


wins  PI 


PINE 


38g 


through  a  covered  bridge,  one  can  see  through  the  cracks 
of  the  boards  all  the  landscape  complete,  although  these 
cracks  are  but  a  very  small  part  of  the  space,  the  remainder 
being  entirely  impervious  to  vision.  Ellen  has  seen  it  esti* 
mated  that  rays  of  sunlight  are  at  least  30,000  miles  apart. 
And  the  old  Pine  can  sec  that  if  they  aroi  they  will  go  this 
distance  in  less  than  one-sixth  of  a  second,  going  as  they  do, 
in  a  second,  185,000  miles,  more  or  less.  And  therefore  there 
is  room  enough  for  all  these  innumerable  rays  to  be  circulating 
tn  the  universe. 

"  And  so  there  is  plenty  of  room  when  we  get  away  from 
the  big  universe  down  upon  this  little  world  of  ours,  with 
its  lovely  oceans  and  lakes,  and  the  pretty  mountains,  and, 
above  all  these,  the  air,  where  the  clouds  are  draped  tn  heavy 
masses,  or  lightly  gather,  and  the  rainbows  arrange  tlicm- 
selves,  and  the  birds  ft\\  In  this  air  where  Ellen  wanders, 
and  the  old  Fine  sways;  where  millions  and  millions  of 
insects  and  all  kinds  of  winged  animals  arc  constantly  pass- 
ing ;  where  clouds  of  dust  frequently  obscure  the  vision  ;  where 
the  beautiful  leaves,  all  the  innumerable  number  of  them,  live 
and  fall;  where  also,  with  all  these  things,  are  sounds; — there 
is  room  enough  for  all^ — lots  of  room.  Nor  do  things  interfere 
with  each  other  much,  but  all  have  a  beautiful  time. 

*' And  thus  the  air  is  full  of  sounds,  all  kinds  of  sounds,  Httlc 
sounds  and  big  sounds,  sweet  sounds  and  ugly  sounds.  They 
live  and  die  like  other  things,  being  what  the  old  Pine  and 
Ellen  would  call  very  short  lived.  And  so  they  pass  each  other 
like  other  things;  and  as  they  all  wander  In  every  direction 
they  arc  all   the  time  passing  each  other,  but  being  infinites- 


390  ELLEN   OR  THE 

imal  there  is  generally  plenty  of  room,  just  as  there  is  for  the 
insects,  and  the  horses,  and  cows,  and  sheep  to  pass  each  other. 
**  In  this  way  do  the  sounds  circulate ;  and  in  this  way  do  all 
things  move  in  the  universe.  At  least  they  do  down  here  in 
our  little  universe  where  we  can  see  them.  And  there  isn't 
any  other  way.  There  never  was  any  other  way.  All  nature's 
laws  are  universal ;  and  this  is  one  of  those  laws.  It's  the  way 
that  things  pass  each  other." 


WHISPERINGS    OF    AN    OLI>   PINE 


XXV. 


^^  A  ND  how  does  sound  operate  in  a  telephone  and  grapho- 

^*^     phonc»  Ellen?"  I  asked, 

"The  best  results,"  she  answered,  **are  usually  obtained 
in  the  Bell  magneto  electric  telephone.     Ganot  says: 

*To  the  number  of  instruments  depending  on  induction  may  be 
added  the  kiepkone^  which  is  equally  remarkable  for  the  surprising  char- 
acter of  the  results  which  it  produces,  and  for  the  simplicity  of  the 
means  by  which  they  are  produced.  Fig.  19  represents  a  section  of 
Graham  Bell's  telephone. 

'It  consists  essentially  of  a  steel  magnet,  of  alK)ut  four  inches  in 
length  by  half  an  inch  in  diameter,  enclosed  in  a  wooden  case.  Kound 
one  end  of  this  magnet  is  fitted  a  thin  flat  bobbin,  BB,  of  fine  insulated 
copper  wire.  For  a  magnet  of  this  sixe  a  length  of  250  metres  of 
No.  3S  wire,  offering  a  resistance  of  350  ohms,  is  well  suited. 

'The  ends  of  this  coil  pass  through  longitudinal  holes,  LL,  in  the 
case,  and  are  connected  with  the  binding  screws  CC.  In  front  of  the 
magnet,  and  at  a  distance  which  can  be  regulated  by  a  screw,  but  which 
is  something  less  than  a  millimetre  [.03937 -f  of  an  inch]»  is  the  essential 
feature  of  the  instrument,  a  diaphragm,  D,  of  soft  iron,  not  much 
thicker  than  a  sheet  of  stout  letter  paper.  This  diaphragm  is  screwed 
down  by  the  moulh-piece  E,  which  is  similar  to,  though  somewhat 
larger  than,  that  of  a  stethoscope. 

'  The  instruments  are  connected  by  wires,  for  one  of  which  the  earth 
may  he  substituted,  as  in  ordinary  telegraphic  communication  (908)* 
Each  instrument  can  be  used  either  as  sender  or  receiver,  though  in 
actual  practice  it  is  more  convenient  for  each  oi>erator  to  have  two 


WmSHERINGS   OF   AN    OLU    I'LNE 


393 


particular  directinn.  There  is  no  current  so  long  as  the  coil  and  the 
magnet  are  stationary.  When,  however,  the  magnet  is  suddenly  with 
drawn,  a  current  is  produced  in  the  opposite  direction*  Sinnilar  effects 
are  produced  tf,  while  the  magnet  is  in  the  coil,  its  magnetism  is  by  any 
means  increased  or  diminished.  [In  Figure  20  the  instrument  at  the 
right  is  a  galvanometer]. 

*  Now  in  the  telephone  the  magnet  and  the  coil,  when  once  properly 
adjusted,  remain  fixed.  But  the  magnet  M  magnetises  by  induction  the 
soft  iron  membrane  D  in  front  of  it — thai  is,  converts  it  into  a  magnet. 
When,  by  the  mouthpiece  being  spoken  into,  this  irou  membrane  vibrates 
backwards  and  forwards,  these  vibrations  give  rise  to  an  alteration  in  the 
number  of  lines  of  magnetic  induction  passing  through  the  coil,  the 
effect  of  which  is  thai  currents  are  produced  in  alternate  directions  in 
the  coil  surrounding  the  pole*  These  alternating  currents,  being  trans- 
mitted through  the  circuit  to  the  distant  coil,  alternately  atlract,  and 
cease  to  attract,  the  corresponding  diafram.  They  thereby  put  this  in 
vibration,  and  wht^n  the  mouthpiece  of  this  telephone  is  held  to  the  ear 
these  vibrations  are  jjerreived  as  sound  corresponding  to  that  which  is 
transmitted.  [By  this  theory  the  sound  is  not  transmitted,  but  instead 
electric  currents^  supposetl  to  cause  vibrations,  which  reiiroduce  sound. 
This  error  may  be  the  fault  of  the  translator].  Hence,  whatever  sound 
produces  the  vibration  of  the  diafram  of  the  sending  instrument  is 
repeated  by  that  of  the  receiver* 

*The  reproduction  of  the  sound  in  the  receiving  instrument  is  perfect 
as  far  as  articulation  is  concerned,  but  it  is  considerably  enfeebled,  as 
might  be  expected.  The  sound  has  something  of  a  metallic  character, 
appearing  as  if  heard  through  a  long  length  of  tubing,  while  it  faithfully 
reproduces  the  characteristics  of  the  person  speaking.  It  does  not 
result  from  a  series  of  sharp  and  distinct  makes  and  breaks,  but  in  each 
of  the  momentary  currents  there  is  a  continuous  rise  and  fall,  cor- 
resjionding  in  every  gradation  and  intlection  to  the  motion  of  the  air 
agitated  by  the  speaker. 


394  ELLEN   OR  THE 

*  Various  attempts  have  been  made  to  improve  the  loudness  of  the 
sounds  produced  in  the  telephone,  by  varying  the  form  of  the  various 
parts,  and  using  more  powerful  magnets  of  horseshoe  and  circular 
forms ;  Ader's  telephone,  which  is  largely  used  in  France,  is  constructed 
with  a  circular  horseshoe  magnet. 

*The  amplitude  of  the  vibration  of  the  disc  is  extremely  smalL 
'The  current  in  a  telephone  is  estimated  by  De  la  Rue  as  not 
exceeding  that  which  would  be  produced  by  one  DanielPs  cell  in  a 
circuit  of  copper  wire  4  mm.  in  diameter  of  a  length  sufficient  to  go 
290  times  round  the  earth.  This  current  would  have  to  pass  19  years 
through  a  voltameter,  to  produce  i  cc.  of  detonating  gas.  This  is 
about  1 ,000  million  times  less  than  the  currents  in  ordinary  use.  Such 
currents  are,  however,  sufficient  to  cause  the  contraction  of  a  frog's  leg. 

*  Siemens  estimated  that  not  more  than  xxriinr  ^^  ^^^  mass  of  sound 
which  the  sender  receives  is  produced.  That  it  is  possible  to  perceive 
this,  is  due  to  the  great  sensitiveness  and  range  of  the  ear,  which  can 
endure  the  sound  of  a  cannon  at  a  distance  of  5  yards,  and  still  per- 
ceives it  at  a  distance  10,000  times  as  great.  This  represents  a  ratio  erf 
intensities  of  one  to  one  hundred  millions. 

'The  extreme  delicacy  of  the  telephone  is  its  drawback  to  speaking 
through  ordinary  telegraph  circuits.  The  currents  in  adjacent  wires, 
the  vibration  of  the  posts  and  of  the  insulators,  or  the  passage  of  a  cart 
over  the  streets,  acts  by  induction  on  the  telephone  circuit,  and  over- 
powers its  indications.  When  a  telephone  circuit  was  placed  at  a 
distance  of  20  metres  from  a  well-insulated  line,  through  which  signals 
were  sent  by  means  of  a  battery  of  a  few  elements,  sounds  were  dis- 
tinctly heard  in  the  telephone.  Speaking  under  such  circumstances  is 
like  speaking  in  a  storm.  The  powerful  currents  used  for  systems  of 
electric  lighting  produce  such  a  roar  in  an  adjacent  telephone  circuit 
that  it  is  impossible  to  speak  through  the  telephone.  The  only 
effective  way  of  diminishing  the  inductive  action  of  adjacent  systems  is 


WHISPERINGS   OF  AN   OLD    PINE 


395 


to  have  two  insulated  wires  close  to  each  other,  forming  a  hop  circuiL 
They  are  thus  at  the  same  distance  from  the  inducing  circuit,  and  as 

one  of  the  wires  is  used  for  going  and  the  other  for  returning,  the  similar 
influences  must  be  in  opposite  directions,  and  therefore  neutralize 
each  other. 

''Iron  wires  present  a  special  difficulty  in  telephoning  through  long 
distances*  Telephone  circuits  are  alternating  ones,  and  at  each 
reversal  an  extra  current  is  produced,  which  enfeebles  the  original 
one,  and  alters  its  character.  This  extra  current  is  more  pronounced 
the  longer  the  circuit,  and  with  iron  it  is  300  times  as  strong  as  with 
copper.  Hence  for  long  distances  a  loop  circuit  of  copper  or  bronze 
wire  is  used,  and  with  such  circuits  it  is  possible  to  telephone  through 
very  long  distances.  In  America,  New  York  and  Chicago,  a  distant  e  of 
930  miles  apart,  are  in  telephonic  communication  ;  the  greatest  distance 
in  Europe  is  from  Ixjndon  to  Marseilles,  via  Paris. 

'If  a  telephone  is  inserted  in  the  circuit  of  a  Morse's  instrument,  the 
sound  of  the  working  is  heard,  and  the  messages  can  be  read ;  this  is 
the  case  also  of  the  telephone  in  the  branch  circuit  of  a  Morse.  If  one 
telephone  is  joined  up  with  the  primary,  and  another  with  the  secondary 
wire  of  an  induction  coil,  communication  is  almost  as  good  as  if  the  two 
apparatus  were  directly  united. 

'Telephones  have  been  constructed  in  which  the  thin  iron  plate  is 
replaced  by  a  thicker  one,  or  by  an  unmagnetic  one  ;  or  if  the  tele- 
phone is  held  close  to  the  ear,  the  plate  can  be  dispensed  with  alto- 
gether* 


*When  a  telephone  is  held  to  the  ear  during  a  thunderstorm,  every 
lightning  flash  in  the  sky  is  simullaiftously  heard  to  be  accompanied  by 
a  sharp  crack. 

'Dolbear  has  constracted  a  telephone  in  which  the  electrostatic 
action  of  currents  is  used.     It  consists  of  two  circular  flat  discs  of  metal 


396  ELLEN    OR   THE 

rigidly  fixed  to  each  other  in  an  insulated  case  of  ebonite.  One  of  the 
discs  is  in  metallic  connection  with  the  line  wire,  in  which  are  a  battery 
and  an  induction  coil ;  in  this  way,  while  one  disc  is  electrified  posi- 
tively, the  other  is  negatively  electrified  by  induction,  and  if  the  current 
is  varied  by  speaking  through  a  transmitter  in  'the  circuit  their  varying 
effects  are  faithfully  reproduced,  and  reappear  as  sound  vibrations  on 
the  receiver. 

<  *  *  ♦  When  the  wires  of  an  electric  circuit,  in  which  is  inter- 
posed a  telephone,  are  broken,  and  rest  loosely  on  each  other,  sounds 
produced  near  the  point  of  contact  are  reproduced  and  magnified  in 
the  telephone.  The  microphoney  invented  by  Prof.  Hughes,  depends 
on  this  fact ;  its  arrangement  may  be  greatly  varied ;  one  of  the 
simplest  and  most  convenient  forms  is  that  represented  in  fig.  21.  A 
piece  of  thin  wood  is  fitted  vertically  on  a  base  of  the  same  material ; 
two  small  pieces  of  gas  carbon  about  \  of  an  inch  thick,  are  fixed 
horizontally  in  the  upright ;  they  are  in  metallic  connection  with 
the  wires  of  a  circuit  in  which  are  a  small  battery  and  a  tele- 
phone ;  and  in  each  of  them  is  a  cavity.  A  third  piece,  of  the 
same  material,  and  about  one  inch  long,  is  pointed  at  each  end,  one 
of  which  rests  in  the  lower  cavity,  while  the  other  pivots  loosely  in 
the  ui)i)er  one.  When  a  watch  is  placed  on  the  base,  its  ticking 
is  heard  in  the  telephone  with  surprising  loudness;  the  walking  of 
a  fly  on  the  base  suggests  the  stamping  of  a  horse ;  the  scratching 
of  a  (|uill,  the  rustling  of  silk,  the  beating  of  the  pulse,  are  perceived  in 
the  telephone  at  a  distance  of  a  hundred  miles  from  the  source  of 
sound ;  while  a  drop  of  water  falling  on  the  base  has  a  loud  crashing 
sound.  To  obtain  the  best  results  with  a  particular  instrument,  the 
position  of  the  carbon  must  be  carefully  adjusted  by  trial  ;  and  indeed 
the  form  of  the  instrument  itself  must  be  variously  modified  for  the 
special  object  in  view  :  in  some  cases  great  sensitiveness  is  required,  in 
others  great  range.     In  order  to  eliminate  as  far  as  possible  the  effect 


WHISPERINGS   OK  AN  OLD    I'lNE 


399 


of  accidental  vibrations  due  to  the  supports,  the  base  slir»ul«l  irst  on 
pieces  of  vulcanized  tubing,  or  on  wadding. 

*  It  is  known  that  the  compression  of  a  semiconductor,  such  as 
carbon,  diminishes  its  resistance,  while  a  diminution  in  the  compression 
increases  the  resistance.  'I'he  action  of  the  microphone  is  to  be 
ascribed  to  this;  in  consequence  of  the  minute  alterations  in  the 
]>ressure  and  in  the  degree  of  contact  at  the  break,  the  electrical  resist- 


^5a 


Fig.  ai. 


ance  in  the  circuit  varies  in  accordance  with  the  sound  waves,  and  con- 
sequently  the  strength  of  the  curren  t  varies  too,  llie  result  of  this  is, 
that  what  we  may  call  undulating  currents  of  electricity  are  produceil, 
whose  amplitude,  length,  and  form  are  in  exact  correspondence  with 
the  sound  waves.  The  effect  of  the  microphone  is  to  act  as  a  relay, 
drawing  supplies  of  energy  from  the  battery,  which  then  appear  in  the 
telephone. 

*The  fonii  of  the  original  microphone  has  been  variously  modified. 
It  is  desirable  to  increase  the  number  of  contacts,  so  as  to  avoid 
scratching  noises.  The  Adcr  microphone  consists  of  ten  carbon  rotls 
laid  in  two  sets  of  five  each  on  three  cross-pieces,  also  of  carbon,  lixed 
to  the  same  piece  of  wood.     Good  results  are  also  obtained  by  using 


40O  ELLEN   OR  THE 

small  fragments  or  filaments  of  carbon.  One  of  the  best  microphones 
consists  essentially  of  a  thin  plate  of  carbon  resting  on  a  packing  of  the 
filaments  of  incandescent  lamps/ 

"  In  the  fifth  paragraph  an  explanation  of  the  action  of  the 
telephone  is  attempted.  In  examining  this  question  we  have 
for  data,  first,  that  sounds  made  at  a  transmitter  are  heard 
almost  instantly  many  miles  away  at  the  receiver;  second,  that 
only  such  sounds  are  heard  over  the  wire,  at  the  receiver, 
as  are  audible  at  the  transmitter.  Are  the  sounds  heard  at  the 
receiver  those  made  at  the  transmitter,  or  are  they  made  by 
vibrations  reproduced  at  the  receiver?  In  either  case,  wher- 
ever made,  sound  remains  equally  an  entity. 


mis  PE  RINGS 


ol 


401 


XXVI. 

^^|N  considering  what  the  sound  is,  heard  at  the  receiver  of 
^  the  telephone,  Ellen  will  return  and  discuss  the  statement 
made  by  Mr.  Tyndall  from  Poisson's  Traite  de  Mecanique, 
Vol,  II.,  p3Lge  707,  that  the  intensity  of  a  sound  depends  upon 
the  density  of  the  air  in  which  the  sound  is  generated,  and  nut 
on  that  of  the  air  in  which  it  is  heard.* 

**  Referring  to  this  principle  the  Encyclopedia  Britannica,  in 
article  on  Acoustics,  says; 

*ll  is  a  well  known  fact  that,  in  all  but  very  exceptional  cases,  the 
loudness  of  any  soimd  is  less  as  the  distance  increases  between  the 
source  uf  sound  and  the  ear.  The  law  according  to  which  this  decay 
takes  place  is  the  same  as  obtains  in  other  natural  piienomena,  viz.,  that 
in  an  unhmited  and  uniform  medium  the  loudness  or  intensity  of  the 
sound  proceeding  from  a  very  ssinall  sounding  Uxly  (strictly  speaking,  a 
pomt)  vanes  inversely  as  the  square  of  the  distance.     •     •     •     Xhis 


'A* 


follows  from  considering  that  the  ear  A  C  receives  only  the  conical  por* 
tion  OAC  of  the  whole  volume  of  sound  emanating  from  O,  and  that 
in  order  that  an  ear  BD,  placed  at  a  greater  distanre  from  O,  may 
admit   the  same    quantity^   its  area    must    be    to    that   of    AC  :  as 

•  See  page  183- 


402  ELLEN   OR   THE 

0B3  :  0A2.  But  if  A'^AC  be  situated  at  same  distance  as  BD, 
the  amount  of  sound  received  by  it  and  by  B  0  (and  therefore  by 
A  C)  will  be  as  the  area  of  A'  or  A  C  to  that  of  B  D.  Hence,  the 
intensities  of  the  sound  as  heard  by  the  same  ear  at  the  distances  O  A 
and  OB  are  to  each  other  as  OB^  to  OA^. 

'  In  order  to  verify  the  above  law  when  the  atmosphere  forms  the  in- 
tervening medium,  it  would  be  necessary  to  test  it  at  a  considerable 
elevation  above  the  earth's  surface,  the  ear  and  the  source  of  sound 
being  separated  by  air  of  constant  density.  As  the  density  of  the  air 
diminishes,  we  should  then  find  that  the  loudness  of  the  sound  at  a 
given  distance  would  decrease,  as  is  the  case  in  the  air-pump  experi- 
ment previously  described.  This  arises  from  the  decrease  of  the  quan- 
tity of  matter  impinging  on  the  ear,  and  the  consequent  diminution  of 
its  vis-viva.  The  decay  of  sound  due  to  this  cause  is  observable  in  the 
rarefied  air  of  high  mountainous  regions.  De  Saussure,  the  celebrated 
Alpine  traveler,  mentions  that  the  report  of  a  pistol  at  a  great  elevation 
appeared  no  louder  than  would  a  smaller  cracker  at  a  lower  level. 

*  But  it  is  to  be  remarked  that,  ac(  ording  to  Poisson,  when  air-strata 
of  different  densities  are  interposed  between  the  scource  of  sound  and 
the  ear  placed  at  a  given  distance,  the  intensity  depends  only  on  the 
<iensity  of  the  air  at  the  source  itself;  whence  it  follows  that  sounds 
proceeding  from  the  surface  of  the  earth  may  be  heard  at  equal  dis- 
tances as  distinctly  by  a  i)erson  in  a  (loating  balloon  as  by  one  situated 
on  the  surface  itself;  whereas  any  noise  originating  in  the  balloon  would 
be  heard  at  the  surface  as  faintly  as  if  the  ear  was  placed  in  the  rare- 
fied air  on  a  level  with  the  balloon.  This  was  exemplified  during  a 
balloon  ascent  by  Glaisher  and  Coxwell,  who,  when  at  an  elevation  of 
20,000  feet,  heard  with  great  distinctness  the  whistle  of  a  locomotive 
passing  beneath  them.* 

'*The  statement  in  the  second  paragraph  that  'This  arises 
from   the  decrease  of  the   quantity  of  matter,  etc.,*  is  entirely 


\VIMS1*EI 


403 


incorrect,  the  evidence  in  the  next  paragraph  proving  it  to 

be  so.  For  if  it  was  true  it  must  ahvays  be  true  of  two  equal 
sounds,  heard  at  a  point  equally  distant  from  both.  But  this 
is  not  the  fact, 

"Thus  draw  the  square  A  B  C  D.  C  D  being  on  the  surface 
of  the  earth,  and  A  B  at  th^  height  above  the  earth  where 
the  air  is  of  half  density  Let  equal  sounds  be  made  at  A 
and  D,  and  we  will  suppose  A  R  to  be  where  the  test  referred 
to  in  the  Encyclop;i^dia  article  above  was  made»  A  being  the 
source  of  sound  and  l\  the  location  of  tlie  ear, 

'*  Because  the  intensity  of  sound  depends  upon  the  density  ul 
the  air  where  it  is  made,  the  intensity  of  the  sound  at  D 
will  be  double  at  B  that  of  the  equal  sound  at  A,  also  equally 
distant  And  therefore  the  loudness  of  a  sound  has  nothing 
to  do  with  the  decrease  of  the  quantity  of  the  matter  impinging 
on  the  ear  For,  as  Ellen  has  said,  if  it  was  true  in  one 
instance  it  would  be  in  all 


B 


**Evidently  this  writer  gave  the  explanation  because  in  accord 
with  the  undulatory  theories.  For  if  they  were  true  it  would 
be  true.  That  it  is  not  true  is  a  demonstration  that  all  undu- 
latory tlieories  are  fictitious. 

**This  last  statement  cannot  be  too  strongly  made,  or  carefully 


404  ELLEN   OR  THE 

considered.  For  this  undulatory  theory  of  sound  couldn't 
be  true  without  its  following  as  a  sequence  that  the  intensity  of 
sound  depended  upon  the  density  of  the  air  where  it  was  heard 

**The  eminent  physicist  who  writes  the  article  on  sound  in  the 
Encyclopaedia  Britannica,  further  says:  *The  decay  of  sounds 
due  to  this  cause  [i.  e.  a  decrease  of  quantity  of  matter  imping- 
ing on  the  ear,  and  consequent  diminution  of  the  vis-vival,  is 
observable  in  the  rarefied  air  of  high  mountainous  regions.' 

**  Ellen  repeats,  the  fact  that  the  intensity  of  sound  depends 
upon  the  density  of  the  air  where  it  is  made,  instead  of  that 
where  it  is  heard,  makes  the  undulatory  theory  of  sound 
impossible ;  and  is  a  practical  demonstration  that  sound  is  an 
entity,  made  like  everything  else  in  this  material  universe  by 
the  combination  of  matter  in  its  different  conditions  and 
proportions.  For  it  is  impossible  to  explain  the  conditions 
except  that  sound  is  made,  in  full  or  in  part,  from  the  material 
which  exists  in  the  air  or  other  gases. 

"And  this  makes  two  demonstrations,  neither  of  which 
admit  of  any  possible  answer,  that  the  undulatory  theories 
cannot  be  true;  first,  that  the  action  of  sound  is  inconsistent 
with  such  theories,  and  second,  that  sound  is  an  entity.  Ellen 
says  undulatory  theories,  because  it  is  well  known  that  if  one 
falls,  they  both  fall. 

"The  great  English  physicist  Huxley  in  speaking  of  hypoth- 
eses,— and  this  undulatory  theory  of  sound  was  never  any- 
thing more,  though  most  dishonestly  taught  in  many  schools 
and  all  colleges  as  true, — says : 

'  Every  hypothesis  is  bound  to  explain,  or  at  any  rate  not  to  be  incon- 
sistent with,  the  whole  of  the  facts  it  professes  to  account  for ;  and  if 


WHISI'ERINGS   OF  AN    OLD    PINE 


40s 


there  is  a  single  one  of  these  facts  which  can  be  shown  to  be  inconsist- 
ent with  (I  do  not  merely  mean  inexplicable  by,  but  contrary  to)  the 
hypothesis,  such  hypothesis  falls  to  the  ground— it  is  worth  nothing. 
One  fact  with  which  it  is  positively  inconsistent  is  worth  as  muchj  and 
h  as  powerful  in  negativing  the  hypothesis,  as  Kive  hundred.'*' 

** And  cannot  sound  be  made  under  water?**  I  asked, 
**Yes,"  she  replied^  "but  its  intensity,  when  heard  in  air,  is 
much  lessened,  although  Ellen  understands  if  heard  by  an  ear 
underwater  it  is  louder  than  if  made  in  air.  And  this  suggests 
that  sound  like  electricity  follows  a  path  of  least  resistance, 
changing  slowly  from  one  medium  to  another  This  is  illus- 
trated in  the  sound  made  in  a  toning  fork,  which  is  thrown  off 
slowly  from  the  fork  into  the  air,  but  will  run  rapidly  from 
the  bottom  of  the  fork  into  a  sounding  board  or  other  similar 
medium.  So  long  as  it  remains  in  the  fork  it  circulates  through 
it,  causing  it  to  vibrate,  but  as  soon  as  it  enters  a  uniform 
medium  of  extended  dimensions,  as  the  air,  it  usually  spreads 
in  all  directions  like  a  cloud ;  but  if  conducted  into  a  body 
extending  in  but  one  direction,  as  a  wire,  it  will  practically 
confine  itself  to  that  channel,  going  as  far  as  its  length  of  life 
permits.  Later  Ellen  will  give  experiments  showing  the  differ- 
ent time  in  which  the  sound  may  run  out  from  such  fork. 

"The  above  facts  also  show  that  the  sound  we  hear  is  made 
by  the  initial  sounding  body,  Ellen  once  suggested,  foolishly 
accepting,  without  examination,  the  scientific  or  text-book 
explanation  of  the  action  of  sound  at  a  telephone,  that  perhaps 
additional  supplies  might  take  place  in  the  spreading  of  sound* 
as  in  a  conflagration  of  fire  from  the  burning  of  new  material. 
But  we  see  from  the  Poisson  experiment  that  this   is  not  true. 


406  ELLEN   OR  THE 

And  it  follows  that  the  sound/ which  is  transferred  in  all  direc- 
tions through  the  air,  is  made  where  its  cause  takes  place,  in 
quantities  sufficient  to  be  distributed  in  all  directions  the  dis- 
tance which  it  extends. 

*'  In  this  respect  it  would  be  like  a  hill  of  potatoes.  And  so 
most  things  are  made,  at  least  many  things.  A  stream  bubbles 
up  from  under  a  rock,  from  which  water  is  distributed  to  the 
neighboring  localities,  and,  in  its  abundance,  may  flow  for  quite 
long  distances,  but  the  supplies  sent  out  from  that  spring  can- 
not create  other  springs,  except  by  supplying  the  water.  There 
is  no  kindling  of  a  conflagration  of  waters  through  the  action 
of  water  upon  new  material,  as  in  a  conflagration  of  fire. 

**The  cloud  that  furnishes  rain  moves  in  many  directions,  or 
may,  over  the  country,  and  Ellen  thinks  is  increased  by  the 
conditions  of  the  atmosphere  which  form  new  clouds,  just  as  a 
stream  from  a  spring  is  increased,  or  maybe,  by  supplies  from 
other  springs,  but  these  supplies  have  no  direct  connection  with 
the  original  spring  or  cloud.  That  is,  it  is  not  the  original 
sj)ring  or  cloud  which  causes  them,  but  the  same  conditions 
which  caused  the  original  spring  or  cloud. 

"The  same  is  true  of  the  hill  of  potatoes.  If  there  is  an  in- 
creased suj)ply  it  comes  from  other  hills  of  potatoes,  which  are 
not  at  all  dependent  upon  the  existence  of  any  particular 
hill.  And  this,  as  VAlcn  thinks,  is  the  general  law.  But  it  is 
not  so  with  the  conflagration  started  by  a  match.  Such  con- 
flagration would  not  take  place  but  for  another  conflagration, 
that  of  the  match.  And  in  this  case,  or  all  similar  cases,  the 
amount  of  conflagration,  as  an  aggregate,  depends  upon  the 
material  at  hand  from  which  to  make  new  conflagration.     That 


WHISPERINGS    OF   AN   OLD    PINE 


407 


Is,  the  result  is  dependent  upon  the  amount  of  new  material 
which  may  be  brought  into  combustion.  And  the  status  of  the 
fire^  at  any  one  place,  depends  entirely  upon  the  amount  of 
such  new  material  obtainable  at  that  place,  and  not  upon  the 
amount  of  conflagration  made  by  the  match  which  started  it. 

''*This  is  very  different  with  sound.  It  is  made  at  some  par- 
ticular place,  by  some  particular  body,  and  is  distributed  in  all 
directions  as  rapidly  as  it  is  formed." 

'*  But/*  I  said,  'Uhe  same  sounds  might  be  made  by  other 
bodies,  as  is  shown  by  the  graphophone." 

"Yes/'  she  answered,  ** the  graphophone  records  show  this, 
but  these  records  have  to  be  made  before  they  can  utter 
sound,  and  the  making  of  them  is  one  thing  and  their  uttering 
sound  another.  But  when  played  upon  they  will  repeat  a  sim- 
ilar sound,  to  that  of  the  sound  which  made  them,  only  of  much 
diminished  intensity, — which  shows" it  to  be  intended  for  some 
different  purpose  than  the  original,  A  new  mill  for  the  manu- 
facture of  sound  is  made,  but  no  law  is  changed,  and  no  new 
law  expounded.  The  sound  which  makes  the  instrument,  or 
record,  from  which  precisely  similar  sounds  as  itself  may  be 
repeatedly  repeated,  has  nothing  further  to  do  with  it,  any 
more  than  the  oak  with  the  acorn  which  it  produces,  nor,  as 
Ellen  says,  can  there  be  any  sound  made  from  the  record  thus 
made,  until  the  proper  instrument,  or  machinery  for  doing  it, 
is  brought  into  actian.  And  this  is  always  at  some  future 
time. 

"The  conditions  are  not  at  all  tike  those  of  a  prairie  fire  or 
any  conflagration.  But  instead  the  production  of  sound  is 
accomplished  by  the  sounding  body  at  once  and  completely, 


408  ELLEN   OK  THE 

when  at  once  also  the  sound  spreads  practically  in  all  directions 
at  a  fixed  rate,  according  to  conditions." 

"But  how  can  Ellen  imagine  that  any  substance  could  be 
produced  which  would  spread  in  all  directions,  and  be  in 
sufficient  quantity,  often,  to  reach  many  miles?" 

*'By  the  power  of  God,"  she  answered.  "  Ellen  knows  full 
well  that  the  power  which  can  decree  that  an  oak  shall  develop 
from  an  acorn,  and  all  plants  from  a  seed,  would  be  abundantly 
able  to  create  a  substance  that  should  spread  in  all  directions, 
moving  at  a  fixed  rate,  and  performing  the  phenomena  of 
sound." 

'*  The  old  Pine  sees,"  I  said,  *'  Ellen's  argument,  but  he 
wonders  if  perhaps  that  which  causes  vibration  in  the  initiatory- 
body,  might  not  enter  contiguous  bodies,  causing  them  to 
vibrate,  and  thus  produce  more  sound  ;  and  thus  continue  doing 
as  it  spreads  throughout  the  atmosphere,  but  adapting  itself 
each  time  to  the  condition  of  the  bodies  which  it  enters,  so  as 
to  vibrate  a  bigger  quantity  of  air  in  a  contiguous  body,  that  is, 
a  longer  body  of  air,  if  the  air  became  less  dense,  and  in  this 
way  continue  the  average  intensity  of  sound  in  spite  of  the  fact 
that  the  air  was  constantly  becoming  less  dense?" 

"Ellon  thinks  the  old  Pine  more  ingenious  than  wise  in  such 
suggestion.  It  is  certain  that  nature  performs  no  such  peculiar 
antics,  but  that  her  operations  are  both  straightforward  and 
simple. 

•'In  the  first  place  it  is  a  fundamental  principle  of  sound,  that 
it  cannot  cause  another  body  to  vibrate  unless  one  having  the 
same  normal  vibration  as  itself.  And  this  principle,  alone, 
would  prevent  any  sound   from   making  other  bodies  vibrate. 


WHISPERiJ^GS  OF  AN  OLD   PINE 


409 


except  in  very  exceptional  cases.  And  Ellen  wants  the  old 
Pine  to  remember  this,  as  it  will  have  much  to  do  with  the 
explanation  given  by  scientists  of  the  action  of  sound  in  a 
telephone  or  graphophone, 

"The  supplies,  then»  of  sound  are  made  by  the  original 
sounding  body,  or  bodies^  and  cannot  be  made  by  any  other. 
They  are  all  gathered  from  the  operation  of  separate  bodies, 
that  are  entirely  independent  of  each  other,  as  Ellen  has  said» 
as  much  as  apples  come  from  the  aggregation  of  fruit  borne  by 
different  trees  that  are  entirely  independent  of  each  other." 

"And  does  Ellen  know,**  I  asked.  '* where  all  of  this  leads?  * 

"  She  knows  very  well,"  she  answered,  "  as  she  has  suggested, 
but  let  it  lead  where  it  will,  the  fact  she  is  after  now  is  the  action 
of  sound  in  its  ordinary  conditions.  The  old  Pine  is  thinking 
of  the  telephone?  " 

**  Yes,*'  I  said^  *'  and  he  is  thinking  again  how  sound  will  make 
a  record  which  will  repeat  sounds,  the  same  sounds,  not  once 
but  many  times.** 

•'  And  each  time/*  she  answered,  **  the  sounds  repeated  are 
scattered  by  their  own  energies  in  precisely  the  same  manner  as 
other  sounds/* 

'*  That  is  all  true,*'  I  said,  but  the  graphophone  shows  that  it 
is  possible  to  repeat  sounds.  Then  may  not  nature  in  some 
similar  way  constantly  increase  the  supply?" 

*' Ellen  thinks  not,"  she  answered,     '* Nature  makes  a  great 
many   sound-producing    instruments,    but    she    never    makes 
them  unnecessarily,  nor  ever   designs  that  any  one  or  every 
one,  should  perform  the  work   of  all.     The  thing  is  absurd 
and  incredible.** 


4IO  ELLEN   OR  THE 


XXVII. 

^^  A  ^^  ^^^  about  the  telephone,  Ellen?  Whence  come  the 

^•^     sounds  heard  at  the  receiver?  " 

'*  Ellen  was  leading  up  to  that/'  she  answered.  **The  expla- 
nation given  by  Mr.  Ganot,  and  universally  accepted  in  science, 
was,  that  the  sounds  heard  at  the  receiver  were  made  by  vibra- 
tions reproduced  in  its  diafram  by  the  electric  current.  And 
when  it  was  found  that  the  sounds  might  be  heard  when  there 
were  no  diaf rams,  it  was  suggested  that  the  so-called  vibrations, 
said  to  originate  with  the  sound  uttered  into  the  receiving  tele- 
phone, were  repeated  by  the  vibration  of  other  portions  of  the 
receiving  instrument,  as  the  magnet,  or  when  that  was  out,  the 
helix,  or  coils  of  wire,  and  when  magnet  and  helix  were  both 
out,  the  sounds  still  being  heard,  the  box  was  supposed  to  thus 
vibrate  and  repeat  them,  although  it  would  be  absolutely  impos- 
sible for  any  one  of  these  things  to  vibrate,  so  as  to  repeat  any 
sound,  unless  one  having  the  same  vibration." 

**Hut  sound  will  make  a  body  vibrate,  will  it  not  Ellen?  " 

**U  made  in  the  body,  or  entering  a  bod\'  having  the  same 
normal  vibration,  otherwise  not.  When  sound  itself  passes 
through  a  body  it  makes  a  trembling  motion  in  that  body.  And 
such  motion  might  affect  the  diafram  ;  Ellen  does  not  know. 
But  she  does  knuw  that  ordinarily  no  such  movement  will  cause 
a  diafram  or  anything  else  to  repeat  a  sound,  unless  such  diafram 


j 

":  ] 

■ 

w 

1 

1' 

^B          ^K^^S 

■ 

1 

1 

kT  ^^^^^^I 

^^^H 

fl 

'>^^^S 

1 

#■ 

J 

^INGS   OF 


4T3 


or  thing  vibrates  in  tinisoii^  or  nearly  so»  with  the  body  in  which 
the  sound  originated.  The  principle  being  that  the  sounds  must 
be  the  same  or  perhaps  may  differ  by  an  octave  or  a  fifth*  * 
And  therefore  the  talk  about  the  electric  current  or  any  other 
force  making  one  body  vibrate  identically  with  another^  and  thus 
repeat  every  sound,  or  practically  any  sound,  is  one  of  the  vcr>' 
many  things  that  scientists  know  which  are  not  so.  The  electric 
current  could  just  as  easily  harness  a  horse,  or  play  a  game  of 
base  balh  There  are  quite  a  good  many  things  which  the  electric 
current  cannot  do  \  and  talking  or  repeating  sound  is  one  of  them. 

•*  Whatever  the  electric  current  does, — as  moving  cars,  turning 
machinery,  producing  heat  and  light,  reducing  ores,  taking  or 
reproducing  photographs, — is  done  through  magneto-electric 
action  by  the  aid  of  a  make  and  break,  or  by  resistance  to  the 
current  when  passing  through  a  poor  conductor,  or  by  its 
power  to  produce  chemical  changes.  At  first  glance  the  most 
complicated  of  these  operations  would  appear  to  be  telegraph- 
ing, and  the  reproduction  of  photographs  at  a  distance.  Here 
however  the  only  thing  the  current  docs  is  to  act  through  a 
helix  upon  an  armature,  which^  in  the  reproduction  of  photo- 
graphs, opens  to  a  greater  or  less  extent  a  shutter,  thus  admit- 
ting more  or  less  light  onto  a  sensitive  filmi  by  which  the  details 
of  the  reproduced  photograph  are  brought  out, 

**  Such  things  as  these  it  is  entirely  evident  the  current  can  do. 
It  couldn't  directly  make  the  clicks,  or  take  the  picture,  but 
the  armature  is  at  hand  to  do  the  one,  and  light  to  do  the  other ; 
either  of  which,  with  proper  arrangements,  they  can  do  without 
any  current.     But  there  are  no  sound-producing  instruments  at 

•  See  Appendix,  pages  721-727, 


414  ELLEN   OR   THE 

the  receiver  to  make  sounds,  whether  or  not  the  electric  current 
can  set  in  vibration  the  diafram  or  any  other  part  of  the  receiv- 
ing instrument.  Ellen  does  not  believe  the  current  does  this, 
or  can  do  it  under  the  circumstances." 

*'But  Ellen  has  just  said  that  the  current  acts  on  the  electro- 
magnet so  as  to  open  and  close  a  shutter  in  such  a  way  that  the 
varying  light  reproduces  a  picture  with  much  perfection." 

"In  this  case,"  she  replied,  "the  current  passes  through 
selenium,  the  conducting  power  of  which  is  regulated  by  light. 
And  therefore  as  light  falls  on  the  selenium,  the  magnet,  strength- 
ened by  the  increased  current,  acts  on  the  shutter,  which  is 
opened  a  little  and  thus  admits  amounts  of  light  at  the  receiving 
station  which  are  duplicates  of  the  amounts  shining  on  the  sele- 
nium, after  passing  through  a  film  photograph,  at  the  transmit- 
ting station.  But  Ellen  denies  that  sound  can  make  similar  varia- 
tions in  the  current.     All  evidence  obtained  shows  it  cannot." 

"Then  why,"  I  asked,  "should  the  scientists  claim  that  any 
of  these  bodies,  diafram,  core  of  mai^nct,  helix,  or  box,  may 
vibrate  so  as  to  repeat  sound?" 

"Because  of  the  cxi^^cncics  of  their  theory,"  she  answered. 

"There  is  but  one  natural  or  indeed  possible  explanation  of 
the  operation  of  sound  at  a  telephone, — that  the  sound  is  carried 
through  the  wire  by  the  electric  current.  But  this  requires 
giving  up  the  undulatory  theory,  as  it  is  clearly  impossible  that 
air  waves,  some  of  which  are  supposed  to  be  over  seventy  feet 
long,  or  anything  representing  them,  could  thus  be  carried.  And 
therefore  the  ingenious  suggestion  was  made,  by  what  scientist 
Ellen  docs  not  know,  but  it  appears  to  have  been  immediately 
accepted  by  all,  that  the  vibrations,  and  thus  the  sounds,  were 


nSPERINGS   OF   AN   OLD    TINE 


415 


repeated  instantaneously  at  the  receiving  telephone  through  the 
agency  of  electricity^  by  the  weakening  and  strengthening  of  the 
magnet  at  the  receiver. 

**The  full  explanation  formerly  was  that  the  diafram  at  the 
transmitter  vibrated  from  the  effect  of  air  waves ;  that  the  v^ibra- 
tion  strengthened  and  weakened  the  magnet,  by  which  changes 
small  electric  currents  were  added  to  and  subtracted  from  the 
constant  current  of  electricity  passing  through  the  wire,  the 
effect  of  which  was  to  strengthen  and  weaken  the  magnet  at  the 
receiver  and  thus  reproduce  vibrations  in  the  diafram  of  the 
receiver,  precisely  similar  to  those  produced  in  the  diafram  of 
the  transmitter;  and  these  similar  vibrations  were  supposed  to 
reproduce  the  sounds  which  were  heard. 

"This  is  worded  with  so  much  assurance  as  to  command  the 
credence  of  the  thoughful,  but  a  little  careful  thought  suggests, 
as  Ellen  has  shown  the  impossibility  of  a  diafram,  or  anything 
not  especially  made  for  the  purpose,  repeating  sounds.  The 
thing  is  incredible  and  absolutely  fatal  to  the  theory. 

**  It  is,  too,  noticeable  how  constantly  the  theorists  change 
their  theory.  Thus  in  the  most  exact  language  it  is  said  that  the 
vibration  of  the  transmitting  diafram  strengthens  and  weakens 
the  magnet,  etc.  But  when  the  sounds  continued  with  no  diafram 
ill  either  transmitter  or  receiver,  it  was  then  stated  that  the  pole 
of  the  magnet  vibrated  at  the  transmitter,  this,  too,  being  an 
hypothesis,  though  stated  as  a  fact;  and  again  at  the  receiver 
these  hypothetical  vibrations  are  supposed  lobe  repeated,  though 
there  is  less  said  about  it ;  and  finally,  when  the  sounds  continue 
with  diaframs  and  magnets  both  out^  there  is  very  near  a  dead 
silence,  but  no  attempt  to  find  out  what  has  really  happened. 


4^6  ELLEN  OR  THE 

"The  record  of  a  graphophone,  by  a  very  ingenious  con- 
trivance, may  be  made  by  sound.  If  a  megaphone  is  connected 
with  a  recorder,  articulate  speech,  uttered  many  feet  or  even 
rods  away,  will  be  strongly  reproduced  in  the  record.  That 
there  is  no  movement  here  of  the  diafram  of  the  recorder,  by 
air,  can  be  proven  by  holding  a  lighted  candle  at  the  small  end 
of  the  megaphone.  The  light  is  not  stirred,  for  the  distance 
is  too  great  for  the  air  to  pass  over. 

**And  it  is  equally  true  that  there  is  no  movement  of  the 
diafram,  unless  it  vibrates  in  unison  with  some  one  of  the  pass- 
ing sounds,  which,  because  of  its  peculiar  character,  is  practi- 
cally impossible,  and  under  any  circumstances  could  only 
take  place  for  one  sound." 

**But,"  I  said  Ellen,  "these  supposed  sound  air  waves  are  of 
a  peculiar  kind,  are  they  not?" 

"Peculiar  enough  to  be  impossible,"  she  replied.  "To 
illustrate  them  the  water  waves  and  ripples  which  occur  on  the 
surface  of  a  pond,  caused  b}^  the  forces  of  momentum  and 
gravity,  when  a  stone  or  other  body  is  thrown  into  it,  are 
paraded,  although  it  would  be  impossible  for  them  or  anything 
like  them  to  take  place  in  air.  The  comparison  was  one  of 
extreme  stupidity  unless  intended  to  perpetuate  a  fraud. 
Accurately  speaking  no  possible  waves  could  take  place  in  air 
any  more  than  in  the  body  of  the  ocean.  Waves  belong  to  a 
surface. 

"Sound  is  at  home  in  air.  Its  infinitesimal  particles  per- 
meate it  in  all  directions.  Constantly  are  they  dying  and  con- 
stantly are  they  being  renewed.  The  scientist  who  said  that 
the  drum  of  the  ear  appeared  to  be  of  no  use,  would  find  that 


WHISPERINGS   OF   AN    (MJ»    PINK 


4f7 


it  is  exactly  adapted  to  gathering  up  these  particles  of  sound  for 
introduction  to  the  soul;  just  as  well  adapted  as  the  mouth  is 
to  introduce  food  into  the  body,  or  the  nose  odor.  The  shape 
of  the  ear  alone  is  worth  more  to  decide  the  nature  of  sound 
than  all  the  hypotheses  of  all  the  philosophers  that  ever  lived. 

**  If  it  was  true  that  the  diafram  at  the  receiver  repro- 
duces the  soundSp  by  repeating  the  vibrations  of  the  diafram  at 
the  transmitter,  then  the  diafram  at  the  transmitter,  where  one 
is  used,  should  and  must  make  the  same  sounds,  articulate 
speech  or  otheru'ise.  And  this,  because  of  its  position  nearer 
the  original  vibrating  body,  it  must  do  more  distinctly  than 
the  receiving  diafram.  This  is  a  self-evident  proposition, 
though  Ellen  has  seen  no  mention  of  it  by  scientists.  For 
nowhere  has  she  found  any  intelligent  discussion  of  the  subject. 

•*  But  if  the  diafram  at  the  transmitter  talks,  no  one  ever 
heard  it,  although  resonance,  which  takes  place  close  to  the 
original  sounding  body,  is  plainly  enough  heard.  As  a  matter 
of  fact  it  doesn't  talk.  It's  as  dumb  as  a  post,  or  anything  that 
wasn't  made  to  talk ;  and  so  is  the  diafram  of  the  receiver. 

**And  this  again,  it  would  seem,  must  follow:  If  the  trans- 
mitting diafram  talked,  every  substance  into  which  sound  enters, 
must  reproduce  sound,  which  would  mean  that  all  sound  is  con- 
stantly reproducing  itself^  And  this  practically  means  that 
everything  at  times  talks,  plays  the  piano^  laughs^  cries,  crows 
barks,  and  makes  the  hundreds  of  thousands  of  other  sounds 
that  the  world  is  heir  to.  And  all  of  these  sounds  they  make 
equally  well  with  the  instruments  or  things  whicli  arc  made  to 
make  them. 

•*  The  whole  theory  starte  with  the  rotten  assumption  that 


41 8  ELLEN    OR   THE 

sound  consists  of  air  waves,  if  any  one  can  imagine  what  these 
arc.  It  certainly  consists  of  something  which  can  be  gathered 
in  megaphones,  or  ear  trumpets,  or  sent  through  talking  tubes. 
In  neither  case  could  it  possibly  be  these  hypothetical  air 
waves,  some  of  which,  as  Ellen  has  said,  are  supposed  to  be  over 
seventy  feet  long.  This  air  wave  theory  with  every  sensible 
person,  scientist  or  otherwise,  is  dead  ;  but  this  hypothesis,  that 
the  sound  heard  in  a  telephone  is  the  result  of  vibrations  in  the 
receiving  diafram,  if  there  is  one,  and  if  there  isn't,  in  the  vibra- 
tion of  anything  in  the  receiver,  including  the  box,  is  built  up 
from  the  air  wave  theory,  and  but  for  that  would  never  have 
been  conceived. 

"  That  sound,  unless  continuous,  takes  place  successively, 
that  is,  that  it  ceases  at  one  point  when  heard  at  a  more  dis- 
tant one,  is  a  matter  of  universal  experience.  Thus,  if  we  see 
at  a  distance  the  steam  escaping  from  a  whistle,  we  know  that 
at  the  point  where  the  sound  is  made  it  is  heard  when  the 
steam  begins  to  escape,  though  in  each  case  it  is  heard  by  us 
later,  the  difference  in  time  depending  upon  the  distance.  And 
we  know  that  as  it  stops  at  the  point  where  it  is  started,  so  it 
continues  to  stop  at  each  successive  point,  until,  like  all 
material  things,  it  has  ceased  to  exist,  being  transformed  into 
something  else. 

"  Kllcn  cannot  see  that  the  old  Pine  has  any  telephone,  but 
Ellen  has  one ;  and  when  she  talks  with  a  friend  over  in  Rox- 
bur\',  she  has  been  quite  annoyed  in  hearing  other  people  talk, 
not  on  her  line,  but  on  another  contiguous  line,  for  in  the  inter- 
ests of  economy  both  lines  are  fastened  to  the  same  poles. 
Well,   she  hears   the  talk   on   the  other   line,    and  she  has  no 


WHISPERINGS    OF    AN    OLD    PINE 


419 


doubt  that  those  who  are  on  the  other  line  hear  the  talk,  more 
or  less,  on  her  line.  And  she  understands  this  condition  is 
general  where  lines  are  so  situated, 

**  Ellen  \\rill  not  undertake  to  say  just  where  or  how  these 
sounds  are  brought  to  her  house,  but  in  some  way  it  is  certain 
they  are  side-tracked  from  another  wire.  She  supposes  there 
was  sound  enough  in  this  other  wire»  to  keep  up  the  corres- 
pondence in  both  wires.  She  knows  that  the  cross- talk  she 
heard  were  the  words  of  those  who  talked/' 

•'Then  the  scientific  opinion  that  the  words  heard  at  the 
receiving  instrument,  are  re-created  by  the  diafram  of  that 
instrument*  through  the  action  of  electricity  and  the  magnet,  is 
not  correct?" 

•*  It  is  not  correct.  The  fact  that  sound  passes,  or  words 
pass,  from  wire  to  contiguous  wire  or  wires,  shows  to  Ellen  that 
those  sounds  or  words  are  carried  by  the  currents  or  streams 
of  electricity,  very  much  as  logs,  floated  upon  a  stream. 

"  And  Ellen  thinks  the  two  cases  are  very  similar.  The  logs 
arc  absolutely  independent  of  the  stream ;  they  have  no  con- 
nection whatever,  excepting  that  they  may  be  floated  down 
the  stream.     And  so  it  is  with  the  particles  of  sound. 

•*And,  as  it  is  found   ver}'  convenient  in   the  economies  of 
business  to  float  the  logs  down  stream,  so  it  is  found  very  con- 
venient to  float  the  sounds,  especially  words,  down,  on.  or  in 
the  stream  or  current  of  electricity. 

"  And  as  logs  in  different  ways  may  be  stranded  upon  the 
shores  or  shoals  of  streams,  so  sounds,  w^ords  or  otherwise 
may  get  stranded  upon  the  shores  or  shoals  of  electricity,  or 
carried  by  cross  currents  to  other  wires/' 


420  ELLEN  OR  THE 

**  And  the  secret  of  sound?" 

**  Is  no  longer  a  secret.  For  it  is  no  more  certain  that  the 
apple's  rosy  cheek,  and  the  apple  itself,  is  formed  by  com- 
binations of  matter,  than  that  sound  is  made  in  the  same 
manner. 

•*  And  it  is  no  more  certain  that  logs  are  carried  along  the 
river  or  stranded  upon  its  banks,  than  that  sound,  the  particles 
of  sound,  are  borne  on,  or  in,  the  current  of  electricity  in  a 
wire,  and  doubtless  often  are  scattered  along  its  banks ;  cer- 
tainly frequently  transposed  to  other  wires.  It  is  very  evident 
that  these  entities  of  sound  are  at  home  in  electricity;  that 
they  are  in  their  nature  electrical. 

"  The  question  is  why  or  how  at  the  telephone  we  hear  one 
talk  who  is  many  miles  distant.  But  for  the  erroneous  theory 
of  sound  taught  in  the  schools  this  would  hardly  have  ever 
been  asked,  its  answer  would  be  so  self-evident:  That  the 
words  of  the  speaker,  that  is,  the  particles  of  matter  which, 
introduced  into  our  cars,  cause  within  us  the  sensation  of  artic- 
ulate speech,  are  brought  instantaneously  through  the  wire  by 
the  current  of  electricity,  and,  through  adequate  means  pro- 
vided for  that  purpose  conducted  into  our  cars. 

**  But  for  the  teaching  of  science  this  would  be  self-evident; 
for  every  requisite  is  supplied:  The  telegraph  wire  between 
the  speaker  and  auditor;  the  electrical  current,  which  is  know^n 
to  flow  thus  instantaneously  through  the  wire,  and  which  is 
known,  too,  to  be  absolutely  essential  to  the  result;  the  proper 
arrangements,  loose  contact,  for  the  sound  particles  to  get  into 
the  electric  current ;  and  the  proper  arrangements  for  them 
to  get  out,  and  into  the  listener's  ear.     It  is  known,   too,  that 


WHISPERINGS   OF   AN   OLD   PINE  42 1 

to  the  natural  speed  of  sound  in  air  has  to  be  added  that  of 
the  wind. 

**It  is  doubtful  if  there  was  ever  a  phenomenon  in  the  world, 
which  explained  itself  more  perfectly.  The  question  why,  or 
how,  the  Florida  oranges  get  in  so  short  a  time  from  Florida — 
they  couldn't  have  done  it  in  old  stage  times — to  Vermont, 
where  they  enter  the  mouth,  instead  of  the  ears,  of  the  purchas- 
ers, and  through  the  sensation  of  taste,  instead  of  sound,  create 
a  very  pleasurable  and  healthy  result,  is  hardly  more  easily 
answered. 

*'  And  still  the  whole  world  is  taught  by  supposed  authority 
in  such  matters,  that  an  iron  diafram  has  suddenly  become 
endowed  with  speech  and  can  repeat  every  sound  in  the  world. 
Where  are  the  superstitions  of  religion,  oh,  ye  scientists?  Was 
there  ever  one  conceived  that  was  more  absolute  folly?" 


422  £LLSN  OR  TIU 


XXVIII. 

^^TT  begins  to  look  a  little  dark  for  the  scientists,''  I  said 

^  *'  but  the  old  Pine  would  like  to  know  what  is  the  usual 
explanation  of  the  transfer  of  sound  from  one  wire  to  another?' 

"  None  that  is  intelligible,"  she  answered.  "  It  was  at  first 
said  to  be  the  result  of  electromagnetic  induction,  but  this  was 
shown  to  be  incorrect,  and  the  theory  substituted  that  it  was 
by  electrostatic  induction,  which  certainly  has  the  advantage 
of  the  other,  by  two  letters  in  the  spelling. 

'*  Ellen  refers  to  these  differences  of  opinion  to  show  how 
constantly  the  statements  or  explanations  made  by  scientists 
about  these  matters  are  entirely  hypotheses,  ingeniously 
arranged  to  sustain  their  theories,  without  any  other  support 
whatever;  none  attempted,  and  none  pretended.  And  in  fact 
they  are  frequently,  if  not  generally,  entirely  erroneous." 

*'  But  what  is  the  difference  between  these  two  inductions, 
Ellen?"  I  asked. 

**  It  is  pretty  difficult  to  follow  all  the  operations  of  elec- 
tricity, or  magnetism,"  she  replied.  **But,  as  Ellen  under- 
stands, electromagnetic  induction  takes  place  because  of  a 
variable  magnetic  field  of  force  around  a  wire  through  which 


IVinM'ij  iNos 


AN    iHA}   PINK 


a  current  is  flowing;  and  electrostatic  induction  is  attributed 
more  directly  to  the  action  of  two  live  wires  upon  each 
other. 

"  In  electromagnetic  induction  the  induced  current  flows 
from  end  to  end  of  a  wire.  In  electrostatic  it  divides  at  the 
central  point  lengthwise  of  the  wire,  flowing  thence  to  the 
ground  connection  at  each  end.  The  result  being  that  a  tele- 
phone placed  at  the  middle  cf  a  wire  through  which  an  electro- 
static current  is  flowing,  will  hear  no  sound  ;  although  at  tele- 
phon*!s  placed  at  each  end  the  sound  can  be  plainly  heard.  If 
the  induced  or  cross  current  is  electromagnetic,  sound  will  be 
heard  at  all  three  of  the  telephones  on  the  second  wire. 

'*  Very  thorough  experiments  were  made  by  a  practical  enj^i- 
neer  of  New  York  City>  Mr.  J.  J,  Carty,  and  let  in  quite  a  bit 
of  light  on  the  subject  of  cross-talk. 

**  These  experiments  showed  that  in  the  disturbed  telephone 
w  ire,  where  cros5*talk  was  heard  at  end  telephones,  it  was  not 
heard  at  a  telephone  placed  at  the  centre;  showing  the  cross 
current  to  be  electrostatic. 

**Thc  old  Tine  will  see  that  though  certain  things  arc  shown 
here,  it  Is  not  slKJN\n  in  what  either  kind  of  induction  consists, 
or  why  it  consists.  Action  at  a  distance  certainly  docs  not 
take  place;  Ellen  means  action  with  no  intermediate  cause* 

•'  In  such  case  there  would  appear  to  be  a  certain  amount  of 
electricity  between  two  held  currents,  very  much  as  a  certain 
amount  of  moisture  might  circulate  in  the  air»  but  not  enough 
to  make  clouds  or  rain,  Ellen  sees  nothing  strange  that  for  a 
certain  distance  between  all  bodies  charged  with  electricity  a  cer- 
tain amount  of  this  should  circulate,  proportional  to  the  distance 


42^  ELLEN  OR  THE 

'*  Certainly  in  some  way  the  sound  passes,  and  the  expeii- 
ment  with  the  telephones  shows  that  it  follows  a  connecting 
current  between  the  two  wires. 

"This  current  is  said  to  be  caused  by  electrostatic  induction 
or  at  least  those  were  so  in  the  experiments  made  by  Mr 
Carty. 

"Mr.  Carty  says :  '  I  go  so  far  as  to  set  forth  that  the  effects 
of  electromagnetic  induction  between  parallel  telephone  wires 
may  be  neglected.  That  is  that  when  a  man  is  talking  on  one 
wire  and  his  speech  is  heard  by  induction  on  a  parallel  wire, 
that  that  speech  finds  its  way  between  the  two  wires  by  virtue 
of  electrostatic  induction,  and  that  electromagnetic  induction  is 
entirely  negligible.' 

"Mr.  Carty  thus  describes  sounds  which  he  heard  in  his 
experiments : 

" '  Sometimes  it  sounded  as  if  myriads  of  birds  flew  twittering 
by;  again  sounds  like  the  rustling  of  leaves  and  the  croaking 
of  frogs,  would  plainly  be  heard ;  at  other  times  the  noises 
resembled  the  hissing  of  steam  and  the  boiling  of  water.* 

"It  is  very  certain  that  the  leaves  didn't  rustle,  or  the  frogs 
croak,  into  a  telephone,  but  at  some  place  of  loose  contact,  or 
partially  broken  connection,  these  sounds  got  into  the  wire. 

"In  speaking  of  lightning  Mr.  Kempster  B.  Miller  in  his  ex- 
cellent work  "American  Telephone  Practice"  says: 

*  The  noises  due  to  these  natural  phenomena,  whatever  their  tme 
cause  may  be,  are  chiefly  annoying  on  long  lines,  short  lines  being 
only  disturbed  during  heavy  electrical  storms.  This  is  not  the  case, 
however,  with  the  noises  arising  from  the  proximity  of  other  wires 
carrying  varying  electric  currents.    Telegraphic  signals  can  be  plainly 


WHJSPERING«J   OF  AN   OLD    PINE 

heard  in  a  telephone  instniment  on  a  line  running  iiarallel  with  a  neigh- 
boring telegraph  line  for  a  very  short  distance^  The  establishment  of 
an  electric  railway  or  electric  lighting  plant  in  a  town  using  gronn^led 
telephone  lines  will  always  cause  serious  noises  in  the  telephones,  and 
if  the  lighting  current  is  alternating  the  use  of  llie  telephones  is 
wholly  out  of  the  question  at  night  lime  while  the  plant  is  running.*" 

**  And  the  graphophonc,  Ellen/'  I  asked,  '*  how  is  the  record 
made  in  that?  " 

*'  The  beginning  is  with  the  nicgaphone>"  she  answered, 
*'  the  small  end  of  which  is  fastened  to  a  metal  tube,  which 
extends  two  inches,  more  .or  less,  then,  turning  at  right  angles 
opens  to  a  space  covered  by  a  diafram  of  glass  or  mica,  to 
which  is  attached  a  small  glass  instrument  called  a  stylus,  one 
end  of  which  is  fastened  to  the  diafram,  the  other  resting 
upon  a  hollow  cylinder  of  paraffin  and  wax. 

**  This  cylinder  is  rotated  by  clock-work,  whilst  at  the  same 
time  the  stylus  is  moved  longitudinally,  and  thus  cuts  a  spiral 
groove  in  the  paraffin  and  wax, 

**  If  sound  enters  the  megaphone  it  will  be  conducted  to  the 
metal  tube»  and  through  this  to  the  open  space  under  the  dia- 
fram, passing  through  which,  as  it  does  when  returning  from 
the  graphophonc  record,  it  will  follow  the  stylus  into  the  par- 
affin and  wax ;  and  there  leave  its  record.  The  old  Pine  must 
always  remember  that  this  sound  is  infinitesimal  particles  of 
electrical  matter  thrown  off  by  the  sounding  body/' 

**Then,"  1  said,  *'the  statement  in  science  that  the  record 
is  made  by  the  stylus  moved  by  the  diafram  is  not  true?** 

**No/  she  said,  '*  it  is  not  true.  It  is  made  by  the  particlei 
of  sound  themselves,  as  Ellen  will  show  later. 


428  ELLEN    OR   THE 

**  And  as  the  oak  makes  the  acorn,  so  sound  makes  each 
indenture.  And  as  the  acorn  will  produce  another  and  similar 
oak;  so  each  of  these  indentures  will  produce  the  sound  which 
made  it.  And  as  the  particles  of  sound  make  the  forms  which 
will  reproduce  them — all  accomplished  in  infinitesimals, — so  the 
oak,  using  its  whole  vitality,  introduces  in  infinitesimals,  into 
the  acorn,  the  embryo  of  another  oak,  which  develops  slowly 
but  surely  if  circumstances  are  favorable.  And,  the  oak  pro- 
ducing many  acorns,  the  perpetuation  of  its  species  is  reason- 
ably assured. 

*'  In  its  onward  movement  sound  cannot  vibrate,  in  the  sense 
of  equal  vibration  to  and  fro,  though,  as  may  be  perceived 
from  its  passage  through  wood  and  other  bodies,  it  moves  with 
trembling  motion ;  which  may  be  owing  to  the  nature  of  the 
body  through  which  it  flows." 

''And  does  the  sound  make  the  diafram  vibrate?"  I  asked. 

"It  has  been  found  impossible  to  prove  that  sound  makes  a 
diafram  move.  i\s  ICllcn  has  said  it  certainly  doesn't  make  it 
vibrate,  with  any  accurate  interpretation  of  the  word,  except 
when  in  s}Mnpathetic  vibration  with  it." 

"But,"  I  said,  "the  old  Pine  thou^^ht  that  in  the  Reis  experi- 
ment a  make  and  break  was  made  in  the  circuit  by  talking 
against  the  diafram  of  the  sending  instrument?" 

"  This  is  probably  done  by  the  breath,"  she  answered,  "which 
in  talking  affects  the  air  in  a  similar  manner  as  when  we 
blow  out  a  candle.  Possibly  a  suflicient  quantity  of  .sound, 
spoken  against  the  diafram,  would  make  it  move,  but  as  Ellen 
has  said,  it  cannot  make  it  vibrate  unless  the  two  have  the  same 
normal  vibration. 


WHISPERINGS    OF    AN    OLD    TINE 


429 


'*As  sound  contains  within  itself  a  power  of  movement,  and 
as  its  particles  certainly  pass  through  the  diafram,  it  might 
cause  it  to  move^  but  as  sound  is  very  infinitesimal,  it  may 
get  through  the  interstices  without  moving  the  diafram. 

"Vibration  certainly  plays  an  important  part  in  the  moulding 
of  sound.  It  would  appear  to  be  the  mills  at  work  throughout 
the  universe,  at  least  that  part  of  it  that  Ellen  and  the  old  Pine 
are  acquainted  with,  which  take  sound  in  the  rough  and  pre- 
pare it  for  the  market* 

*'  Some  of  the  finest  of  these  mills  are  situated  in  the  human 
body — ^the  vocal  organs;  and  some  are  in  the  throats  of 
birds,  producing  most  exquisite  music.  But  sounds,  like  every* 
thing  else  in  this  universe  are  individualized.  And  thus  Nature 
furnishes  an  infinite  variety  of  sounds, 

*'  The  things  which  appeal  to  the  sight,  to  the  taste,  to  the 
smell,  as  Ellen  thinks,  are  no  more  wonderful,  and  hardly  more 
useful,  than  those  which  appeal  to  hearing.  And  in  all  these, 
phenomena  are  accomplished  in  a  similar  manner. 

"  That  is,  in  every  case  sensations  are  produced  in  the  spirit, 
or  soul,  by  the  operations  uf  matter.  That  of  vision,  through  a 
picture  in  the  eye.  That  of  touch  by  contact;  that  of  taste, 
odor  and  sound,  by  the  introduction  of  particles  of  matter 
into  the  head. 

*'  Nor  is  it  any  more  remarkable  that  sound  should  thus  affect 
the  soul,  than  that  a  peach  or  apple  should,  through  the  sensa- 
tion of  taste;  or  beautiful  things  through  that  of  vision ;  or 
odorous  ones  by  that  of  smell/* 

"And  how,"  I  asked,  "are  these  sounds  reproduced  from  the 
record?" 


41^  ELLEN    OR   THE 

"hy  'r-.  glas=  bead  of  ab<:ut  the  same  ^izc  of  the  >t\*Ius,  and 
fas:er.':d  to  a  similar  diafram.  passing  over  this  record,  with 
similar  movement  of  machinery-.  Ellen  says  over,  but  it  is  im- 
portant that  this  repr*  -djcer  enter  the  record.  And  this  can  be 
reproduced  many  time-  in  the  same  manner,  showing  that  the 
record  :-  firmly  held  by  the  material  of  which  it  is  made. 
This  means  that  the  record  is  an  instmment  capable  of  being 
played  upon  like  any  other  instrument. 

"And  the  record  is  made  by  sound,  as  much  as  an  acorn  is 
made  by  an  oak.  And  from  it  sound  may  be  reproduced  ver>' 
similarly  and  with  the  same  certainty  that  an  oak  is  from  an 
acorn.  The  record  certainly  is  not  any  more  wonderful  than 
the  oak.  Both  are  the  operation  of  the  same  intelligence,  and 
both  are  on  very  similar  lines.  Ellen  thinks  it  was  dreadfully 
cute  to  have  oaks  made  by  oaks,  and  sound  made  by  sound. 

•*Thus  flowers  arc  made  by  flowers,  a!l  of  them,  and  animals 
by  animals.  That  is  their  bodies  are  s<»  made,  and  thus  each, 
UfV.'Avln'^  certain  lav.s,  reproduces  its  kind. 

••  In  a  certain  sense  at  Ica^t  thi-^  law  w«)u:d  appear  to  be  uni- 
ver-^al.  For  a  picture  can  be  made  of  anything;,  and  from  the 
pict'.ire  a  similar  thin;^  be  prot^luccd :  which  is  all  that  takes 
place  in  sound.  For  not  the  same  particles  of  sound  arc 
repeated,  but  similar  particles  are  made,  which,  through  sensa- 
tion, affect  the  soul  similarly,  and  therefore  we  speak  of  them 
as  the  same  sounds. 

"And  thus  it  is  with  odor.  The  beautiful  sweet  peas,  which 
throw  their  odor  into  Ellen's  face,  do  so  again  and  again,  and 
every  time  it  comes  to  her  the  same.  She  can  see  no  difference, 
so  perfect  arc  the  laws  of  nature  which  make  things.     The  odor 


WHISPEKJiNGS    OF    AN    OLD    PINE 


43  r 


mills  of  the  pinks  arc  equally  good.  And  lhiis»  too,  are  those 
of  the  roses.  A  million  or  a  thousand  million  particles  of 
odor  are  made  and  every  one  alike.  At  least  they  are  alike  to 
Ellen/^ 

'*  But  why/'  I  askedi  "should  this  record,  when  thus  played 
upon,  produce  the  same  sounds  ?  ** 

•'  There  can  be  but  one  answer  to  this  question/*  she  replied; 
*'  because  the  sounds  uttered  into  it  make  the  necessary 
machinery. 

'*  And  this  in  infinitesimals^  a  system  used  in  nature,  univer. 
sally  possible,  and  illustrated  in  the  perfect  impression  of  an 
outside  universe  upon  the  retina  of  the  eye.  It  is  illustrated 
too,  in  the  operation  of  homeopathy;  and  again,  as  Ellen  has 
suggested,  in  the  development  of  an  oak  irom  an  acorn,  or  any 
plant  from  a  seed. 

**  For,  as  Ellen  thinks,  not  any  of  these  things  could  take 
place  without  first,  every  feature  of  the  developed  tree,  or  cver>^ 
variation  of  the  completed  sound,  being  contained  in  the  seed. 
And  by  seed  Ellen  means  the  thing  from  which  each  phenonf- 
cnon  arises.  And  second,  the  proper  cause  or  condition  for  the 
development  of  the  seed,  whether  oak  or  sound.  For  this, 
earth  and  moisture  is  nccessar}-  for  the  oak,  and  some  instru- 
rumcnt  to  pass  through  the  record  for  the  sound.  And  by 
sound  Ellen  means  that  which  entering  the  ear,  and  thus  being 
brought  in  contact  with,  or  into  the  presence  of  the  soul  or 
spirit,  produces  in  this  latter  the  sensation  of  hearing.  For  it 
is  in  this  manner  that  this  universe,  in  which  the  old  Pine  and 
Ellen  existSi  is  made. 

"That  is,   so  far  as    intelligent  beings  exist   in   a   material 


4S2  ELLEN  OR  THE 

universe  they  derive  their  knowledge  through  sensation,  and  the 
sensations  are  accomplished,  so  far  as  we  can  perceive,  abso- 
lutely  and  entirely  through  the  agency  of  matter,  and  it  would 
appear  that  this  can  be  done  by  the  infinitesimals  of  matter; 
indeed  it  would  appear  that  instruction  and  the  more  inteUigent 
action  are  accomplished  entirely  through  them. 

''  So  far  as  matter  affects  the  body,  or  supplies  the  wants  of 
that  body,  its  operations  are  sufficiently  clear  to  us.  For  it  is 
separated  into  an  infinite  number  of  different  ingredients,  or 
things.  And  these  different  things  are  so  made  that  th^  are 
constantly  disintegrating,  and  thus  made  available  again  for  new 
combinations.  And  many  of  these  combinations  are  introduced 
into  the  body,  to  supply  its  material  wants.  Back  of  this,  is 
the  effect  of  matter  upon  spirit,  or  its  connection  with  spirit ; 
the  spiritual  being  something  within  us  entirely  separate  and 
distinct  from  the  material,  as  Ellen  has  shown,  as  much  so  as 
the  engineer  is  distinct  from  the  engine   which  he  manages." 

"But  why,"  I  asked,  ** to  this  wonderful  essence,  this  im- 
mortal principle  of  knowledge,  power,  and  action,  should  mat- 
ter be  so  essential  ?  " 

"  Ellen  can  see  that  a  substance  with  an  infinite  power  to  act 
must  have  something  to  act  upon,"  she  replied,  "or,  with 
an  infinite  power  to  use,  must  have  something  to  use,  if  it 
would  exercise  that  power;  and  this,  to  a  certain  extent,  ex- 
plains the  nature,  and  object  of  matter.  Or,  accepting  the 
principle,  certainly  a  most  reasonable  one,  that  intelligence 
doesn't  mean  knowledge  of  everything,  or,  indeed,  necessarily 
of  anything,  but  rather  a  power  of  acquiring  knowledge;  mat- 
ter, so  far  as  Ellen  can  see,  might  as  well  be  used  for  such 


WHISPERINGS    OF  AN   OLD    PINE  433 

purposes,  as  any  thing  else.  Indeed,  it  would  bother  Ellen 
to  get  up  any  better  scheme  for  acquiring  information,  or 
obtaining  such  things  as  are  necessary  or  desirable  for  the  use 
of  intelligence,  certainly  in  material  conditions.  It  seems  to 
work  remarkably  well,  and  on  a  pretty  big  scale. 


434 


ELLEN  OR  THE 


XXlX. 


^^f  N  quite  a  similar  manner  as  the  graphophone  is  made,  a 

^  piano,  melodeon,  trumpet,  drum,  all  sound -producing 
instruments,  are  made.  And  thus  everything  artificial  is  made, 
and  nffust  be  made  complete  in  its  essential  conditions,  before  it 
can  operate  successfully,  if  at  all.  Ellen  knows  of  no  exception 
to  this  law,  and  she  doesn't  believe  that  there  is  any, 

"A  rocket  rises  high  in  the  air,  delivering  both  sound 
and  fire,  perhaps  in  different  tones,  colors  and  shapes.  Cer- 
tainly  for  every  such  variation  there  is  a  cause  in  the  rocket; 
and  all  causes  for  material  things  are  material;  there  are  no 
other  known  to  us. 

**  Well  Ellen  sees  that  the  graphophone,  and  the  telegraphone 
are  the  production  of  sound,  as  much  as  the  acorn  is  the  pro- 
duction of  an  oak,  and  she  thinks  that  undoubtedly  still  more 
wonderful  sound-instruments  are  made  by  nature  for  different 
purposes,  and  especially  to  be  added  to  the  records  of  memory 
in  the  brain,  as  suggested  by  Mr.  Hooke,  a  contemporary  of 
Newton,  and  of  whom  the  Chambers  Enclycopedia  says  that 
no  person  has  appeared  before  or  since,  whose  intuitions  of  the 
nature  of  things,  were  so  remarkable  as  his — which  Ellen  has 
referred  to  before. 

**  But  as  Ellen  doesn't  know  of  anything  which  will  produce 
an  oak  except  an  acorn,  or  a  scion,  either  root  or  branch,  from 


WHISPERlNt.^    Oh  AN    OLD    PINE 


the  oak — with  the  law  of  their  development  as  fixed  as  that  of 
their  production — so  she  dues  not  believe  it  is  any  different 
with  sound,  but  that  there,  too,  and  indeed  everywhere,  the  law 
of  the  use  of  instruments  desiFned  for  any  purpose,  is  as  fixed 
aSt  and  entirely  distinct  from,  the  law  of  their  production. 

**  Order  is  nature's  first  law. 

"Every  instrument  used  in  the  economies  of  nature  is  made, 
and  made  for  a  purpose,  but  in  no  case  can  that  purpose  be 
performed  until  after  the  instrument  is  made. 

**What  would  the  old  Pine  think  of  rockets,  going  off  whilst 
being  made,  or  anything  else  acting  in  that  way? 

•*And  again,  things  made  for  a  certain  purpose,  as  a  rule, 
don't  do  other  things,  or  when  they  do,  do  them  poorly.  Elien 
has  a  lamp  arranged  to  give  light.  There  is  very  little  else 
it  is  good  for.  She  has  a  plate  to  eat  her  meals  on,  and  there 
is  very  little  else  it  is  good  for.  And  so  a  piano  to  play  on,  a 
rug  for  a  floor ;  and  little  else  they  are  good  for.  Everything 
made  is  for  a  purpose,  and  most  things  certainly,  if  not  all, 
are  poorly  prepared  for  any  other  purpose. 

*"What  does  the  old  Pine  think  that  the  vocal  organs  are 
for,  whether  of  man,  or  other  animals?" 

"To  make  certain  sounds,"  I  said,  *' useful  in  many  ways." 

**  Made  on  purpose  to  do  this?  '* 

-Yes/' 

**And  they  perform  their  functions  well?** 

**  Most  remarkably  so.  The  note  of  the  bobolink  is  one  of 
the  sweetest  things  in  nature.  The  power  of  the  human 
voice  and  its  usefulness,  especially  in  oratory  to  persuade  and 
control,    make     it     one    of    the     most    desirable,    as    well     as 


43^  ELLEN   OR  THE 

remarkable  functions  of  man.  And  so,  too,  the  voices  of 
many  animals  have  great  power,  and  of  many  birds  great 
sweetness." 

**  And  do  any  of  these  animals  look  like  a  diafram?" 

*'  They  have  very  little  resemblance  to  any  diafram  the  old 
Pine  has  ever  seen,"  I  answered,  **  whether  of  iron,  wood  or 
mica." 

**0r  do  the  vocal  organs  of  any  of  these  animals  look  like  a 
diafram?" 

'*  So  far  as  the  old  Pine  has  knowledge,  certainly,"  I  said, 
**  they  do  not." 

"  And  does  the  old  Pine  think  that  these  diaframs  can  repeat 
the  sounds  made  by  all  animals,  so  perfectly  that,  in  the  case 
of  man,  each  individual  voice  is  recognized?" 

"As  Ellen  has  illustrated  the  matter  the  old  Pine  perceives," 
I  said,  **that  the  thing  is  impossible." 

**  Certainly,"  she  said,  "  it  is  impossible,  and  Ellen  thinks 
that  the  old  Pine  can  distinguish  the  difference  between  a 
graphophone  or  tclcf^raphone  record  doing  this ;  or  something 
else  doing  it,  not  previously  made  for  such  purpose. 

"  And  he  can  sec,  too,  from  the  analogy  of  nature,  that 
such  an  instrument  must  have  a  certain  stability  and  perma- 
nence. That  is,  only  an  instrument  so  made  that  it  can 
manufacture  the  particles  of  matter  which  make  or  represent 
every  possible  sound,  and  by  which  only  every  possible  sound 
can  be  represented,  could  accomplish  this  result." 

*'The  old  Pine  can  certainly  see  all  this,"  1  answered, 
** thanks  to  Ellen's  thorough  analysis  of  the  conditions;  and  he 
begins    to  see   that    Ellen's    hypothesis    is    correct — that    the 


^HlsrERINGS    OF 

sounds  heard  at  the  receiver  of  a  telephone  arc  the  sounds 
littered  into  the  sending  instrument,  transferred  by  the  elec- 
tric current/* 

"  Rut  Ellen  doesn't  deal  in  hypotheses."  she  answered,  *'  she- 
detests  them,  preferring,  instead,  knowledge,  something  that 
we  can  all  get  on  any  subject,  if  we  seek,  and  as  long  as  we 
continue  to  seek;   so  that  there  is  no  excuse  for  guessing. 

••The  time  to  talk  is  wlien  we  have  knowledge,  and  only  as 
we  have  it.  When  wc  haven't  knowledge  is  the  time  not  to 
talk.  Guesses,  in  all  such  matters,  are  worthless,  or  worse.  For 
almost  always  they  arc  the  seed  of  error.  And  from  them 
more  than  all  other  causes,  is  due  those  blunders  in  science, 
which  must  soon  force  all  text*books  to  be  destroyed  or  revised. 
For  the  science  of  to-day  throughout  the  world  is  to  quite  an 
extent  the  densest  ignorance. 

•'  The  great  English  physicist  Faraday,  remarkable  for  his 
good  sense  and  sound  judgment,  in  a  letter  dated  Jan.  25, 
1844,  to  his  publisher,  Richard  Taylor,  said: 


*  But  it  is  always  safe  and  philosophic  to  distinguish,  as  inuch  as  in 

our  power,  fact  from  theory ;  the  experience  of  past  ages  is  sufficient 

to  show  us  the  wisdom  of  such  a  course  ;  and  considering  the  constant 

tendency  of  the  mind  to  rest  on  an  assumption,  and  when  it  answers 

every  present   purpose,   to  forget  that  it,   in  such  cases,  becomes  3 

prejudice,  and  inevitably  interferes,  more  or  less,  with  a  clear  sighted 

judgment,  I  cannot  Jouht  but  that  he,  who,  as  a  wise  philosopher,  has 

most   power   of   penetrating    the   secrets  of  nature,  and  guessing  by 

hypotheses  at  her  mode  of  working,  will  also  be  most  careful,  for  his 

own  safe  progress  and  that  of  others,  to  distingtiish  that  which  consists 

of  assumption,  by  which  I  mean  theory  and  hypothesis,  from  that  which 


440  ELLEN   OR  THE 

is  the  knowledge  of  facts  and  laws ;  never  raising  the  former  to  the 
diginity  or  authority  of  the  latter,  nor  confusing  ihe  latter  more  than  is 
inevitable  with  the  former.' 

"  In  the  present  case  Ellen  thinks  that  these  experiments 
from  Poisson's  Mccaniquc,  which  she  has  reported,  demon- 
strate y  that  always  the  sound  which  is  heard  is  that  of  the  original 
sounding  body,  except  where  there  is  sympathetic  vibration, 
which  takes  place  but  rarely,  and  in  the  telephone  or  grapho- 
phone  is  practically  impossible. 

"Thus  Ellen  sees  that  sound  may  be  a  valuable  assistant  in 
making  an  instrument  that  may  reproduce  sound,  any  par- 
ticular sound ;  and  possibly  with  all  conditions  favorable  it 
might  do  this  so  well  that  the  new  instrument  would  reproduce 
sounds  equal  to  the  original,  though  she  has  never  heard  them ; 
but  the  usual  sounds  now  heard  at  the  telephone  are  entirely- 
similar  to  those  of  the  speaker,  for  the  full  and  sufficient  reason 
that  they  arc  the  same  sounds. 

*'  Ellen  hardly  thinks  it  would  be  possible  for  sound  to  make 
a  record,  such  as  a  graphophonc,  which  could  repeat  the 
sounds  anywhere  near  as  loud  as  those  made  by  the  original 
sounding  body. 

"Without  artificial  aids,  such  as  the  diafram  and  megaphone 
the  sounds  of  a  graphophone  record  would  be  very  weak.     Rut 
we   know  that  these   sounds    come   from    the  record    for   they 
can    be    heard,    though     both     megaphone     and     diafram    are 
removed. 

'*  And  it  is  very  evident  that  the  part  of  the  diafram  in  the 
receiving  telephone,  like  that  of  a  megaphone,  is  to  collect 
and  magnify  sound,  though,   of  course,  if   the   diafram  at  the 


^VIKSl'ERINGS    t)F  AN   OLD    I'lNE 


441 


telephone  made  sound,  the  diafram  at  the  f^raphophone  should 
do  the  same  thing." 

'*But  how  can  diaframs  magnif}'  sound?'* 

'*Hy  increasing  the  supply;  but  there  is  but  one  law  in 
nature  by  which  anything  can  be  increased,  and  that  is  in  the 
accumulation  of  itself »  and  therefore  it  must  accumulate  8ound 
as  in  a  reservoir,  from  which  it  pours  forth  in  increased  quantity. 
Different  instruments  are  used  to  increase  sound,  that  is*  to 
gather  it,  as  the  drum  of  the  ear,  or  artificially  an  ear  trumpet, 
era  megaphone.  A  tube  will  pre\t'nt  it  fn»m  scattering,  and 
conduct  it.  A  diafram  would  appear  to  act  with  sound  very 
much  as  a  stove  does  with  heat.  The  stove  cannot  t*f  itself 
make  heat,  but  it  is  a  great  aid  in  collccling  and  distributing  it 
And  so  a  diafram  connected  with  a  telephone  or  a  grapho- 
phone  is  of  great  assistance  in  collecting  and  distributing  sound. 

''The  use  of  the  diafram  in  these  experiments  of  sound  ts 
suggested  by  the  membrane  of  the  car,  which  helps  U>  conduct 
the  sound  from  the  outside  world  to  the  soul  or  spirit;  and  it 
would  be  as  sensible  to  say  that  the  stomach,  which  is  but  a 
part  of  the  machinery  that  introduces  food  to  the  system,  made 
the  food,  the  potatoes  or  the  corn,  and  all  other,  which  it  assists 
in  digesting,  as  to  say  that  this  membrane  or  the  diafram  copied 
from  iU  made  the  sound  whtch  it  assists  in  introducing  to  the 
soul  or  spirit — that  intellectual  part  of  man,  in  which,  and  which 
alone,  man  consists, 

"A  mirror  does  not  make  hght,  but  it  will  reflect  it.  The 
drum  of  the  ear  is  very  useful,  perhaps  absolutely  necessary  in 
hearing,  but  it  does  it  by  gathering  the  particles  of  sound 
floating  near  it,  thus  increasing  the  effect  of  sound  when  brought 


44-  ELLEN   OR  THE 

in  contact  with  the  soul ;   not  at  all  by  making  it     The  moon, 
too,  reflects,  but  does  not  make  light. 

"And  the  object  of  a  graphophone  is  not  to  manufacture  that 
which  can  be  better  done  by  the  original  sounding  body,  but 
for  the  reproduction  of  sounds  when  the  original  sounding  body 
is  not  at  command.  And,  as  Ellen  has  suggested,  she  thinks 
such  arrangements  may  be  made  especially  for  the  purposes  of 
memor>'.     They  can  also  be  used  in  other  ways." 

'*  But  why  do  scientists  say  that  the  diaframs  can  talk,"  I 
asked  ? 

'•  Kllen  doesn't  think  that  they  ever  did."  she  replied,  "  until 
dazed  by  the  operation  of  the  telephone.  Then  this  absurd 
explanation  was  given.  For  it  was  inconceivable,  as  Ellen  has 
before  remarked,  even  to  those  who  taught  the  undulatory 
theory  of  sound,  that  the  so-called  air  waves  should  enter  and 
be  carried  through  the  electric  current. 

"  Hut  the  old,  broken-down,  di-^credited  and  practically  obso- 
1-te  air  wave  theory  is  still  taii^Mit.  so  far  as  Kllen  knows,  in  all 
the  schools  and  collc^^cs  in  the  world,  where  science  is  taught, 
and  hence  a  necessity  vt  defending  this  vital  point,  and  a  bias 
in  believing  that  the  explanation  given  might  be  true. 

"  And  so  wonderful  are  the  phenomena  connected  with 
clectricit}',  that  Kllen  at  first  was  disposed  to  accept  this  scien- 
tific explanation  of  the  action  of  the  telephone,  seeing  that  it 
did  not  antagonize  the  fact  that  sound  was  an  entity.  Rut  as 
soon  as  she  took  time  to  consider  it,  she  saw  that  it  was  in 
violation  of  fundamental  principles  and  could  not  be  true. 

"  l^lectricity  is  one  of  the  phases  of  matter,  and,  so  far  a.s 
known,  one  of  its  most  wonderful  phases.      It  belongs,  too,  to 


WHISPERINGS   OF    AN   OLD    PINE 


443 


that  hidden  part  of  matter,  the  borderland  only  of  which  comes 
within  the  scope  of  our  vision.  It  is  of  course  a  substance  and 
would  appear  to  consist  of  an  infinite  number  of  infinitesimal 
particles,  which  are  capable  of  great  speedj  as  illustrated  in 
the  lightning,  or  the  aurora,  or  the  telegraph, 

•*  In  the  telegraph  or  telephone  wire,  electricity  tlows  in  a 
current  with  what  seems  to  us  wonderful  rapidity;  and,  as 
manipulated  by  man,  performs  some  very  remarkable  and  use- 
ful service. 

'*  MUen  has  not  the  time  to  discuss  today  with  the  old  Pine 
all  the  known  phenomena  connected  with  the  operations  of 
electricity  flowing  in  w^ircs,  which  is  the  only  phase  of  it  we 
are  now  considering,  but  in  their  study  it  was  discovered  that, 
by  the  aid  of  another  principle,  that  of  magnetism,  very  closely 
connected  with  electricity,  a  current  of  electricity  in  a  wire, 
could  be  used  to  make  signals,  instantaneously,  a  longer  or 
shorter  distance  away/' 

**  And  how*  was  this  done?  "  I  asked. 

*'  By  an  electro-magnet/'  she  replied.  '^A  magnet  has 
the  quality  of  attracting  or  repelling  certain  things,  as,  for 
instance,  iron.  And  a  current  of  electricit>'  passed  through 
a  wire  surrounding  an  iron  core  or  bar  of  iron  at  the  dis- 
tant station  will  magnetize  this  bar, — then  called  an  electro- 
magnet,— so  that  it  will  attract  an  iron  armature,  placed 
near  it.  But  if  this  current  of  electricity  is  shut  off,  the  bar 
instantly  ceases  to  be  a  magnet,  and  drops  the  armature. 

•'  In  doing  this  a  click  is  made  each  time  by  the  moved  arm- 
ature, and  as  the  current  may  be  constantly  and  almost  instan- 
taneously  changed,    that   is,    let    on    or  shut  off,  these  clicks 


444  ELLEN   Ok   THE 

varying  in  their  inter\'als  of  time,  by  arrangement,  may  be  used 
(or    an    alphabet,  and  thus  messages    sent   instantly  over  the 

ivorld. 

**  About  I  840  Prof.  S.  F.  B.  Morse  established  successfully 
this  method  of  telegraphing. 

**The  old  Pine  will  see,  that,  the  principles  of  electricitj"  and 
magnetism  being  accepted  as  facts,  the  operation  of  telegraphy 
is  very  plain  and  simple,  as  are  all  the  phenomena  of  nature 
when  correctly  understood.  No  fundamental  laws  are  violated 
or  absurd  happenings  supposed  to  take  place  in  either.  Of 
course  the  operations  of  the  telephone  and  graphophone  are 
equally  plain  and  simple,  the  absurdities  which  scientists 
advance,  being  entirely  a  product  of  their  imagination,  disquali- 
fied for  correct  reasoning  by  an  erroneous  theor>-  of  sound. 

**  In  1854  Charles  Bourscul,  a  Frenchman,  predicted  the 
transmission  of  speech,  publishing  the  same  in  *  L'  Illustra* 
tion  '  of  Paris,  \'ol.  XXIV.,  Aug.  16,  1854,  as  follows: 

**  *  I  have  asked  myself,  f<»r  example,  if  the  spoken  word  itself 
could  not  be  transmitted  by  electricity,  in  a  word,  if  what  was 
spoken  in  \'ienna  may  n(»t  be  heard  in  Paris?  The  thing  is 
practicable  in  this  way: 

*••  Suppose  that  a  man  speaks  near  a  movable  disc,  sufficient- 
ly flexible  to  l<>se  n<nie  (»f  the  vibrations  of  the  voice,  that  this 
disc  alternately  makes  and  breaks  the  connecticm  from  a  bat- 
tery:  you  ma\'  have  at  a  distance  another  disc  which  will  sini- 
ultaneousl}'  execute  the  same  vibrations.' 

"This,  so  far  as  Kllen  knows,  is  the  first  suggestion  of  such  a 
result.  It  was  natural  enou^i;h,  in  the  astonishment  caused  by 
the   success   of   the  telegraph,   that   such  an  idea  as  the  above 


WHISPERINGS   OF  AN    tJLl*    PINE 


44S 


should  havre  sut^gcsted  itself  to  sonic  one,  and  especially  with 
ihe  theory  then  held  of  sound. 

'*In  referring  to  the  above  Mr.  KenipstcrB.  Miller  in  Ameri- 
can Telephone  Practice,  continues: 

"'In  i86t  Phelps  Reis,  a  (Jerraan  inventor,  constructed  what  he 
tailed  a  telephone,  following  implicitly  the  path  outlined  by  Bourseul, 
He  mounted  a  flexible  diafram  over  an  n])ening  in  a  wooden  box,  and 
on  ihe  centre  of  the  diafram  fastened  a  small  j>iece  uf  platinmn.  Near 
this  he  mounted  a  heavy  brass  spring,  with  which  the  platinum 
alternately  made  and  broke  contact,  when  the  diafram  was  caused  to 
vibrate.  These  contact  points  formed  the  terminals  of  a  circuit  con- 
taining a  1>atter)'  and  the  receiving  instrument.  His  receiver  assumed 
various  foons,  prominent  among  which  w^as  a  knitting  needle  wrapped 
with  silk  insulated  copper  wire,  and  mounted  on  a  cigar  box  for  a 
sounding  boanL  !ts  oi>eration  was  as  follows:  The  sound  waves  set 
up  in  the  air  struck  against  the  tliafram  of  Ihe  transmitter,  causing  it 
to  vibrate  with  them.  This  caused  the  alternate  making  and  lireaking 
of  the  circuit  at  the  point  of  contact  between  the  platinum  and  the 
spring,  and  allowed  intermittent  currents  to  flow  through  the  receiver. 
This  caused  a  series  of  sounds  in  the  knitting  needle.  The  sounding 
boards  vilirated  in  unison  with  the  molecular  vibrations  of  the  needle, 
and  the  sound  was  thus  greatly  am[jlified.*  *' 

**But  wh)/'  I  asked,  *' didn't  the  experiment  succeed?" 
"Because  the  diafram  had  never  learned  to  talk/*  she 
answered,  '*cou!dn*t  talk;  can't  talk.  The  experiment  was 
thoroughly  tried  for  the  benefit  of  those  who  did  not  know  the 
ignorance  of  the  diafram,  and  was  satisfactor)-  to  them.  For 
cver>'  requirement  of  the  theory  was  conformed  w^ith.  That  is 
the  diafram  moved*  opening  and  closing  the  current,  and  the 


44<^  ELLEN   OR   THE 

movement  must  have  been  repeated  by  the  diafram  of  the 
receiving  instrument,  the  same  as  the  telegraph  signals  are 
repeated.  The  trouble  was  in  the  theory  that  the  diafram 
could  talk,  or  be  made  to  talk,  and  the  demonstration  was 
complete  that  it  cannot  do  it.  Ellen  assumes  that,  with 
the  great  amount  of  trouble  taken  in  the  preparations,  the 
experiment  must  have  been  thoroughly  tried." 

*'But  was  there  no  sound  heard,"  I  asked. 

**  Yes,"  she  answered,  **  sound  enough,  for  this  is  the  way  to 
make  sound,  as  the  sound  of  a  telegraph,  and  very  possibly, 
indeed,  most  probably,  some  words,  got  through  whilst  the 
current  flowed,  though  the  statements  in  regard  to  this  are  said 
to  differ;  Ellen  thinks  they  must,  but  nothing  could  be  more 
certain  than  that,  if  the  words  heard  at  the  receiving  telephone 
are  the  words  of  the  speaker  at  the  sending  instrument,  carried 
by  the  current,  they  could  not  be  heard  when  there  was  no  cur- 
rent. That  is,  it  is  absolutely  essential  for  the  successful  work- 
ing of  the  telephone  that  the  current  should  be  continuous. 
Two  other  thini^s  are  necc>sar\',  that  the  particles  of  sound 
should  be  able  to  i;ci  into  tlic  current,  and  also  to  get  out 
where  they  could  be  heard. 

•*  Loose  contact  in  front  of  the  transmitter  is  evidently  a  good 
arraiv^a^mcnl,  if  not  the  best,  for  them  to  i;et  in;  and  the  usual 
receiver  to  c^^et  out,  and  into  the  listener's  ear." 

"The  article  on  Telephone  in  the  Kncyclopa-dia  Britannica 
says : 

*  Reis  caused  a  membrane  to  oi^jen  and  close  an  electric  circuit  at  each 
vibration,  thus  transmitting  as  many  electric  pulses  through  the  circuit 
as  there  were  vibrations  in  the  sound.     These  electric  pulses  were  made 


WHISPERINGS   OF    AN   OLD    PINE 


447 


to  acton  an  electromagnet  at  the  receiving  station,  which  in  accordance 
with  Page's  discovery  gave  out  a  sound  of  a  pitch  corresponding  to  the 
number  of  times  it  was  magnetized  or  demagnetized  per  second.  Reis* 
object  was  to  reproduce  at  a  distance  not  only  music  hnt  also  human 
speech ;  but  that  he  did  not  wholly  succeed  is  clear  from  the  following 
extract  from  his  lecture  :  "  Hitherto  it  has  not  been  possilde  to  reproduce 
human  speech  with  sufficient  distinctness."  Considering  the  time  at 
which  he  wrote,  Reis  seemed  to  have  understood  very  well  the  nature 
of  the  vibrations  he  had  to  reproduce,  but  he  failed  lo  comprehend  how 
they  could  he  reproduced  by  electricity.  His  fundamental  idea — the 
interniption  of  the  current— was  ^  ftital  misiake  which  was  not  at  that 
lime  properly  understood.' 

**The  EncyclopLt;dia  Britannica  in  article  on  Telegraph  says: 

*The  first  requisite  for  electro-telegraphic  coniTTiuuication  between 
two  localities  is  an  insulated  conductor  extending  from  one  lo  the 
other.  This  with  proper  apparatus  for  originating  electric  currents  at  one 
end  and  for  discovering  the  effects  produced  by  them  at  the  other  end 
constitute  an  electric  telegraph.  Faraday's  term  '*  Electrode*'  literally 
a  way  for  electricity  to  travel  along,  might  be  well  applied  to  designate 
the  insulated  conductor  along  which  the  electric  messenger  is  dispatclied. 
It  is,  however,  more  conmionly  and  familiarly  called  '*lhe  wire*'  or 
*Mhe  line."' 

**  Repeatedly  Ellen  has  demonstrated  her  proposition,  that 
sound  consists  of  electrical  matter  thrown  off  by  the  sounding 
body.  First,  in  the  demonstration  that  the  intensity  of  sound 
does  not  necessarily  depend  upon  the  density  of  the  air  where  it 
is  heard ;  second,  that  it  depends  upon  the  density  of  the  air 
where  it  is  made;  third,  in  the  demonstration  that  sound  is 
made  by  the  initial  sounding  body;   fourth,  in  the  cross  talk  of 


448  ELLEN    OR   THE 

neighboring  wires;  and  fifth  in  the  above  Reis  experiment. 
The  principle,  too,  so  well  expressed  by  Newton  that  nature 
doesn't  do  unnecessary  work ;  and  last,  but  not  least,  the  great 
principle  of  the  universality  of  natural  law,  which  is  always 
before  us  if  we  will  but  study  it,  a  key  to  all  knowledge ;  are 
both  additional  demonstrations. 

**In  her  argument  Ellen  has  shown  that  the  wonderful  law 
through  which,  and  through  which  only,  nature  re-creates  each 
thing  after  its  kind,  is,  first,  that  each  kind  re-creates  itself,  and 
second  that  the  thing  rc-crcatcd  is  developed  later,  in  part  at 
least,  and  with  material  things  entirely,  by  other  agencies.  Ellen 
instances  the  re-creation  of  all  plants  or  animals,  from  a  seed 
or  scion.  Thus  the  oak  is  fairly  responsible  for  the  acorn,  but 
not  for  its  development. 

*' Ellen  might  include  in  this  category  that  as  there  is  a  lens 
to  collect  light  and  increase  the  power  of  vision ;  and  different 
bodies,  like  a  slovc,  to  collect  and  reflect  heat;  so  in  accord- 
ance with  the  principle  of  the  universality  of  natural  law,  there 
should  be  sonielhin.c,^  similar  to  collect  and  reflect  sound. 

"The  graphophone,  which  we  know  does  reproduce  sounds, 
is  made  very  different  from  a  diafram.  The  diafram,  from  its 
quality  and  shape,  we  might  well  suppose  was  made  to  reflect 
or  gather  sound,  but  the  graphophonc  record,  we  can  well 
imagine,  is  made  to  repeat  it.  Common  sense  should  be 
always  a  great  help  in  finding  out  things.  And  we  might  easily 
be  assured  that  if  a  graphophonc  record  could  repeat  sound, 
a  diafram  couldn't.  Neither  would  any  one  ever  conceive  a 
graphophonc  record  was  made  to  collect  or  reflect  sound. 

*' Again,  so  far  as  Ellen  knows,  there  is  no  sufficient  evidence 


449 

tumished  by  science,  and  never  has  been,  that  the  diafram  at  the 
receiver  moves  at  all,  in  the  present  system  of  telephones. 
As  Ellen  has  said  it  may  move  by  the  passage  of  the  particles 
of  sound  through  it,  but  it  is  quite  possible  that  these  particles 
arc  so  small  as  to  get  through  its  interstices  without  moving  it/' 

"Then  Ellen  thinks/*  I  said>  "that  the  particles  of  sound 
caused  by  shocks  move  through  elastic  bodies,  to  and  fro,  and 
make  them  vibrate*  because  there  are  channels  or  interstices  in 
them,  through  which  they  can  move?  ** 

**  It  is  impossible  to  see  how  they  could  make  them  vibrate 
without/'  she  replied^  **or  how  that  anvthing  can  ever  get 
through  another,  as  light  through  glass,  or  sound  through  any- 
thing, or  a  boy  through  a  fence,  if  not  breaking  it,  unless  there  is 
an  opening.  And  therefore  there  is  no  known  reason  why  sound 
should  move  the  diafram;  but  as  possibly  in  going  through, 
the  particles  of  sound  touch  it  more  or  less,  that  is,  squeeze 
their  way  through^  the  question  will  have  to  be  decided  by  the 
best  evidence  that  can  be  had ;  and  this  is  practically  com- 
plete that  they  do  not  move  it,  And  certainly  with  a  possible 
exception  of  a  single  sound  vibrating  in  unison,  they  do  not 
and  cannot  make  it  vibrate,  so  as  to  produce  sound.  * 


*  Fur  very  accurate  experimentj  conceming  the  vibratioiu  of  disfr&mii,  »ec  pages 
620-621. 


J&^ 


ELLKN    "k    I  HE 


XXX. 

^^NTATL'RE'S   way  to  make  sound  i?  by  suund-producing 

*  ^  instruments.  And  she  has  no  other.  Included  in 
these  are  records  of  sound,  made  by  sound,  and  which  may 
be  playc'd  ujK-n  so  as  to  repn.duce  the  sounds  which  made 
them.  IVjt  no  diafram  or  anything  el-e.  not  made  to  do  it,  can 
repeat  >oun(!. 

'•  Kllen  has  referred  to  cro-s-talk  in  a  telephone  from   other 
wire--,  a   tiling   of  very   common  occurrence,  and  which   it  is 
absolutely  imjios-ible  to   explain   intelli[;ently,   excepting  that 
-ound  is  an  entity  which  may  ^ei  into  any  wire  where   sfeams 
of  electricity  arc  flowing,  and  thus  frequent!}'  crosses  from  one 
wire  t  '  an^'tht.r.      I'or  a-  i-  wcil   known   Lleciricit}- han^s    over 
and  aro::iul  tr.f  different  wires,  as   f«  :,.-  .rr.d   m«.i-ture  often  rise 
above  and  ni'-rL-  i^r  le-s   envelfpc  -irL-ams    ^r  b«'dies  of   water. 
All  of  nat::rt'-  law-  are  universal  anJ.  ibis  is  one  of  them  which 
appertain-   l'»  lli:id<.     Ami   .-•>  b^^lwetn    a!;   >Lrcams,   there   are 
irc^jij' nlly   M"-^    -trcanis.    e-iK'ciall\-    if   the    streams   arc    near 
to;;etlier.  and  the-L-   cro^s  stream-   nitiy  carry  an\tliinjj^  that  will 
fl'^at  in  th'  m.  ^-r  at  least  snmc  thin;>,s  lb  at  wiil.  fn»m  t»ne  stream 
to  anoth'.T. 

'•  ICxjjlain  thi-  ^'entlemcn.  Net  with  h\j)«>theses  which  have 
no  ba-i-  in  either  common  sense  <»r  fact,  but  with  demonstration 
that  will  .-tand  the  racket   of  the-  a;^es  ;    or  rr\\c   up  your  tlieory. 


WHISPERINGS   OF  AN   OLD    PINE 


"Ellen  boldly  charges  that  no  where  hitherto  have  you  pro- 
duced a  single  jot  or  tittle  of  evidence  to  support  your  theor}' 
that  sound  is  something  mythical  that  you  call  atr  waves. 

**  And  you  haven't  because  you  couldn't.  There  is  no  other 
possible  reason.  Nor  can  you  now.  You  know  nothing  what- 
ever about  the  action  of  sound  in  a  telephone.  The  explana- 
tions which  you  have  hitherto  attempted  to  give,  every  one  of 
them  discredited  by  experiments  which  should  have  been  tried 
before  the  explanations  were  given,  and  everyone  of  them 
founded  upon  the  theory  that  grapes  may  be  gathered  from 
thorns,  or  figs  from  thistles,  demonstrate  this, 

'*  And  now  will  the  old  Pine  tell  Ellen  what  sound  is?" 

"Infinitesimal  particles  of  matter,*'  I  replied. 

**  Certainly  it  is,*'  she  answered.  "To  any  one  who  understands 
the  universality  of  natural  law.  it  couldn't  be  anything  else.  In 
these  odor  consists,  and  light,  as  Newton  demonstratedi  and  as 
all  able  thinkers  again  accept.  Nor  is  there  any  other  known 
cause  of  sensation  excepting  matter,  whose  different  effects  arc 
due  to  its  different  combinations;  that  is,  each  particular  sensa- 
tion is  caused  by  a  certain  combination  of  matter,  and  all 
sensations  by  some  combination.  Always,  too,  the  same  com- 
binations produce  the  same  sensation. 

**  And  as  we  have  seen  these  particles  of  sound  are  electrical. 
Our  knowledge,  too,  is  that  whilst  they  exist  they  continue  to 
move.  We  know  also,  that  they  are  carried  by  the  wind,  blown 
away  from  us  in  a  big  wind,  so  that  we  cannot  hear  them  ;  and 
we  know  that  every  sound  uttered  into  a  telephone  enters  the 
wire,  for  this  is  proven  by  the  box  and  string  or  wire  telephone. 

"Again,  Ellen  sees,  that   in  the  economies  of  the  universe 


454  ELLEN  OR  THE 

there  is.  a  proper  field  for  a  graphophone,  or  any  similar 
instrument,  for  repeating  sounds  when  the  original  sounding 
body  is  absent.  The  arrangement  that  ail  things,  by  a  simple 
process,  can  be  made  to  re-create  themselves,  is  of  far  reaching 
importance,  and  in  line  with  the  grandeur  and  perfectness 
of  design  by  which  this  universe  was  created.  But  there  is 
ho  reason  why  all  the  sound-producing  instruments  of  the  world 
should  be  made  over,  billions  and  hundreds  of  billions  of 
times, — an  infinite  amount  of  useless  work. 

"  In  Mr.  Bell's  first  telephones,  transmitter  and  receiver  were 
alike,  but  by  experiment  it  was  found  that  a  much  better 
arrangement  in  the  transmitter  was  one  of  loose  contact  in  the 
current,  called  a  variable  resistance  transmitter.  This  was  first 
got  by  connecting  the  current  at  one  point  by  water,  but  after 
various  experiments  the  present  transmitter,  having  a  field  of 
variable  resistance  connecting  the  ends  of  the  circuit,  formed 
by  loose  particles  of  carbon  thrown  in  a  box,  has  proven  to  be 
the  best  yet  tried. 

"  From  all  of  which  it  appears,  first,  that  a  continual  current 
of  electricity  is  absolutely  essential  to  any  successful  telephone ; 
and,  second,  that  in  the  transmitting  instrument  and  close  to 
where  the  words  are  uttered,  a  field  of  variable  resistance,  that 
is,  a  partially  interrupted  current,  is  desirable;  precisely  the 
conditions  that  would  be  expected,  if  the  sound,  made  by  the 
sounding  body,  enters  the  electric  current,  and  is  borne  by  it 
to  the  receiving  instrument,  where  the  arrangements  arie  such 
that  it  leaves  the  current,  is  gathered  and  thus  magnified  by  the 
diafram,  conducted  to  the  ear  of  the  listener,  and  frequently, 
more  or  less,  enters  the  room  where  the  receiver  is. 


WHIJSPERINGS   OF   AN   OLD    TINE 


455 


**  It  would  hardly  be  possible  to  have  a  more  complete  dem- 
onstration ol  the  action  of  the  telephone,  or  the  nature  of  sound," 

**  Eltcn  has  repeatedly  proven  her  contention/'  I  said,  *'  and 
eventually,  at  least,  it  must  be  accepted.  Bui  what  the  old  Ptnc 
is  the  most  surprised  about  is  that  it  has  not  been  before 
explained,  not  by  one.  but  by  ten  thousand," 

**  NothintJ  remarkable  about  that,'*  she  answered,  **  Practi- 
cally the  whole  world  becomes  '  tongue-tied  by  authority/ 
But  Ellen  hasn't  be^nin  to  give  the  whole  argument  yet,  fcjr  it 
is  all  one  side,  and  there  is  much  more  of  it." 

'•  But  the  old  Pine  understands,*'  I  said,  **  that  there  is  a  new 
kind  of  graphophonc  called  the  tclegraphune,  that  talks  back, 
repeating  all  sounds,  words  or  otherwise,  made  into  it,  but  has 
no  record,  at  least  none  that  can  be  seen.  How  does  Ellen 
explain  this? " 

*•  The  old  Fine  has  explained  it,"  she  saidt  "in  the  qualify- 
ing phrase,  *  none  that  can  be  seen.*  But  there  is  just  as  much 
a  record  in  this  machine  as  in  a  graphophone;  a  record  upon 
a  wire.  And,  as  in  the  graphophone,  the  telegraphone  record 
is  made  at  one  time,  and  operated  at  another.  Like  all 
sound-producing  instruments  it  must  be  made  before  it  can  be 
played*  And  it  is  only  when  the  necessary  agency  is  applied 
to  this  record  that  its  records  can  be  reproduced.  But  with 
such  arrangement,  as  with  the  graphophone.  it  can  be  repro- 
duced many  times.  The  sounds,  too.  are  gathered  similarly  as 
those  of  the  graphophone  and  brought  to  the  listening  ear." 

•*  And  arc  they  as  distinct  and  loud,'*  I  asked,  *•  as  those  of 
the  graphophone  or  telephone?  *' 

**  As  distinct,  perhaps,**  she  answered*  *'but  not  as  loud,  not 


4S6  ELLEN   OR  THE 

near  as  loud,  and  yet  loud  enough  to  be  valuable.  In  both  of 
these  instruments,  without  the  aid  of  the  diafram  and  mega- 
phone, the  sounds  would  be  far  less  loud  than  those  of  the 
voice." 

"But  exactly  how,"  I  asked,  *'is  this  telegraphone  made?" 

"In  the  first  place  Ellen  would  say  that  this  instrument,  as 
nearly  or  quite  all  other  instruments,  is  made  by  man,  the  intelli- 
gence ol  man,  and  would  not  be  made  at  all  otherwise.  A  very 
small  steel  wire  through  machinery  is  unwound  from  a  bobbin 
and  passes  between  two  magnets,  very  close  to  them.  If  now 
some  one  talks  into  the  instrument  in  which  this  is  being  done, 
a  record  is  made,  through  the  voice,  by  magnetic  action  upon 
the  wire,  which  then  becomes  a  sound-producing  instrument, 
that,  by  a  new  arrangement  of  machinery,  may  be  played  upon, 
and  will  repeat  the  sounds,  not  once  only,  but  many  times. 

"That  is,  man,  with  his  intelligence,  can  make  such  an  instru- 
ment, using  the  forces  of  electricit}',  magnetism,  and  sound,  as 
he  does  those  of  water  or  wind  when  he  builds  a  water  or  a 
wind  mill ;  or  those  of  steam  to  run  an  engine.  But  everything 
of  this  kind  is  done  within  the  laws  of  order  which  rule  in  the 
universe.  The  old  Pine  knows,  and  the  scientists  may  yet 
learn,  that  whilst  these  laws  will  permit  sound-instruments  and 
many  other  instruments,  as  telescopes,  cameras,  etc.,  to  be  made 
by  man,  they  do  not  permit  him,  much  less  any  material  thing, 
to  change  the  order  of  the  universe.  And  that  will  be  as  much 
changed  when  diaframs,  or  chimneys,  or  nails,  are  made  to  talk, 
as  though  thistles,  or  burdocks,  or  cabbages,  were  made  to 
bear  grapes. 

"Sound  then  is  an  entity,  produced  by  certain  contrivances, 


WIUSPERINGS    OF   AN    OLD    PINE 


457 


and  entlowed  with  certain  attributes,  among  the  most  important 
of  which  is  a  power  of  circulatiorii  and  this  includes  floating  in 
an  electric  current  But  still  more  wonderful  is  a  power  of  use 
by  Spirits  which  very  greatly  increases  the  opportunities  of  the 
latter  for  useful  and  desirable  existence  in  material  conditions. 

**  And  this  is  what  sound  is  for.  It  is  what  all  things  are  for. 
As  Ellen  has  repeatedly  said*  intelligence  creates  all  things. 
and  all  things  which  it  creates  are  for  the  uses  of  intelligence. 
Intelligence,  too,  is  always  individualized.  That  is  the  nature 
of  existence ;  it  is  all  arranged  that  way.  But  sound  might  be 
used  by  many  individual  intelligences*  educated  to  its  use,  just 
as  all  other  things  may  be.  For  this  universe  is  a  common  one, 
made  for  all 

'*And  Ellen  thinks  it  very  possible,"  she  continued,  ** indeed 
almost  certain*  that  other  very  remarkable  conditions  for  the 
making  of  records,  or  the  use  of  records,  may  arise,  but  she 
knows  that  nothing  can  alter  the  foundation  principles  by 
which  sound  is  created.  For  every  km  w  *  instance  proves,  that 
following  the  universal  law  of  material  creation,  sound  is  made 
by  the  combination  of  matter;  that  it  consists  of  particles  so 
small,  that  according  to  our  conception  a  host  of  them  can  run 
up  the  point  of  the  finest  needle, — for  this  Ellen  has  proven  by 
experiment,  and  a  most  remarkable  demonstration  it  was  of  the 
character  of  sound,  including  its  wonderful  minuteness  of  size, — 
that  these  particles  have  the  innate  power  to  spread  in  all  direc- 
tions, like  a  mist,  permeating  the  atmosphere,  and  permeating 
equally  anj^hing  which  they  enter.  They  are  great  travelers, 
going  in  all  directions,  and  some  of  them  make  long  trips.  But 
their  great  chance  is  when  they  get  into  the  electric  current, 


45^  ELLEN    OR   THE 

where  they  are  so  politely  helped  in  and  out.  Then  they  may 
see  a  large  extent  of  country,  and  tell  their  stories  to  new 
acquaintances. 

*'  Ellen  has  told  the  old  Pine  of  the  sound  of  bells  off  the  coast 
of  Brazil,  at  the  distance  of  lOO  miles  from  where  the  bells 
were  rung,  brought  to  focus  by  a  sail,  and  heard  distinctly  by 
all  when  passing  a  particular  part  of  the  deck ;  and  she  doesn't 
think  that  there  is  anyone  who  can  be  stupid  enough,  or  ignor- 
ant enough,  to  suppose  that  the  remnants  of  sound  gathered  in 
the  cavity  of  that  sail  were  composed  of  air,  however  formed. 
But  this  instance  alone  is  decisive  as  to  the  character  of  sound, 
and  is  a  demonstration  that  it  must  be  composed  of  some 
substance  which  may  float  in  the  atmosphere  for  lOO  miles, 
more  or  less,  and  then  be  accumulated  in  a  pocket  in  suf- 
ficient amount  to  make  itself  audible.* 

"  And  so  the  sound  gathered  by  the  flange  and  poured  down 
the  tube  of  an  ear  trumpet  into  the  ear,  or  indeed  that  gathered 
by  the  drum  of  the  car  and  conducted  into  the  car,  or  again, 
that  which  is  uttered  into  the  larger  end  of  a  megaphone,  or 
gathered  by  the  larger  end  and  conducted  into  the  ear  by  the 
smaller, — demonstrate  the  same  thing. 

"These  illustrations  arc  as  good  as  a  million, — either  one  of 
them — to  prove  and  do  prove  that  sound  is  a  material  thing, 
and  of  such  consistency  that  it  can  be  gathered  like  corn  in  a 
hopper,  and  poured  through  a  funnel.  For  it  isn't  nature  which 
undertakes  the  impossible. 

''Possibly  the  scientists  never  knew,  or  have  forgotten,  that 
always  increased  effects  come   from   increased  amounts.     And 

♦  See  page  203. 


WHISPERINGS   OF   AN   OLD    PINE  459 

therefore  is  it  that  the  drum  of  the  ear  assists  in  the  sensation 
of  hearing,  for  it  gathers  the  particles  of  sound  floating  in  the 
atmosphere,  thus  conducting  increased  amounts  into  the  ear. 

**  Ellen  saw  recqntly  the  remark  made  in  a  scientific  journal 
that  apparently  the  drum  of  the  ear  was  useless.  In  such  a 
case  nature  is  never  the  fool.  Good  sense  would  teach  any 
one  that,  and  prevent  them  from  accepting  any  hypotheses 
which  suggested  it. 

**The  impossible  is  never  undertaken  by  nature,  but  it  would 
be  as  impossible  to  collect  the  so-called  air  waves  that  sound 
is  represented  to  be,  and  so  increase  the  effect  of  sound,  that 
is,  so  increase  sound,  as  it  would  to  make  ropes  of  sand,  or 
ladders  of  sunshine '' 


4^X)  ELLEN    OR   THE 


XXXf. 

^^  A  ^D  can  Ellen  tell,"   I  asked,  *'thc  distance  that  sound 

-**"     was  ever  known  to  be  heard  ?  " 

**  Ellen  will  reply,"  she  said,  '*  by  quotinjj  from  Professor 
Silliman  of  Yale  College,  who,  in  '  Principles  of  Physics.*  pub- 
lished by  him,  second  edition.  1866,  says: 

'The  distance  at  which  sounds  are  audible  does  not  admit  of  precise 
measurement.  In  general,  it  may  be  stated,  that  a  sound  will  be 
heard  further,  the  greater  its  original  intensity,  and  the  denser  the 
medium  in  which  it  is  propagated.  It  also  depends,  greatly,  on  the 
delicacy  of  hearing  of  dilTerent  individuals.  The  intensity  of  sound, 
like  that  of  .ill  forces  acting  in  lines,  diminishes  in  the  inverse  ratio  of 
the  Sfjuarcs  of  tlie  distant  c  <jf  the  sounding  body.  Thus,  if  the  linear 
dimensions  of  a  theatre  be  doubled,  the  \olunie  of  the  performers' 
voices  at  any  part  of  the  circunu'erenc  e  will  be  diminished  in  a  fourfold 
proj)ortion. 

*Tluit  the  difference  of  the  agitating  im])ressi()n  is  the  true  cause,  is 
shown  by  confining  the  air  on  all  sides  in  a  tube.  IJiot  experimented 
with  2860  feet  of  the  water-j)ii)es  of  Paris.  At  this  distance  the  lowest 
whisi)er  made  at  one  end  was  accurately  heard  at  the  other  extremity 
ot  the  tube. 

*  A  j)Owerfui  human  voi(X^  in  the  ojien  air,  at  the  ordinary  tempera- 
ture is  audible  at  the  distance  of  seven  hundred  feet.  In  a  frosty  air, 
undisturbed  by  winds  or  current,  sound  is  heard  at  a  much  greater  dis- 
tan("e  with  surprising  distinctness.     Lieut.    Korster,   in  the  third   polar 


WHISPERINGS   OF    AN   OLD    PINE 


4<53 


cx|>e(iilion  of  Capt.  Parry,  held  a  conversation  with  a  man  across  the 
harbor  of  Port  Bowen,  a  distance  of  one  and  a  quarler  miles.  Dr. 
Voung  states,  on  the  authority  of  Derhara»  that  the  watchword  **  all's 
well  '*  has  been  distinctly  heard  from  Old  to  New  (libraltar,  a  distance 
often  miles.  The  marching  of  a  company  of  soldiers  may  be  heard, 
on  a  still  night,  at  from  five  hundred  and  eighty  to  eight  hundred  and 
thirty  paces ;  a  squadron  of  cavalry  at  foot  pace,  at  seven  hundred  and 
fifty  paces ;  trotting,  or  galloping,  one  thousand  and  eighty  paces  dis- 
tant. When  the  air  is  cahii  and  dry,  the  report  of  a  musket  is  audible 
at  eight  thousand  paces.  The  sound  of  the  cannonading  at  Waterloo 
was  heard  at  Dover. 

*  Sounds  travel  further  on  the  earth^s  surface  than  through  the  atmos- 
phere. Thus  it  is  said,  that  at  the  siege  of  Antwerp  in  1S32,  the  can- 
nonading was  heard  in  the  mines  of  Saxony,  which  are  about  three 
htmdred  and  seventy  miles  distant.  The  cannonading  at  the  battle  of 
Jena  was  heard  feebly  in  the  open  fields  near  Dresden,  92  miles  dis- 
tant, but  in  the  casemates  of  the  fortifications  it  was  heard  with  great 
distinctness.  The  noise  of  a  sea  fight  between  the  English  and  the 
Dutch  in  1672,  was  heard  at  Shrewsbury^  a  distance  of  two  hundred 
miles.  Sound  has  been  carried  by  the  atmosphere  to  the  distance  of 
three  hundred  and  forty-five  miles»  and  it  is  asserted  that  the  very  violent 
explosions  of  the  volcano  at  St.  Vincent's  have  been  heard  at  Demarara. 

'Sir  Stamford  Rafflns  records  however  a  similar,  though  much  more 
extraordinary,  fact.  The  eruption  in  Tombers,  in  Sumbawa,  was  per- 
haps the  most  violent  volcanic  action  recorded ;  occasional  paroxysms 
were  heard,  he  says,  more  than  nine  hundred  miles  distant.' 

•*Mr.  Sillimaii  has  the  following  on  the  length  of  what  he  calls 
sonorous  waves: 


'Length  of  sonorous  waves,^ — It  is  easy  to  ascertain  the  length  of 
a  sonorous  vibration,  if  we  know  the  number  of  vibrations  made  in  a 


464  ELLEN   OR  THE 

second.  For,  as  sound  travels  at  the  rate  of  1 1 1 8  feet  per  second,  if 
but  one  vibration  is  made  in  that  time,  the  length  of  the  wave  must  be 
1 1 18  feet;  if  two  vibrations,  the  length  of  each  must  be  half  of  11 18, 
=559  feet,  &c. 

*C  corresponds,  as  we  have  seen,  to  128  vibrations  per  second;  the 
length  of  its  waves  is,  therefore,  (1118  -r- 128)  =8.73  feet. 

*The  following  table  indicates  the  length  of  the  waves  corresponding 
to  the  C  of  successive  scales  : 

Length  of  waves  in  feet.        Number  of  vibrations  ''n  a  second. 

C-3 70.          16 

C-2 35 32 

C-i 17.5        64 

Ci 8.73 128 

C2 4.375 256 

C3 2.187 512 

C4 1 093 1024 

"  The  utter  impossibility  of  this  theory  being  true,  is  again 
illustrated  by  the  assumed  length  of  these  supposed  air  waves. 
For  two  things  are  positively  stated  in  text-books,  the  length 
of  the  waves,  as  above,  and  the  further  fact  that  these  waves 
are  the  correlative  of  sound,  and  as  such  that  every  part  of  the 
wave  has  its  effect  upon,  that  is,  helps  make,  the  sound. 

"  Thus  it  is  universally  stated  in  the  different  text-books  of 
ph}'sics  that  the  loudness  of  a  note  depends  on  the  width, 
height  and  length  of  the  oscillations  producing  it,  and  the  timbre 
upon  the /or;;/  of  the  vibration  of  the  aerial  particles  by  which 
sound  is  transmitted,  which  doesn't  mean  anything  to  any  sensi- 
ble person,  but  is  supposed  to  mean  something  to  a  physicist.  * 

*  See  pages  197,  198,  270-274. 


WHISPERINGS   OF   AN    OLD    PINE 


46s 


**  But  whilst  these  facts  are  definitely  and  fully  staled,  that 
every  part  of  diese  waves,  varying  rrom  one  to  seventy  feet 
in  length,  assists  in  making  the  sound,  and  is  absolutely  essen- 
tial to  such  sound's  completeness,  every  person  on  earth  knows, 
or  can  know  by  experiment,  that  the  sounds  are  perfectly 
made  and  perfccdy  understood,  if  spoken  direcUy  into  the  ear, 
with  but  at  the  most  two  or  three  inches  space  to  extend  in. 
And  still  full  grown  men  by  the  thousands  and  tens  of  thous- 
ands will  stand  up,  or  sit  down,  and  teach  this  stuff,  apparently 
unconscious  that  in  doing  it  they  demonstrate  themselves  to 
be  idiots  or  fools,  There  are  not  words  strong  enough  in  the 
English  language  for  Ellen  to  express  her  abhorrence  and 
contempt  for  such  teachings, 

'*Odur,  too,  is  infinitesimal  particles  of  matter  thrown  off  by 
the  odoriferous  body,  permeating  equally  the  atmosphere,  the 
odoriferous  body  lasting  at  times  for  months  with  no  apparent 
diminution.** 

**And  how  does  Ellen  explain  this?*'  I  afeked. 

'*As  Ellen  thinks  the  explanation  is  in  our  ignorance  of  the 
true  conditions,  and  perhaps  is  entirely  connected  with  the 
limits  of  our  vision.  Far  enough  off,  the  greatest  sphere  is  a 
mere  speck  in  the  sky,  and  man  does  not  know  this  until  he 
learns  it — the  child  reaches  for  the  moon  as  well  as  for  a  ball — 
which  shows  the  illusive  nature  of  vision.  A  sudden  explo- 
sion of  steam  or  dynamite  shows  the  possible  expansion  which 
exists  in  apparently  small  space.  And  therefore  Ellen  assumes 
that  anything  of  this  kind  can  occur,  because  she  knows  that 
some  such  things  do  occur.  In  the  infinitely  small  there  would 
appear  to  be  no  limits,  as  well  as  in  the  infinitely  large.     This 


466  ELLEN   OR  THE 

Ellen  has  repeatedly  spoken  of.  And  she  thinks  the  conditions 
are  illustrated  in  the  failure  of  eyesight,  when  those  things  which 
had  been  plainly  visible  grow  to  us  smaller  and  smaller,  until 
they  disappear.  By  aids  to  vision  they  will  become  larger 
and  larger ;  nor  does  Ellen  think  that  there  is  any  limit  in  either 
direction  to  these  conditions;  and,  if  there  is  not,  the  hopeless 
task  of  counting  those  things  which  we  do  not  see,  or  estimating 
correctly  their  number  or  size,  may  be  imagined. 

"Sound  then,  any  sound,  has  the  power  of  movement,  but, 
like  everything  else  material,  its  life  is  limited.  And  yet, 
where  apparently  there  is  none,  it  may  be  gathered  by  proper 
machinery  in  sufficient  quantity  to  be  heard.  And  this  illus- 
trates that  principle  in  nature  which  Ellen  has  repeatedly 
referred  to,  that  effect  is  proportionate  to  amount. 

*'Dust  is  frequently  scattered  into  the  air  so  that  it  seems  to 
fill  the  whole  of  it.  A  flock  of  birds  may  seem  to  do  the 
same  thing.  Thus  light  permeates,  its  particles  being  thrown 
out  in  sufficient  quantities  from  the  illuminating  body,  though 
it  is  said  that  there  is  a  large  distance  between  the  successive 
particles  of  light  which  come  from  the  sun ;  and  this  again 
illustrates  the  illusion  or  delusion  of  vision. 

**\Vell,  sound  is  thus  poured  out  in  quantities  from  the  initial 
sounding  body,  with  a  power  of  spreading  over  quite  an  ex- 
tended space. 

*•  It  is  proven  that  artificially  instruments  may  be  made  with 
which  to  repeat  it.  And  these  may  be  made  in  different 
ways,  how  many  l^llen  knows  not.  Some  of  them,  like  the 
graphophone  or  telegraphone,  are  wonderfully  simple,  and  quite 
capable ;    but    these    as    well    as    all    other    instruments,    as    a 


WHISPERINGS  OF  AN  OLD    PINE 


4^7 


drum,  a  fife,  a  piano,  or  a  violin,  all  instruments  which  produce 
sound:4,  Ellen  thinks  there  is  no  exception,  have  to  be  manipu- 
lated or  played  upon  to  make  sound.  The  same  is  true  of  the 
human  voice,  or  the  leaves  of  the  forest,  or  waters  of  the  sea. 
And  all  may  repeat  certain  sounds  whilst  they  last.  But  none 
of  them  can  repeat  any  sound  excepting  the  one  kind  they 
were  made  to  repeat.** 

**  And  what/'  I  asked,  **is  the  operation  of  a  sounding  board? 
The  old  Pine  has  noticed  that  they  will  throw  off  numerous 
sounds  at  the  same  time?'* 

**  But  can  make  none  of  them/*  she  replied.  **  Sound  from 
the  sounding  instrument  goes  into  the  mounding  board,  fmm 
which  It  more  readily  enters  the  air,  perhaps  solely  because  the 
sounding  board  presents  much  more  surface  to  the  air  The 
audible  sound  is  at  once  very  loudly  increased,  but  stops  in- 
stantly with  the  sounding  body.  Nor  is  it  possible  to  get  the 
same  sound  from  the  sounding  board,  unless  it  is  supplied  by 
the  sounding  body  made  to  produce  such  sound. 

**  These  sounds  flow  into  a  sounding  board,  as  streams  or 
rivulets  into  a  pond,  and  will  cover  it  completely  over,  nor  will 
they  mix,  but  each  retains  its  own  character 

•*In  this  respect  the  sounding  board  is  entirely  different  from 
the  record,  for  that  will  constantl}'  repeat  each  individual  sound 
which  it  represents.  That  is,  each  particular  part  of  the  record 
will  repeat  its  own  sound ;  and  is  therefore  an  initial  sound- 
ing body. 

*'  Such  a  repeating  sounding  body  as  this  Ellen  can  under- 
stand. For,  in  the  first  place,  it  isn't  an  hypothesis,  but  a 
known  fact,  which  makes  a  thousand  to  one  in  its  favor,'' 


468  ELLEN    OR   THE 

"But."  I  said,  **thc  diafram  of  the  graphophone,  as  well  as 
the  sounding  board,  increases  the  effect  of  the  sound  thrown 
off  by  the  sounding  body." 

**Ycs,"  she  answered,  **  and,  as  Ellen  thinks,  by  gathering 
sound,  as  water  is  gathered  in  a  mill  pond,  and  thus  increasing 
its  onward  flow.  And  therefore  membranes  and  diaframs  add 
to  the  effect  of  sounds,  as  car  trumpets  or  megaphones  do,  by 
increasing  its  quantity  at  a  particular  point.  With  the  sound- 
ing board  there  may  be  also  increased  effect  from  reverbera- 
tion. But,  whatever  happens,  the  origin  of  the  sound  is  the 
sounding  body  made  expressly  to  make  such  sound. 

*'  So  far  as  Ellen  knows,  every  phenomenon  of  sound  is 
explained  fully  and  readily  by  the  principle  that  all  sound, 
except  a  very  little  that  comes  from  unison  vibration,  is  made  by 
the  initiatory  sounding  bodies.  Nor  is  there  a  single  phenom- 
enon but  is  instantaneously  and  completely  explained  on  the 
assumption  that  sound  is  an  entity,  and  not  one  of  them  that 
can  be  explained  in  an\'  other  wa\'.  h^)r  the  onl}'  other  pos- 
sible explanation  is,  that  a  diafram  talks  with  great  skill  and 
fluency,  which  is  manifestly  absurd. 

"A  diafram,  which  is  supposed  to  make  all  sound,  contains 
none  of  the  machinery  b}'  which  these  sounds  arc  made.  No- 
body pretends  it  does,  such  as  the  strings  or  wires  of  a  piano, 
the  different  stops  of  a  llute,  the  vocal  organs  of  animals,  in- 
sects or  birds,  or  an\'thing  else  of  the  sound-making  machinery 
of  the  world.  These  must  be  created  in  the  diafram,  should  it 
repeat  such  sounds.  That,  under  favorable  conditions,  ma- 
chinery nu'ght  be  made  on  purpose  to  repeat  each  individual 
sound  spoken  or  made,   isn't  to  Ellen   especially  strange,    for 


WHISPEKTNGS   OF  AN   OLD    PINE 


she  knows  that  sound  consists  of  particles  of  matter,  in 
some  way  forced  together;  and  she  knows,  too,  that  each 
individual  particle  is  made^  in  part  at  least,  from  material  that 
exists  everywhere  in  the  atmosphere,  and  she  can  imagine 
that  machinery,  very  infinitesimal  in  sixe,  might  be  made  to 
produce  such  result.  All  of  this  she  can  imagine  because  it  is 
in  accordance  with  natural  laws;  but  she  knows  that  these 
results  cannot  be  brought  about  without  machinery,  and  she 
does  not  believe  that  such  machiner}'  could  operate  simulta* 
neously  with  its  being  made.  As  Ellen  has  said*  neither  the 
graphophone  or  telegraphone  record  does  this.  But  both  act 
as  all  such  instruments  do,  whether  made  naturally  or  artificially. 
That  is,  they  arc  first  made  and  then,  at  a  future  time,  with 
extraneous  assistance,  repeat  their  parts." 

•*And  how  is  sound  maide?"  I  asked. 

"  It  is  made  by  shock  or  disturbance,"  she  replied.  *' And  it 
would  seem  that  the  sound  made  by  a  blow  was  all  the  supply 
there  was  until  more  was  made  by  another  blow,  or  disturb- 
ance. For  the  vibration  of  the  fork,  which  is  made  by  sound, 
starts  with  the  blow,  and  diminishes  in  exact  proportion  with 
the  diminishing  or  throwing  off  of  the  sound;  which  Ellen 
considers  a  demonstration  that  shock  alone  makes  the  sound. 

*'  Electricity,  magnetism,  and  sound,  combined,  can  in 
no  way  assist  in  repeating  sound,  excepting  what  they  can 
make  themselves,  in  any  otlier  way  than  by  making  a  sound- 
repeating  instrument.  No  such  instrument  is  made  of  the 
diafram  at  the  telephones  or  elsewhere,  nor  is  there  any 
pretense  by  anyone  that  there  is,  or  any  possibility  thut  there 
can  be. 


47^  ELLEN  OR  THE 

"Thus  Sylvanus  P.  Thompson  of  London,  England,  very 
high  scientific  authority,  says : 

'In  1876  Graham  Bell  invented  the  magneto-telephone.  In  thia  m- 
stniment  the  speaker  talks  to  an  elastic  plate  of  thin  sheet  iron,  ifliich 
vibrates  and  transmits  its  every  movement  electrically  to  a  similar  plate 
in  a  similar  telephone  at  a  distant  station,  causing  it  to  vibrate  in  an 
identical  manner,  and  thereby  to  emit  identical  sound*' 

''This  statement,  as  Ellen  has  shown,  is  entirely  erroneous. 
The  elastic  plate,  said  to  be  talked  to,  and  the  similar  plate  at 
the  receiving  telephone,  soon  come  to  their  limits.  And  these 
are  that  the  magnet  at  the  receiving  instrument  may  be 
strengthened  and  weakened  by  the  intermittent  action  of  the 
electric  current,  so  as  to  make  signals  with  the  receiving  dia- 
fram,  as  in .  telegraphy.  This  it  does  in  accordance  with  the 
laws  which  govern  electricity  and  magnetism.  All  the  rest 
is  guess  work,  in  support  of  an  erroneous  theory,  and  is 
wholly  incorrect.  Ellen  wants  no  further  evidence  of  this, 
for  what  takes  place  is  self-evident.  But  if  any  want  it  the 
et^idence  is,  that  sound  will  be  heard  at  the  receiver,  although 
the  transmitter  has  no  diafram,  and  in  some  cases  will  be  heard 
equally  well. 

**  But  whether  the  sound  was  heard  equally  well  or  not,  if  it 
was  heard  at  all,  Ellen  would  like  to  know  by  what  theory. 
Ellen  has  already  repeated  numerous  experiments  which  show 
that  the  explanation  given  by  Mr.  Thompson  does  not  explain 
She  will  now  read  from  a  book  which  she  finds  does  practically 
explain  the  different  things — at  least  several  of  them — supposed 
to  vibrate  so  as  to  talk  and  repeat  sound.     The  old  Pine  will 


WHISPERINGS   OF  AN   OLD   PINE  47 1 

see  that  this  includes  a  chimney,  fireplace,  flag-stone,  live  wire 
and  nails.  Quite  an  assortment,  and  being  unusually  intelli- 
gent it  makes  no  difference  to  them  what  language  is  used. 

**And  so  Ellen,  in  walking  the  streets  at  Washington  heard 
all  kinds  of  things  talking,  that  is,  she  heard  all  kinds  of  talk. 
And  so  she  does  everywhere  she  goes,  especially  when  she 
passes  folks.  But  she  always  supposed  it  was  the  people  that 
were  talking ;  never  thought  of  its  being  the  shop  windows  and 
the  houses  and  curbstones. 


472  ELLEN    OR   THE 


XXXIT. 


^^ FALLEN  will  now  quote  from  a  book  called,  *  The  Modern 
-■— '      Applications  of  Electricity,*  by   E.  Ilospitalicr,  trans- 
lated and  enlarged  by  Julius  Maier,  Ph.  D.,  and  published  by 
D.  Appleton&  Co.,  New^  York,  1883. 

SPKCI A  I.   TET  .KPHON  KS. 

*  In  all  the  telei)hones  described  in  the  ])receding  pages,  we  invari- 
ably find  a  magneti(^  transmitter,  either  carbon  or  microphonic  trans- 
mitter, sending  an  undnlatory  current  along  the  line,  and  this  undalatory 
current  acting  on  a  receiving  tele])hone,  in  which  we  always  find  as 
essential  parts:  i,  a  vi])rating  ])late  ;  2,  a  magnetic  core,  and  some 
times  nn  electro-magnet ;  3,  a  coil. 

'  Not  one  of  these  parts  can  be  said  to  be  indisj^ensable  for  the 
reception  of  articulate  sounds  in  the  telephone.  Certain  receiving 
a])])aratus  do  not  employ  even  a  single  one  of  them  ;  in  some  tele- 
j>honic  transmissions  the  words  have  been  heard  without  a  receiver  ;  in 
others,  as  in  I)eirs  photophone,  transmission  is  elTected  without  wire, 
by  the  help  of  a  luminous  ray  ;  in  other  tele]>hones  the  receivers 
assume  irregular  forms, — the  princi])les  on  whi(  h  they  are  constructed 
are  not  ])ased  on  niagnetic  action  ;  in  some  we  have  physiological 
actions,    as     in  (iray's    receivers;  in    others,    chemical    action,    as    in 


■ 

■ 

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TBERKWTOMK 
PUBLIC  LIBRART 

AStORi  LKM9X  AKI> 
IILDSN  rOUiJDAtlOMI 

m                     L 

^^1 

1 

« 

WHISPEI 


475 


Edison's  electro-motograph,  etc.     We  are  going  to  examine  the  most 
important  and  most  original  of  the  apparatus. 

*  Telephones  without  Vibrating  Plate. — The  first  simplification  to  be 
applied  to  BelFs  telephone  consists  in  the  suppression  of  the  vibrating 
plate.  In  that  case  words  are  no  longer  distinctly  transmitted  if  the 
transmitter  is  a  magnetic  telephone,  but  the  receiver  articulates  on 
using  a  carlxjn  transmitter  and  induced  currents,  as  in  Kdison's  tel- 
ephone. The  words,  however,  are  very  faint ;  but  liu  Moncel,  who 
has  made  a  great  many  experiments  on  this  suhjectj  has  found  that  the 
effect  is  the  more  Intense  the  more  strongly  the  core  is  magnetized  and 
the  smaller  its  .size. 

*By  employing  a  thoroughly  magnetized  watch-spring  with  a  coil  of 
fine  wire  at  the  end,  Du  Moncel  has  been  al>le  to  hear  spoken  words 
with  Bell's  magnetic  telephone.  This  fact  and  a  number  of  others,  the 
results  of  various  experiments,  will  be  considered  hereafter. 

*  By  the  side  of  these  telephones  without  diafram,  Brcguet's  experi- 
ments may  conveniently  be  mentioned,  in  which  the  thickness  of  the 
membrane  has  been  increased  up  to  fifteen  centimeters  without  def^riv- 
ing  the  telephone  of  its  power  or  its  faculty  of  articulation.  In  the 
former  there  is  no  plate  at  all,  in  the  latter  there  is  too  much  of  it,  and 
the  telephone  articulates  in  either  case. 

'Telephones  without  Membrane  and  Magnet.  Ader's  Experiments 
— The  pressure  of  a  magnetized  core  in  the  receiver  is  not  indispensa- 
ble, and  we  have  seen  that  Ader's  electrophone  em'ploys  small  micro- 
scopical electro- magnets  of  soft  iron.  Whilst  making  experiments  with 
these  apparatus,  Ader  was  led  to  construct  a  receiver  composed  of  one 
siii'iplc  iron  rod  of  one  tuillimeter  diameter,  surrounded  by  a  coil  of 
fine  wire,  and  has  been  able,  under  these  conditions,  to  transmit  words 
with  great  clearness.  ITie  small  irOD  wire  was  stuck  into  a  board,  and 
he  found  that,  by  applying  a  heavy  mass  to  the  free  end  of  the  wire, 
the  intensity  of  the  sounds  was  more  than  iloublcd. 


476  ELLEN  OR  THE 

'  He  then  constructed  the  simple  receiver  represented  in  Ilgiiie  50,  * 
formed,  of  a  handle  6,  a  soft-iron  rod  CC  of  one  millimetre  diameter 
stack  into  a  pine  block  PP  five  centimetres  wide,  and  a  small  bobbin 
A  rolled  round  a  goose  quill.  The  transmitter  employed  by  Ader  ma 
that  of  his  electrophone,  but  the  telephone  thus  constructed  will 
speak  with  any  carbon  transmitter.  A  very  amusing  spiritualistic 
trick  can  be  performed  with  this  little  instrument  by  &stening  the  iron 
wire  CC  to  the  reverse  of  a  table-board,  carefully  concesling  tte  ogo- 
ducting  wires,  and  having  a  confederate  speaking  into  a  transmitter  m 
a  distant  room.  If  the  trick  is  performed  in  silence,  the  whde  table 
speaks — ^it  can  be  heard  by  all  those  standing  round.' 

''  In  this  case  the  individual  sounds  flow  into  the  table-board  by 
the  wire ;  these,  as  in  all  such  cases,  preserve  their  individuali^.^ 

'Continuing  his  experiments,  Ader  constructed  a  second,  still  simpler, 
telephone  (Figure  51).  It  consists  of  a  small  board  AB  and  a  coil  C 
fastened  to  the  board,  round  which  a  fine  wire  is  loosely  wound.  This 
apparatus  speaks  under  the  influence  of  a  carbon  transmitter  and  three 
Leclanch^  elements.  If  the  spirals  of  the  coil  are  too  close  or  too  thickly 
coated  with  gum,  the  telephone  no  longer  speaks,  but  on  introducing  in- 
to the  coil  a  nail  D,  a  small  iron  wire,  or  a  magnetized  needle  pressing 
against  the  board,  the  words  are  immediately  heard  with  perfect  clear- 
ness.    On  taking  the  nail  out,  the  telephone  again  becomes  mute. 

'Telephone  without  Membrane,  Magnet  and  Coil— The  following 
telephone  is  simpler  still : — It  consists  of  a  soft- iron  rod  A  (Figure  52) 
and  a  small  wooden  bar  B.  By  applying  the  bar  B  to  the  ear,  and  a 
heavy  metallic  mass  to  the  other  end  of  wire  A,  Ader  has  reproduced 
words  by  employing  a  carbon  transmitter.  De  la  Rive,  in  1846,  had 
found  that  sounds  eould  be  produced  under  similar  conditions  by  in- 
termittent currents,  but  Ader  was  the  first  who  produced  articulate 
sounds  by  such  simple  means. 

♦  See  Figures  50-52,  page  728,  Appendix. 


WHISPERINGS    OF   AN   OLD    PINE 


477 


'Since  Ader's  experiments,  Boiidette  of  Paris  has  constructed  a 
receiving  telephone  similar  to  the  one  represented  in  Fig.  51,  in  which 
the  wooden  board  is  replaced  by  a  steel  diafrara.  This  apparatus 
reprotluces  words  with  the  microphone  speaker  of  the  same  inventor,  by 
employing  a  single  Leclanch^*  Percival  Jenns  has  also  constructed  a 
receiving  telephone  without  membrane  or  magnet,  formed  of  a  coil 
with  iron  wire.  The  apparatus  reproduces  words  by  employing  Edison's 
carbon  transmitter  as  speaker, 

•  Microphone  Transmitters  used  as  Receivers. — ^Preecc  attributes  10 
similar  causes  the  phenomena  observed  for  the  first  time  by  Hughes, 
shortly  after  the  discovery  of  the  microphone.  Hughes  showed  thai 
the  microphone  was  reversible,  like  the  magnetic  telephone,  capable  of 
transmitting  as  well  as  receiving  vibrations.  There  w^as  no  further  need 
of  plate,  or  coil,  or  magnet,  or  magnetic  wire ;  nothing  but  two  pieces 
of  carbon  at  each  station,  connected  by  two  conducting  wires  with  a 
battery  interpolated  in  the  circuit/ 

**  Apparently  there  is  no  mouth-piece  or  anything  excepting 
two  pieces  of  carbon  touching  each  other,  each  connected  with 
the  wire  and  thus  forming  a  circuit,  in  which  there  is  a  single 
cell.  This  is  evidently  quite  similar  to  the  experiment  given  on 
page  549  of  transmitting  sound  by  loose  electrical  contact 

*The  experiment  is  rather  delicate,  and  all  microphones  do  not  in 
the  same  degree  reproduce  the  phenomena  we  have  mentioned. 
Boudet's  microphone  gives  the  best  results,  but  the  two  identical  appa- 
ratuses, speaker  and  receiver,  must  be  adjtisted  to  perfection  for  the 
purfiose.     A  single  Leclanch^  is  then  sufficient  to  produce  these  effects, 

'Pollard  and  Garnier,  too,  have  obtained  words  from  their  carbon 
transmitters,  and  Carlo  Resio,  of  Genoa,  has  used  his  liquid  transmitter 
as  receiver.  It  is  impossible,  in  the  present  state  of  science,  exactly 
to  explain  what  happens  in  these  telephonic  transmissions. 


4/8  ELLEN   OR   THE 

'Blythe*s  Speaking  Microphone. — Into  a  flat  box  of  thirty  centi 
meters  by  twenty  centimeters,  Blythe  places  some  gas  cinders  and  two 
plates  of  sheet  iron  at  the  extremities  of  the  box ;  this  constitutes  the 
microphone.  According  to  Blythe,  by  placing  two  of  his  microphones 
in  the  circuit  of  a  battery  of  two  Grove's  elements,  words  pronounced 
before  one  of  the  microphones  can  be  heard  in  the  other,  which  acts  as 
receiver.  Du  Moncel  has  modified  Blythe's  apparatus  by  employing 
large  fragments  of  coke  and  two  electrodes,  one  of  zinc,  the  other  of 
copper.  By  putting  water  into  the  box  and  connecting  the  two  elec- 
trodes of  the  apparatus  with  the  two  terminals  of  a  Bell's  telephone,  a 
telephone  system  is  formed,  in  which  the  battery  serves  as  transmitter 
and  the  transmitter  serves  as  batter>\ 

*Antoine  Breguet's  Mercury  Telephone. — Brdguet's  apparatus  utilizes 
electro-capillary  forces  and  the  electric  currents  produced  by  them. 
The  phenomenon  which  led  to  the  construction  of  this  instrument  is 
absolutely  reversible ;  the  transmitter  and  the  receiver  are,  therefore, 
two  identical  apparatus.     ♦     *     * 

'Telephone  without  Receiver. — Some  ver}' curious  experiments  made 
by  a  French  officer  of  the  Engineers  at  Lun<5ville,  have  shown  that  the 
words  emitted  by  the  transmitter  can  be  heard  at  the  receiving  station 
without  any  telephone  whatever.  M.  Ocpaux  gave  the  following 
account  of  these  ex])eriments  at  a  meeting  of  the  Soci(^t(}  d'Kncourage- 
ment  on  the  13th  of  June,  i^'jg  : 

* ''There  exists  at  Luneville  a  tele])honic  system  established  under 
rather  ])rimitive  conditions.  The  live  wire  is  of  galvanized  iron,  three 
millimetres  thick,  and  tightly  stretched.  It  is  fixed  to  a  post  at  the  top 
of  a  hay-loft,  and  runs  in  an  obtuse  angle  along  the  chimney-stack  of  a 
neighboring  house  at  a  distance  of  about  ten  metres.  The  chimney- 
stack  naturally  corresi)onds  with  the  fire-])lace  of  a  room  in  the  first 
fioor  of  the  building.  On  s])eaking  into  the  tele])hone  from  one  station 
to  the  other,  not  only  the  receiver  s])eaks  and  can  be  heard  on  holding 
it  close  to  the  ear,  but,  and  this  is  most  inex])licable,  the  chimney  along 


WHISPEPJNGS   or  AN  OLD   PINE  479 

which  the  wire  runs  speaks,  the  fire -place  speaks,  and  a  person  lying  in 
()ed  in  the  room  hears  from  his  bed  all  the  words  transmitted  to  the 
w>e  more  distinctly  than  those  who  at  the  end  of  the  line  use  the 
receiving  apparatus.  It  is  imjKJssible  to  deny  this  fact,  of  which  I  have 
been  a  fre<pient  witness.  The  wire  of  Ihe  chimney-stack  has  been  in- 
sulated by  glass  plates,  and  yet  the  words  have  been  heard  as  before ; 
at  the  most  remote  station,  at  a  distance  of  about  200  to  250  metres,  a 
simiiar  tact  has  been  observed. 

*"The  earth  wire  foUow*s  in  its  path  a  zinc  drainage  pipe,  this  pipe 
has  ramifications  leading  to  the  flagstone ;  the  flag-stone  speaks. 

*  '*  1  have  been  told  that  at  each  connecting  point  the  live  wire 
speaks;  by  bending  it  several  times  around  a  nail  fixed  in  the  wall 
the  knot  thus  produced  speaks. 

*"It  is  probable  that  the  fact,  which  I  warrant  to  be  correct,  is  only 
produced  in  the  neighborhood  of  the  jxiint  of  convention  and  of 
contact,*' ' 

••Any  of  the  above  facts  is  a  demonstration  that  the  articu- 
late speech  heard  at  a  receiving  telephone  is  that  of  the  person 
talking  into  the  sending  instrument.  For  this  explains  every 
experiment,  and  all  possible  conditions,  and  nothing  else  will 
or  can. 

"  Ellen  will  repeat  the  great  English  scientist  Huxley's  remark 
about  hypotheses: 

*  Every  hypothesis  is  bound  to  explain,  or  at  any  rate  not  to  be  incon- 
sistent with,  the  whole  of  the  facts  it  professes  to  account  for ;  and  if 
there  is  a  single  one  of  thei^e  facts  which  can  be  shown  to  be  inconsist- 
ent with  (1  do  not  merely  mean  inexplicable  by,  but  contrary  to>  the 
h>Tx>thesis,  such  hypothesis  falls  to  the  ground— it  is  worth  nothing. 
One  fact  with  which  it  is  positively  inconsistent  is  worth  as  much,  and 
is  as  i>owcrful  in  negativing  the  hypothesis,  as  five  hundred,* 


48o 


ELLEN  OR  nil 


XXXUl. 


^^f  N  the  first  place,  and  sufficient  to  demolish  a  million  hypo- 
^  theses  like  this,  is  the  supposition,  that  a  thing  can  per- 
form any  important  function  that  it  was  not  made  to  perform, 
as  that  a  diafram,  or  the  core  of  a  magnet,  or  a  coil  of  wire,  or 
chimney,  or  a  curbstone,  or  a  nail,  or  live  wire,  could  not  only 
do  what  man  can,  provided  with  vocal  organs,  one  of  the  most 
remarkable  of  all  the  contrivances  of  nature, — utter  articulate 
speech;  but  also,  in  the  way  of  sound,  could  double  distance 
man's  ability  so  many  times  that  he  wouldn't  be  in  it  at  all, — 
utter  not  a  million  only  but  a  hundred  millions  other  sounds, 
including  that  of  every  musical  instrument,  in  the  world,  cer^ 
tainly,  if  not  in  the  universe;  of  every  bird;  of  every  insect;  of 
every  beast;  of  every  trembling  leaf;  of  every  trickling  drop  of 
water,  swelling  river  or  roaring  billow;  of  every  breath  of  air, 
from  the  lovely  strains  of  an  ^Eolian  harp,  to  the  wild  march 
of  a  hurricane;  Ellen  hasn't  begun  to  enumerate  the  amount  of 
melody  that  the  diafram  can  make,  or  the  curbstone  or  nail,  or 
whatever  else  happens  to  be  connected  with  an  electric 
current,  the  supposition  being  that  the  function  of  an  electric 
current  is  to  make  anything,  or  anything  it  chooses,  repeat 
sound. 

"  Well    the   scientists  had  two  chances ;    all  of  this  for  the 
diafram  to  do,  or  their  air  waves  to  get  into  the  electric  current; 


1 

■ 

m 

THE  NEW  YORK 
PUBLIC  LIBRARY 

A»tOA.  LBHOX.  AH* 

I1LB«M  rOUMOATMHI 

1       K                             >• 

^^1 

1 

vvnrsPERiNGs  vy  an  uld  pine 


48.^ 


and  get  out  again  ready  for  business  after  their  ride  of  a  thous- 
and miles  more  or  less.  And  they  chose  the  lesser  evil.  Ellen 
thinks  they  were  right  in  their  judgment.  No  one  would  have 
been  deceived  that  the  air  waves  got  into  the  electric  current; 
but  many  have  been  deceived  in  regard  to  the  ability  of  the 
diafram. 

**  The  whole  question  grows  too  sickening  for  discussion. 
There  is  nothing  to  do  but  to  admit  that  we  were  deceived  be- 
cause we  didn*t  consider, — and  re-adjust  our  physics. 

*' In  connection  Ellen  would  call  attention  to  the  fact  men- 
tioned by  Ganot  that  when  a  telephone  is  held  to  the  ear  during 
a  thunderstorm  every  lightning  flash  in  the  sky  is  simultaneous- 
ly heard  to  be  accompanied  by  a  sharp  crack. 

*•  And  she  would  call  attention,  too,  to  the  fact  that  particles 
of  sound  may  be  transmitted  by  a  ray  of  light  And  un- 
doubtedly, as  Ellen  thinks,  sound  will  yet  be  sent  through  a 
wireless  telephone. 

**But  more  than  this,  we  find  that  every  sound  can  make  an 
instrument  that  will  reproduce  itself,  if  only  arrangement  is  sup* 
plied  by  which  it  can  leave  an  impression  of  itself  upon  material 
of  such  a  consistency  that  the  impression  becomes  enduring. 
And  this  would  appear  to  mean  that  sound  in  its  form,  if  not  in 
its  size,  is  a  copy  of  the  instrument  which  makes  it.  Nor 
does  Ellen  know  why  it  might  not  be,  fur  it  must  be  of  some 
form  and  it  might  be  of  this  form.  This  is  true  of  the  off-spring 
ol  all  animals,  and  of  all  plants.  In  these  cases  the  form  starts 
the  samCi  and  for  a  certain  period  increases  in  sijte,  that  is»  in- 
creases to  a  certain  size,  the  form  being  preserved.  For  aught 
Ellen  knows  the  beautiful  snow^  flakes,  or  the  rain  drops,  may 


484  ELLEN  OK  THE 

do  the  same  thing.  Such  an  arrangement  is  remarkable,  but 
not  at  all  inharmonious  or  inconsistent  with  the  method  by 
which  other  things  are  made.  Indeed  Ellen  begins  to  think 
it  is  the  universal  law.  That  it  is  thus  that  the  lovely  shells  are 
made,  and  the  beautiful  stones  often  rounded  so  sweetly.  In 
all  things  the  period  of  growth  may  be  very  quick,  or  very 
slow,  for  in  all  the  duration  of  life  varies.  But  every  material 
thing  may  be  fashioned,  so  far  as  Ellen  knows,  by  its  prototype. 
At  any  rate  many  are,  included  among  which  is  the  category  of 
sounds." 

"And  the  eagle's  wing?"  I  said. 

"  Is  the  off-spring  of  another  eagle's  wing,  with  all  its  power 
and  majesty,  and  so  the  wings  of  the  smaller  birds,  with  all  their 
delicacy  and  beauty.  The  fruit  too,  which  adorns  the  trees,  and 
the  flowers  that  float  upon  the  air ;  all  are  but  reproductions 
in  a  universe  where  existence  as  a  whole  is  made  up  of  such 
changing  phases." 

"But  the  spiritual,  Ellen?" 

**  Rises  above  all  this,  studies  and  uses  it,  and  in  that  consists 
its  existence.  And  its  conditions  are  equally  changing.  For 
all  existence  is  cliange.  But,  as  Ellen  thinks,  the  changes  in 
spiritual  existence  arc  always  under  the  control,  or  largely  so, 
of  spirit,  which  is  individualized,  and  to  which  belongs  the  prin- 
ciple of  choice.  And  therefore,  to  a  certain  extent,  each  in- 
dividual works  out  his  own  destiny. 

"The  radius  that  generates  half  the  circumference,  at  one 
point,  only,  makes  right  angles.  And  so  there  is  but  (yie  sound 
which  can  make  the  instrument  that  can  make  the  same  sound. 
Unquestionably  other  sounds  will  approach  very  near  to  it  in 


WHISPERINGS   OF   AN    OLD   PINE 


making  the  vibration  that  it  makes,  Vcn^  near,  but  it  only 
reaches  the  goal/* 

*'  But  why?''  1  asked,  **  should  sound  be  able  to  make  an  in- 
strument which  will  repeat  the  sound?*' 

"Because  the  instrument  that  made  it,  made  it  like  itself; 
not  in  size,  but  in  form.  Ellen  cannot  think  of  any  other 
possible  reason, 

"And  Ellen  thinks  that  always  a  sound-producing  instru- 
ment makes  sound  after  its  own  pattern  only  smaller,  and  the 
soimd  may  make  another  sound-producing  instrument  modeled 
after  itself;  and  so  this  smaller  instrument  makes  a  still  smaller 
sounds  one  image  receding  after  the  other  in  this  order,  until  the 
little  machine  is  reached  which  records  in  the  brain  the  memory 
of  sounds. 

"The  old  Pine  can  see  how  infinitesimal  it  all  becomes. 
But  whether  such  infinity  is  accomplished  by  the  effect  of  dis- 
tance, or  how,  Ellen  does  not  know.  It  is  a  part  of  the  crea- 
tion, no  less  real  than  the  tuning  fork,  but  why  under  such  dif- 
ferent colors,  Ellen  docs  not  know.  She  is  suspicious  that  the 
glamour  may  be  in  the  changing  cye»  not  in  the  changing 
thing.  For  the  distant  tree  may  be  smaller  to  Ellen,  but  as 
large  as  the  one  that  leans  over  her.  And  the  star  grows 
infinitely  small,  not  changing  itself,  but  left  in  the  wake  of 
distance.  But  whatever  may  be  the  explanation  of  appear- 
ances, one  fact  is  clear  to  the  mind,  that  either  sound,  or  sound 
in  motion,  is  in  form  a  fac-similt  of  the  instrument  which 
made  it, — because  its  record  or  impression  makes  another  simi- 
lar sound-producing  instrument. 

•*  And  thus  as  Ellen  has  suggestedi  all  things  visible  may  be 


i^^. 


486  ELLEN  OR  THE 

instantaneously  duplicated,  by  reflection  in  all  its  different 
phases,  or  through  the  agency  of  man  by  the  camera,  or 
in  slower  process  by  a  painting. 

"All  of  these  wonderful  things  are  constantly  done  in 
nature.  Indeed,  it  is  in  such  marvelous  things  that  nature 
consists. 

"  But  in  no  case  is  such  a  thing  accomplished  exc^ttng*  by 
something  made  expressly  to  do  it.  Throughout  the  universe 
the  old  Pine  will  find  no  exception  to  this.  Law  and  order 
govern  the  whole.  It  is  equally  true  to-day  as  when  Christ 
spoke,  that  men  cannot  gather  grapes  from  thorns,  or  figs 
of  thistles.  The  grapes  will  grow  upon  the  grape  vine»  and 
the  figs  upon  the  fig  tree.  And  so  that  instrument  and  that 
only  whicli  was  made  to  make  any  particular  sound,  will 
make  it 

"Neither  the  diafram  that  was  formed  to  collect  and  reflect 
sound,  will  do  it;  nor  the  pole  of  the  magnet  adapted  to 
very  different  work ;  nor  any  other  contrivance  which  by  acci- 
dent may  belong  to  a  receiving  telephone ;  nothiitg  but  an 
instrument  made  to  make  that  particular  sound,  and  this,  only 
in  accordance  with  a  law  of  performance  as  fixed  as  that  of  its 
creation,  entirely  independent  of  that  creation,  and  of  necessity 
succeeding  it." 

"But  exactly  how  is  the  record  of  the  graphophone  repro- 
duced?" I  asked. 

**  Practically,  as  Ellen  has  said,  by  a  reversal  of  the  opera- 
tion which  made  it  Thus  a  glass  bead,  of  right  size  to  enter 
the  record,  is  fastened  to  a  similar  diafram,  and  passes  over 
this  record  with  similar   movement  of  machinery.     In  doing 


WHISPERINGS   OF   AN  OLD    PINE 


487 


this  it  re-creates  the  sounds,  evidently  because  the  indentures 
have  the  same  normal  vibrations,  as  those  by  which  the  original 
sounds  were  made.  And  this  means,  as  Hllen  has  said,  that 
each  sound,  or  else  the  impression  of  it  whilst  in  motion,  is  of 
the  same  form  as  the  instrument  which  made  it, 

*•  Ellen  doesn*t  say  that  it  is  composed  of  the  same  material, 
nor  that  it  is  of  the  same  size,  but  that  its  shape  is  sucli  as 
to  create  the  same  sound,  which  is  a  su^'gestion  that  all  sound 
is  produced,  ur  may  be,  in  a  matrix  or  mold ;  every  sound 
in  its  own  peculiar  matrix  or  mold.  Ellen  uses  this  word  in  a 
broad  sense, — that  which  gives  form  or  modifies  anything, 

**  In  this  sense  a  saw-mill  is  a  mold,  giving  dimensions,  that 
is,  shape,  to  the  different  things  which  it  distributes.  And  it 
distributes  goods  of  many  descriptions,  boards  and  planks  of 
different  thicknesses  and  widths,  clapboards,  shingles  and  staves. 
The  same  is  true  of  an  infinite  number  of  other  mills,  including 
certain  ones  of  sound  as  a  piano,  or  organ — complicated 
instruments,  producing  sounds  of  different  pitch  and  different 
intensity.  Indeed  they  all  come  under  the  same  category,  and, 
in  certain  respects,  are  governed  by  the  same  laws.  Nor  da 
any  of  them  produce  the  material  from  which  they  make  their 
goods.  Whether  logs,  cotton,  wool,  silk  or  any  other  material, 
it  ail  comes  from  outside  sources. 

'*  And  so  with  a  sound  mill,  as  is  easily  demonstrated  by  a 
tuning  fork.  Gathered  from  the  great  forests  of  electricity  suund 
is  brought  together  by  shock,  and  delivered  to  the  mills,  where 
it  is   fashioned  by  vibration,  and  distributed  for  its  various  uses. 

"  But  whether  the  distribution  of  things  is  by  a  saw-mill  or 
sound  mill,  the  effect  upon  spirit  or  the  soul  of  man  varies  with 


488  ELLEN  OR  THE 

the  thing,  each   individual  thing,  and  not  more   so  in  those 
things  perceived  by  vision  than  in  those  furnished  by  sound. 

**  In  each  case  the  peculiar  sensation  received'  is  due  to  the 
particular  thing  causing  it,  the  slightest  variation  of  the  thing 
making  a  corresponding  sensation  upon  the  soul.  But,  as  Ellen 
says,  there  is  nothing  at  all  strange  in  this,  as  every  sensation 
which  the  soul  experiences  in  this  life  is  accomplished  in  the 
same  way;  that  is  by  different  combinations  of  matter  brought 
in  contact  with  it.  And  always  the  same  combination  produces 
the  same  sensation.  Thus  a  pumpkin  pie,  a  peach,  or  a  g^ass 
of  water,  always  represents  practically  the  same  combination  of 
matter,  and  always  delights  or  affects  the  soul  similarly. 

''And  Ellen  thinks  it  is  far  better  that  each  particular 
sound  should  be  produced  by  a  particular  instrument,  than 
that  all  sound  should  be  produced  by  every  instrument. 

"And  Ellen  thinks,  too,  that  the  last  method  would  be  impos- 
sible, as  much  so,  and  similarly  so,  as  it  would  for  every  manu- 
facturing establishment  to  make  everything;  as  that  a  piano 
manufactory  should  make  mowing  machines,  and  butter  tubs, 
and  every  known  thing  that  is  manufactured  in  the  world,  as 
well  as  pianos ;  and  also  every  manufacturinpr  establishment 
do  the  same. 

"It  is  evident  that  the  piano  manufactory  couldn't  make 
mowing  machines,  without  adding  the  necessary  machinery,  nor 
butter  tubs  or  anything  else  without  doing  the  same.  Nor 
could  any  other  manufacturing  establishment.  None  of  them 
«an  make  anything  unless  they  have  the  machinery  to  make  it. 
Nor  would  it  be  possible  for  any  of  them  to  add  much  foreign 
machinery  without  the  establishment  was  extended.    And  there- 


WIIlsrERINGS    or**   AN    (J|J>    PINE 


489 


iSr^ach  addilion  would  make  practically  a  new  establishment, 
and  ior  many  reasons  this  would  be  most  inconsistent,  and  soon 
impossible. 

•*  It*s  the  same  with  sound.  The  diafram  couldn't  repeat 
articulate  speech  or  sounds  ol  any  kind»  without  the  machinery 
for  doing  it.  This  w^ould  be  equally  true  u(  the  core  of  the 
magnet,  or  the  helix,  or  a  chimney,  or  curbstone,  or  any 
thing  else.  For  this  is  the  way  the  universe  is  made,  always  a 
sufficient  cause  for  any  effecL  And  always  wherever  any- 
thing is  made.^there  must  be  the  necessary  machinery  to 
make  it 

**This  is  so  self-evident  that  we  believe  practically  everyone 
will  see  that  the  scientific  explanation  of  the  action  of  sound  at 
a  telephone,— that  the  diafram  or  any  other  thing  at  the 
receiving  telephone,  not  made  to  do  it,  repeats  sounds, — is  not 
only  entirely  erroneousi  but  impossible.  And  this  is  a  demon- 
stration, as  every  honest  and  sensible  scientist  or  layman,  who 
looks  into  the  matter,  will  see.  that  sound  is  an  entity,  which, 
in  a  telephone,  is  earned  instantaneously  through  the  wire  by 
the  electric  current;  for  the  repeating  of  sounds  by  the  diafram 
or  any  other  thing  at  the  receiving  telephone  being  impossible, 
this  is  the  only  explanation  that  remains. 

**And  this  means  that  nearly  every  sound  is  made  by  the 
initial  sounding  body.  The  conception  of  the  scientists  to  have 
everything  repeating  sound,  all  sounds,  might  answer  to  deceive 
the  unwary  in  the  acceptance  of  absurd  scientific  theories,  but 
can  have  no  other  use,  being  opposed  to  all  law,  and  therefore 
impossible, 

**For»  as  KUcn  has  said,  nature  provides  that  the  sounds  of 


490  ELLEN  OR  THE 

the  world  shall  be  made  by  a  certain  number  of  iastniiiients» 
and  the  number  is  innumerable,  literally  as  the  sands  of  the 
seashore,  for  pretty  much  everything  there  is,  is  capable  ^f 
emitting  some  sound,  although  there  are  but  comparatively  few 
things  which  make  beautiful  sounds.  And  always  the  same 
instrument  makes  the  same  sound.  And  these  sounds  are 
infinitesimal  particles  of  matter  thrown  off  by  the  sounding; 
body.  In  a  similar  manner  nature  provides  for  the  odors  of  the 
world,  infinitesimal  particles  of  matter,  thrown  off  by  the 
odoriferous  bodies.  And  these  entering  the  surrounding 
atmosphere,  find  their  way  by  the  nose  to  the  soul  or  spirit 
dwelling  within  every  body,  thus  producing  the  sensation  of 
smell.  On  the  other  hand,  the  infinitesimal  particles  of  sound 
thrown  off  by  the  sounding  body,  find  their  way  by  the  ear, 
to  the  soul  or  spirit,  and  thus  produce  the  sensation  of  hear- 
ing. Nor  are  the  sounds  repeated  by  everything  any  more 
than  the  odors  are.  That  is,  a  diafram  doesn't  sing  like  a 
Jenny  Lind ;  any  more  than  a  stump  smells  like  a  sweet  pea. 
And  one  would  be  just  as  sensible  and  just  as  possible  as  the 
other. 

"Doesn't  the  old  Pine  like  the  way  that  sounds  are  made?  " 
"Why  yes,"   I  said,  "he  not  only  likes  the  way,  but  he   is 
beginning  to  think  that  Ellen  is  right  as  to  what  the  way  is." 
"In  The  Principia,"  she  continued,  "Sir  Isaac  Newton  says: 

*  We  are  to  admit  no  more  causes  of  natural  things,  than  such  as  are 
both  true  and  sufficient  to  explain  their  appearance. 

*To  this  purpose  the  philosophers  say,  that  nature  does  nothing  in 
vain,  and  more  is  in  vain  where  less  will  serve.  For  nature  is  pleased 
with  simplicity  and  affects  not  the  pomp  of  superfluous  causes.' 


Winsj^ERINGS    OF    AN    OIJJ    PINE 


491 


*' Surely  the  old  Pine  can  easily  perceive  that  to  arrange  a 
system  so  that  every  diafram,  or  microphone  of  loose  contact, 
and  indeed  everything — for  if  anything  so  repeats  sound  every* 
thing  must — should  repeat  sound,  would  be  the  most  egregious 
instance  possible  to  conceive^  of  nature  creating  unnecessary 
causes. 

'*And  therefore  again  can  we  see  why  each  particular 
sound  of  the  world  should  be  made  by  a  particular  body*  and 
then  scattered  by  some  appropriate  law,  rather  than  that  every 
body,  or  even  a  number,  more  or  less,  should  repeat  every 
sound*  And  therefore  also  can  we  see  why  sound  is  always 
made  by  instruments ;  any  particular  sound  by  a  particular 
instrument.  This  we  know  to  be  a  fact  as  we  arc  able  to  see 
the  instruments,  whether  pianos  or  vocal  organs.  And  there- 
fore if  a  diafram  talks,  it  must  include  vocal  organs,  or  some- 
thing, which  can  produce  the  particles  of  sound  made  by 
vocal  organs.  Practically  such  a  system  would  mean  that  every 
body,  or  many  bodies,  would  have  to  be  supplicdi  not  with  one 
instrument  to  make  a  particular  sound,  but  with  a  thousand 
million  instruments  to  make  that  many  different  sounds.  And 
then  the  arrangements  would  have  to  be  made  to  circulate 
these  different  sounds.  Certainly  it  would  be  of  no  use  to  make 
them  if  they  were  not  circulated.  And  if  the  way  to  circulate 
them  was  to  have  everything  near  repeat  them,  everything  about 
them  would  have  to  be  provided  with  this  innumerable  number 
of  instruments.  Nor  is  tt  possible  for  Ellen  to  conceive  where 
in  any  repeating  instrument,  whether  a  diafram  or  an  old  shoe, 
room  could  be  found  for  all  this  machinery,  however  infinitesi* 
mal    it  might  be.     But  aside    from  all  this  Ellen   realizes   the 


49^ 


ELLEN  OR  THE 


want  of  harmony  and  intolerable  stupidity  of  such  conception, 
and  that  it  is  the  scienlitic  or  scientists*  way  of  providing  the 
universe  with  sound, — not  Nature's.  And  she  realizes  that  it 
is  subversive  of  all  order,  and  means  the  destruction  of  the 
universe  whilst  being  builL  Indeed  Ellen  has  never  had  any 
confidence  that  the  scientists  could  make  a  universe*  though 
she  has  no  doubt  they  would  talk  it  off  fine  before  they  began 
and  if  allowed  would  start  in.  They  would  walk  boldl)'  where 
angels  fear  to  tread,  until  they  were  destroyed.  And  then  there 
wouldn't  be  any  scientists;  just  the  universe  and  common  folk, 
who  never  spend  their  time  in  teaching  things  which  are  not  so. 
The  whole  theory  is  absurd  and  impossible/' 

'*  And  how  about  fire?  *'  I  asked,  ■*  That  would  appear  to 
be  catching  and  thus  spreading." 

"  Fire  is  something  of  a  very  different  character/'  she  an- 
swered, "  very  differently  caused.  To  start  a  fire  requires  an 
instrument,  made  in  a  particular  way.  For  fire  is  the  result  of 
chemical  combinations.  So  far  as  Ellen  knows,  any  material 
thing  might  be  destroyed  by  fire.  All  that  is  needed  is  the  fire, 
and  enough  of  it.  The  old  Pine  will  see  at  once  that  the 
two  conditions  are  not  comparable.  For  there  is  no  special 
preparation  required  for  anything  to  burn,  but  there  is  prepara- 
tion required  for  anything  to  make  sound,  although  but  little 
for  the  simpler  sounds 

"  Should  there  be  any  to  suggest  that  in  some  way  an  instru- 
ment is  made  in  the  diafram  to  repeat  sounds,  Ellen  says  first, 
that  none  such  is  made,  under  the  circumstances  the  thing  is 
impossible ;  and  second,  that  so  far  as  the  argument  is  con- 
cerned, it  would  make  no  difference,  as  the  sound  will  take 


BRINGS   OF  Al 


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place,  without  the  diafram*  as  Ellen  has  abundantly  shown,  and 
will  still  more  abundantly  show/' 

'*lt  is  evident,"  I  answered,  '*that  there  is  no  instrument 
made  in  the  diafram  or  elsewhere,  but  is  it  entirely  evident  that 
a  precisely  similar  movement  in  two  different  things  may  not 
create  the  same  sound,  this  sound  being  an  entity  made  from 
material  existing  in  the  air, — rjr  possibly,  in  part,  in  the 
diafram  or  other  body, — as  Ellen  once  suj^gested  to  the  old 
Pine?" 

**  Ellen  knows  she  did,  following  the  statement  of  the  scientists 
without  sufficicntl}'  examining  it.  But  with  a  very  little  ex- 
amination, she  saw  that  this  was  a  mistake;  a  mistake,  too, 
largely  due  to  ignorance  of  the  nature  of  a  graphophonc  record. 
For  as  soon  as  we  study  tliis  we  find  that  a  graphophone  is 
as  much  a  sound-producing  instrument  as  any,  and  as  much 
a  creation  by  intellect,  its  object  being  to  repeat  certain 
sounds* 

"The  old  Pine  asks  if  a  precisely  similar  movement  in  t\i'o 
different  things  may  not  create  the  same  sound?  Unquestion- 
ably it  may,  as  is  illustrated  in  sympathetic  vibration.  That  is, 
precisely  similar  vibrations  can  do  this.  And  perhaps  it  is  this 
perception  which  has  mislead  the  scientists.  But  unquestion- 
ably precisely  similar  vibrations  \n  different  bodies  arc  very 
rare,  and  never  take  place  unless  both  bodies  wxre  created  to 
make  the  same  sound.  And  therefore  all  bodies  would  have  to 
be  alike,  if  all  made  the  same  sound;  and  there  would  only  be 
one  sound  in  the  universe,  and  nothing  else,  as  all  bodies  would 
be  occupied  in  making  this  sound/* 


494  ELLEX    OR   THE 


XXXIV. 

^^  r^UT  docs  not  the  graphophonc  record  show,  or  may  it 
-■— ^     not  show,"  I  asked,  "that  a  certain  movement  of  any- 
thing, or  at  least  of  some  things,  will  produce  certain  sounds^ 
articulate  speech,  or  other  sound?" 

**  It  shows,"  she  answered,  **that  a  certain  instrument,  made 
for  the  purpose,  properly  handled,  will  produce  certain  sounds, 
and  it  shows  nothing  else.  This  was  a  fact  that  Ellen  knew  be- 
fore, and  that  we  all  know.  The  instrument  was  made  in  a 
remarkable  manner;  the  tclcgraphone  in,  perhaps,  a  still  more 
remarkable  manner;  and  I-lllcn  thinks  that  doubtless  there  are 
other  methods,  even  more  remarkable  than  these,  by  which 
sound  instruments  may  be  made. 

"But  whatever  new  souiul-i)r(»(liicing  instrument  maybe  dis- 
covered, or  may  exist,  all  must  conftnin,  as  all  do  conform,  to 
the  laws  governing  sound.  Certainly  they  have  not  been 
changed  to  help  scientists  out  of  tlieir  blunders.  The  sounds 
of  the  world  are  still  made  by  the  sound-producing  instruments; 
each  sound  by  some  particular  instrument.  Nor  can  any  one 
of  these  instruments  make  any  sound  except  that  which  it  was 
made  to  make,  and  with  most  things,  like  diaframs,  or  chim- 
neys, or  curbstones,  or  line  wires,  or  nails,  all  made  for  very 
different  purposes,  that  means  very  plain  sounds.  And  this  is 
just  as  true  of  a  graphophone  or  telegraphone  record  as  of  any 
other  sound-producing  instrument. 


1 

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497 


**Itis  equally  true  that  the  purposes  for  which  instruments 
were  made  Uicy  will  continue  to  accomplish.  Thus  a  diafram 
will  continue  to  gather  and  distribute  sound  in  such  a  way  as  to 
increase  its  effects,  and  a  wire  will  continue  to  carry  it  The 
curb  stone  will  remain  perfectly  quiet  unless  struck  by  something. 
So  w*ill  the  nails  magnet  and  coils  of  wire* 

"And  now  Ellen  will  give  another  demonstration,  that  sound 
consists  of  infinitesimal  particles  of  matter,  and,  in  the  telephone 
is  carried  instantaneously  through  the  wire  by  the  electric 
current.  And  this  is  the  action  of  the  box  telephone,  which 
has  been  in  use  successfully  to  convey  sound  for  over  250  years, 

"This  consisted  of  two  small  boxes  connected  by  a  string  or 
wire.  At  the  bottom  of  each  box,  at  the  centre,  was  a  mem- 
brane,  or  diafram,  through  the  center  of  which  the  string  or 
wire  passed  and  was  fastened  in  the  inside, 

*'The  correspondence  was  carried  on  by  a  person  at  one  end 
talking  into  the  bux,  to  a  person  at  the  other  end  holding  the 
box  to  the  ear,  the  same  boxes  answering  for  sending  or 
receiving  instrument.  The  sound  went  through  the  string  or 
wire. 

*'  Practically  the  operation  is  precisely  similar  to  the  modern 
telephone,  except  the  electric  current  and  magnet  are  lacking. 
Because  they  were  lacking,  the  use  of  the  box  telephone  was 
limited,  as  the  sound  couldn't  go  fast  enough  through  the 
string  or  wire  to  last  for  a  very  long  distance. 

**This  proves  that  sound  under  such  cunditions  enters  a  wire 
or  string,  and  passes  along  or  through  it,  until  its  force  is 
expended,  which  last  is  a  mere  question  of  time.  It  also  proves 
that  sound,  with  such  conditions,  will  get  out  at  the  other  end 


498  ELLEN    OR   THE 

of  the  line,  or  anywhere  else  if  given  opportunity,  and  enter 
the  listener's  ear. 

**It  follows  that  it  must  do  the  same  in  the  modern  telephone, 
where,  just  as  in  the  air  to  the  speed  of  sound  must  be  added 
the  speed  of  the  wind,  there  must  be  added  here  the  speed  of 
the  electric  current.  And  therefore,  and  for  no  other  reason, 
the  distance  of  its  journey  is  immensely  increased. 

"And  this  is  a  demonstration  that  the  sound  heard  at  the 
telephone  is  that  which  enters  the  sending  instrument." 

**And  will  not  Ellen  repeat,"  I  asked,  **this  demonstration?" 

**The  demonstration  is,"  she  replied,  *'that  sound,  articulate 
speech  or  otherwise,  does  get  into  a  wire  and  run  along  through 
it,  always,  when  an  arrangement  like  that  of  a  telephone  trans- 
mitter exists.  And  therefore  it  must  get  into  the  wire  of  a 
telephone.  It  follows  as  a  matter  of  necessity,  that  it  is  carried 
instantaneously  through  this  wire  by  the  current  to  where  it  can 
<^ct  out,  unless  it  is  dcslro\'cd  by  the  curreiU,  and  we  know  it 
is  not  destroyed  but  carried  through.  There  could  hardly  be 
any  more  complete  demonstration. 

*' So  far  as  ICllcn  knows  ihcir  was  fornierl}'  no  pretence  made 
in  the  use  of  the  box  telephone  that  the  diafram  or  membrane 
repeated  the  sound,  thcnigh  they  acted  then  precisely  as 
they  do  now,  and  now  precisely  as  they  did  then.  Hut  in 
recent  years  this  is  sometimes  added,  so  as  to  make  it  coin- 
cide with  the  statement  in  rei^ard  to  the  present  telephone, 
and  sometimes  not.  It  is  so  evidently  absurd  that  only  the 
necessities  of  the  air  wave  theor\'  of  sound  could  have  ever 
suggested  it." 

*'Then  I^llen  thinks,"  I  said,  "that  the  membrane  or  diafram 


WinsFERINGS    OF    AN    OLD    F'lNL 


499 


assists  in  gathering  and  delivering  sound,  the  sound  itself  mak- 
ing its  own  journey  througli  the  string  or  wire/' 
•*She  knows  such  are  the  facts/'  she  answered, 
'*Thc  Modern  Apph*cations  of  Electricity,  published  by  D. 
Applcton  &  Co*.  New  York,  says: 

•The  first  telephone  deserving  of  this  name  was  the  string  telephone, 
the  invention  of  which  dates  back  more  than  two  centuries ;  in  fact, 
there  is  no  doubt  that  among  the  natives  of  India  this  device  was  of 
still  greater  antif]i)ity. 

'The  simplest  method  is  to  take  two  cylindrical  ttibes  of  metal  or 
cardboard,  to  rlose  one  of  the  extremiliesi  of  each  tube  with  a  mem- 
brane of  paper,  parchment,  or  thin  cardlmard,  and  to  connect  the 
two  vibrating  sheets  thus  formed  by  a  string  fixed  in  the  centre  by  a 
knot. 

*  When  the  string  which  joins  the  two  parts  is  well  stretched,  and  not 
too  long,  and  one  of  the  tubes  is  held  to  the  ear  whilst  another  person 
is  speaking  very  close  to  ihe  mouth-piece  of  the  other  tube,  all  the 
words  are  transmitted  by  the  string  to  the  membrane  of  the  receiveti 
and  a  conversation  can  be  earned  on,  with  a  very  low  voice.  Speech 
can  thus  be  transmitted  as  far  as  200  metres*  By  using  diaframs  of 
very  thin  iron,  and  insulating  the  wire  on  glass  supports,  Huntley, 
who  made  the  exi^criment,  was  heard  at  a  distance  of  2450  feet,  in 
spite  of  the  zigzags  of  the  line.  String  telephones  have  for  a  long  time 
remained  in  oblivion/'* 

**And  yet/'  I  said,  "KUen  can  see  that  in  the  graphophone 
record,  and  the  still  more  wonderful  telegraphone  record,  nature 
does  provide  for  the  repeating  of  such  sounds/' 

*•  Yes/*  she  replied.  **In  furnishing  the  world  provision  has 
been  made  for  the  reduplication  of  all  material  things,  and  by 
wonderful  processes;   but  having  one  wa)*  for  this,  and  that  a 


4 


ELLEN   OR  THE 

kiost  remarkable  one  and  always  of  a  similar  character;  that 
ich  sound,  the  ^ame  as  each  animal  or  each  tree«  should 
^^f-creatc  itself,  in  re-creating  the  instrument  which  can  repeat 
it,  Is  verj'  different  from  having  a  million  more  or  less  unneces- 
sary ways. 

"Thus,  as  Ellen  has  said,  the  oak  makes  the  acorn  which 
reproduces  the  oak,  but  all  the  part  in  this  the  oak  ha^,  is  to 
produce  the  acorn.  So  all  the  part  that  sound  has  is  to  produce 
a  record.  And,  as  Ellen  has  also  said,  the  acorn  and  the  sound 
are  built  upon  similar  principles,  in  this  respect,  that  every  part 
existing  in  the  tree,  or  in  the  s;ound,  Is  included  in  the  acorn 
and  in  the  record. 

*'Did  the  old  Pine  ever  know  an  oak  to  grow  except  from 
another  oak,  either  by  an  acorn  or  a  scion ;  or  any  tree  or 
flower  except  by  similar  method?  But  whether  or  not  it  mightr 
be  possible  for  intelligence, — aside  from  that  intelligence  which 
made  the  oak,  including  its  power  of  producing  the  acorn  from 
which  might  develop  another  oak, — to  make  another  oak,  or 
another  acorn;  Ellen  doubts  not  that  the  machinery  which 
makes  every  sound,  and  that  means  the  instrument  by  which 
any  sound  is  made,  might  be  made  by  the  intelligence  of  man» 
if  only  he  had  the  model.  And  possibly  this  he  may  be  able 
to  get  from  the  different  records  made  by  sound,  although 
these  are  very  infinitesimal." 

**But  is  sound,"  I  asked,  "entirely  a  material  thing?  That 
is,  are  the  vocal  chords  which  utter  articulate  speech,  or  such 
an  instrument  as  makes  the  notes  of  a  bobolink,  as  completely- 
material  as  a  piano  or  violin?  " 

*' Unquestionably  they  are,"  she  answered.     '*The  graphor 


WmSPERlNGS   OF   AN   OLD    PINE 


5or 


pho^c  record  which  may  repeat  sounds  wilh  absolute  fidelity 
demonstrates  they  are/* 

**  And  if  there  is  nothing  in  voice,"  I  asked,  "  but  the  sound 
of  a  material  instrument,  in  what  consists  the  power  and  action 
of  the  soul?" 

'^  In  the  using  of  such  sounds,  or  instruments.  That  is,  in  the 
using  of  material  things,  all  of  which  are  fashioned  for  the  use 
of  intelligence,  and  by  which  only  can  the  spiritual  accomplish 
anything,  at  least  whilst  in  material  conditions,  Ellen  admits 
that  the  soul  is  hampered  in  its  present  conditions,  though  she 
believes  it  may  rise  above  all  such  restraints. 

'*  Ellen  has  shown  that  the  spiritual  and  material  arc  as  inde- 
pendent oi  each  other  as  an  engine  and  engineer.  This  is 
always  true.  The  line  between  them  is  most  distinctly  and 
accurately  drawn,  as  is  plainly  evident  in  this  matter  of  sound, 
For»  as  Ellen  says,  every  possible  sound  belongs  to  the  material 
part  of  creation,  even  to  the  most  trivial  inflection  of  a  voice. 
Ami  provision  has  been  made  for  the  uttering  of  these  sounds, 
\n  the  instruments  to  make  them,  and  the  intelligence  using 
these  instruments. 

*'This  much  at  least  Ellen  is  sure  of:  If  every  tone  uttered 
into  a  graphophone  can  be  repeated  with  absolute  accuracy  by 
that  instrument;  then  every  possible  tone  that  may  be  uttered 
by  man  may  also  be  made  by  a  material  instrument>  and  if 
this  is  so  any  possible  sound  may  be  made  by  a  material  in- 
strument, utterly  regardless  whether  any  per  on  or  iutclh'gent 
being  Is  present  or  not 

'*Thc  lustre  of  sound  will  appear  equally  with  that  of  a  jeweh 
or  the  beauty  of  a  flower.     Neither,  so  far  as  Ellen  can  sec,  of 


02  ELLEN    fMC   THE 

jcessit}'  depends  in  the  slightest  degree  upon  any  individual 

feUigencc  present/* 
ft**  And    does   Ellen   think   that   every  tone  uttered  into  the 
graphophone  can  be  accurately  repeated  ?'* 
^**She  does  think  so.     For  so  far  as  the  ear  can  detect  many 

:hcm  are*  some  of  these  as  remarkable  as  any;  and  greater 
and  greater  accuracy  would  appear  to  be  constantly  attained/' 

**  But/*  I  asked,  **does  Ellen  think  that  those  sounds  which 
would  appear  to  be  made — at  least  guided — by  intelligence, 
such  as  articulate  speech,  or  the  voices  of  the  birds,  would  ever 
be  heard  at  all,  if  not  first  made  by  the  action  of  intelligence  ?  " 

*'  Possibly  not/'  she  answered,  **  but  Ellen  cannot  see  that 
that  is  the  important  point  under  discussion.  That  they  arc 
heard  at  all  would  appear  to  be  because  they  are  possible 
materially.  Perhaps  the  sounds  made  by  the  human  voice,  or 
any  other  voice,  might  never  take  place  but  for  the  intellect 
controlling  the  machiner\'  which  makes  them.  For  as  Ellen 
has  repeatedly  said  all  sound-instruments  are  made  before  they 
are  played,  and  Ellen  will  add,  whilst  intelligence  may  be 
necessary,  perhaps,  in  most  cases— possibly  in  all — to  do  the 
playing,  and  certainly  in  all  to  create  the  instrument ;  still  if 
there  was  not  material— matter— to  make  these  instruments  of, 
there  could  be  no  instrument;  nor  can  there  be  any  sound 
without  an  instrument/' 

**Then,"  I  said,  "intelligence  and  matter  are  equally  neces- 
sary ?  " 

"Yes,"  she  answered,  "in  material  conditions.  And  although 
it  is  true  that  no  instrument  can  be  made  without  intelligence, 
somewhere,  to  make  it;   it  is  equally  true  that  there  is  no  sound 


WHISPERINCS   OF  AN  Ol.D    PfNE 


503 


possible  to  material  conditions,  but  what  there  is»  or  may  be,  a 
material  instrument  to  make  it, 

*'Thus  if  a  person  wishes  to  utter  words  of  endearment,  there 
are  such  words,  and  the  means  at  hand  to  utter  them,  and  these 
means  include  every  possible  modulation  of  voice,  — the  choice 
of  which  being  entirely  with  the  person. 

'*  Man  is  a  creature  of  inspirations,  but  whether  he  would 
have  any  if  it  was  not  for  matter,  Ellen  does  not  know.  That 
matter  in  all  its  different  phases  suggests  them  is  unquestion- 
able. Nor  would  it  be  possible  for  any  of  them  to  be  realized 
without  it. 

''To  the  soul  belongs  the  choice  of  the  different  material 
things,  or  instruments,  by  which  its  feelings  may  be  made 
known.  If  it  would  tell  its  affection  it  must  use  the  material 
langauge — the  language  of  sound/" 

*'Then  this  language,'*  1  said,  **  might  be  entirely  indepcnd- 
cnl  of  any  particular  person,  and,  in  such  case,  be  useless  if  not 
meaningless?** 

'*  Yes,*'  she  answered,  "and  in  an}*  case  meaningless  without 
education ;  at  least  this  is  the  case  with  most  sounds,  but  the  call 
of  a  mother  to  her  young  is,  perhaps,  instantly  understood, 

**God  has  provided  that  all  expression  of  feeling  or  of  fact, 
should  be  made  in  material  conditions  b\*  an  instrument  which 
is  entirely  material;  and  should  consist  as  well  of  a  substance 
e<[ually  material  Wiihout  this  the  beloved  could  never  hear, 
and  might  never  know,  that  he  or  she  was  beloved,  unless 
such  knowledge  was  got  from  the  other  sensations. 

**  From  which,  as  Ellen  thinks,  the  old  Pine  will  see.  first,  that 
sensations  are  most  important  to  cither  the  happiness,  or  reality 


5^4  ELLEN  OR  THE 

of  living,  and  second,  that  without  matter,  by  which  these  sen- 
sations are  caused,  there  could  be  no  life  as  known  to  us.  And 
this  means,  as  Ellen  thinks,  as  known  in  material  conditions." 

"But  what  again,"  I  asked,  "is  the  soul  that  can  be  resolved 
so  readily  into  non-existence?  Or  how  is.it  possible  that  the 
order  o1  a  vibration,  which,  at  the  best,  is  the  result  of  one 
material  thing  moving  upon  another,  should  be  able  to  express 
the  strongest  passions  ?  " 

"Because  it  is  made  to  do  it,"  she  answered.  "For  sound 
as  everything  else,  as  Ellen  has  suggested,  is  designed  by  in- 
telligence for  the  uses  of  intelligence.  This  is  the  one  and  only 
explanation,  when  sound  affects  spirit  in  the  way  the  old  Pine 
suggests.  It  was  made  to  do  it.  Nor,  as  Ellen  thinks,  is  there 
any  possible  sound  whose  effect  has  not  been  estimated.  For 
it  correlates  thought,  so  perfectly  is  this  universe  made  in  all 
its  features. 

"Neither  is  there  any  possible  sound  but  what  is  made  by 
some  instrument  according  to  the  hiw  for  the  manufacturing  of 
sound.  The  instrument  comes  first,  and  then  the  sound ; 
and,  as  we  have  seen  this  sound  may  make  another  instrument, 
which  will  repeat  the  same  sound." 

"And  is  it  necessary,"  I  asked,  "that  intelli*^ence  should 
exist  where  sounds  are  made?" 

'*Not  at  all,"  she  answered;  "as  ICllen  has  often  said,  the 
two  principles  of  matter  and  intelligence,  are  entirely  independ- 
ent of  each  other. 

*•  Sound  is  made  for  the  uses  of  intelligence  all  right,  and 
by  intelligence.  But  it  is  free  as  the  air  is.  Every  particle  of 
matter  is  free  to  be  made  over  and  over  again   into  millions  of 


WHISPERING^   OF  AN   OLD    IINK 


SOS 


different  things,  and  some  of  these  particles  will  never  be 
handled  or  come  in  contact  with  intelligence,  certainly  not  the 
intelligence  of  man.  Nor  need  thfa  make  any  difference  in  any 
material  thing,  or  its  destiny. 

*  Full  many  a  gem  of  purest  ray  serene. 
The  tlark  unfathomed  eaves  of  ocean  bear ; 

Full  many  a  flower  is  born  to  blush  unseen. 
And  waste  its  sweetness  on  the  desert  air/" 

*'Biit  can  man  make  the  principles,*'  I  asked,  "b}*  which  this 
machinery,  or  an\'  niachincr)-,  tjpcratcs? 

''That  is.  can  man  make  an  oak,  or  rather  can  he  make  the 
material  from  which  the  oak,  or  piano,  or  bobolink's  note  is 
made?     Can  he  make  matter?" 

'*Kllen  thinks  she  has  said  several  linus  that  lie  conid  not," 
she  answxTcd.  *"  But  if  the  material  emanates  from  the  spiritual, 
as  it  may,  she  does  not  know  wh\'  it  mi^^ht  not  be  possible  for 
man's  intelligence  to  make  it,  as  well  as  to  make  all  sound- 
priiducing  instrnments.  Neither  could  be  done  without  the 
knowledge  how,  but  perhaps  either  might  be  done  with  that 
knowledge;  and  if  so.  the  acquiring  of  such  knowledge,  cither 
by  accident  or  by  search,  might  always  be  possible. 

**  But  neither  sound,  t:lectricity»  or  magnetism*  or  all  together, 
can  make  the  diafram  talk.  For  it  can't  talk.  Sound,  a  particu- 
lar sound*  as  we  have  seen,  can  raake  a  moilcl.  which*  under 
favorable  conditions,  can  repeat  the  sound  tiiat  made  it.  liut 
that  is  a  very  different  thing  from  making  anything  talk. 
The  one  is  possible,  the  «)ther  beyond  the  Ijound*^  of  possibility* 
The  oak  can  make  an  acorn,  which,  under  favorable  circum- 


506  ELLEN    OR  THE 

Stances,  may  be  developed  into  an  oak,  but  it  cannot  delegate 
its  power  to  a  fence  post,  or  to  any  other  tree.  Neither  can 
it  make  a  squash  bear  cocoanuts  or  in  any  way  change  its 
character. 

"Good  Words,  1878,  page  280,  says: 

*\Ve  are  now  in  a  position  to  understand  the  acoustic  principles  up- 
on which  these  two  principle  telephones  rest.  And  in  passing  it  may 
be  well  to  guard  the  reader  against  a  popular  misapprehension  that 
these  telephones  have  anything  in  common  with  a  little  toy  that  may 
now  be  seen  in  some  of  the  streets  and  shops  of  London.  These  little 
instruments,  it  may  be  true,  transmit  speech  to  distances  out  of  the 
range  of  the  unaided  voice  with  sur])rising  clearness ;  but  as  they  con- 
vey  sonorous  vibrations  by  mere  mechanical  means,  it  is  evident  that 
we  soon  reach  a  limit  beyond  which  it  is  impossible  to  employ  such  an 
arrangement.* " 

'*Biit  what  docs  this  author  mean  by  sonorous  vibrations?"  I 
asked. 

"Ellen  thinks  he  doesn't  know  what  ho  docs  mean.  That's 
his  trouble,  he  doesn't  know  what  he  is  talking  about. 

"For  scientists  arc  tr\ing  to  talk  about  sound,  which  is  infini- 
tesimal particles  of  electrical  matter,  thrown  off  by  sounding 
bodies.  Hut  they  suppose  they  are  talking  about  something 
the\-  call  air  waves,  concerning  which  it  would  be  impossible  for 
anyone  to  have  any  intelligent  idea.  For  the  whole  theor}-  is 
absolutely  inconceivable,  the  wc^rk  of  a  fool. 

"The  nearest  to  sonorous  vibration  that  FJlen  can  find  in  her 
dictionary  is,  *  Sonorous  figures,  figures  formed  by  the  vibrations 
produced  by  sound,  as  when  the  bow  of  a  violin  is  drawn  along 


WHISPERINGS   OF 


SO7 


the  edge  o(  a  piece  of  glass  or  metal  on  which  sand  is  strewed, 
and  the  sand  arranges  itself  in  figures  according  to  the  musical 
tune ; — called  also  acoustic  figures/ 

"The  resemblance  of  these  sonorous  figures  to  magnetic 
figures  and  their  lines  of  magnetic  force  is  most  noticeable. 
There  are  too,  electric  figures  and  electric  lines  of  force;  all 
of  these  showing  an  intimate  relation  to  each  other." 

"*  But  what  is  the  meaning  of  the  words  *  mere  mechanical 
means?"'  I  asked. 

*'The  dictionary  defines  mechanical.  *In  accordance  w*ith  the 
laws  of  motion/  she  answered.  And  the  suggestion  is  that 
sound  thus  moving  wouldn't  go  very  far.  But  that  two  sound 
carr}'ing  arrangements,  operating  in  all  respects,  but  one.  in  a 
precisely  similar  manner,  have  something  in  common  with  each 
other,  wouldn't  appear  to  be  a  popular  misapprehension  to  a 
man  of  average  intelligence.  It  is  only  the  stupidity  of  science 
that  is  at  fault  here.  Indeed  the  action  of  sound  with  a  box 
telephone  is  another  demonstration  of  similar  action  in  the 
electric  telephone,  as  Ellen  has  pointed  out;  that  is,  that  the 
sound  uttered  into  an  ordinary  telephone  goes  into  the  wire, 
where,  as  a  matter  of  course,  it  must  be  carried  w^ith  the  speed 
of  the  electric  current  whilst  it  exists,  or  until  it  can  get  out. 

**This  article  further  says,  page  282: 

•Two  or  three  years  later,  in  1865,  a  skillful  instrument  maker  in  Dub. 
lin,  Mr.  Veates,  showed  to  the  [Philosophical  Society  in  that  city  a  modi- 
fication of  Re  is*  telephone,  wherein  a  near,  though  accidental,  approach 
was  made  to  the  true  principle  of  an  articulating  telephone — nau)ely, 
the  employment  of  a  continuous  electric  current  of  varying  strength* 
This  was  obtained,  though  the  primary  object  was  different^  by  imttint? 


S08  ELLEN  OR  THE 

a  drop  of  water  on  a  fragment  of  moistened  paper  between  ibc  metal 
disc  on  the  membrane  and  the  adjacent  platinum  point  which  com- 
pleted the  electric  circuit  Articulation  of  an  imperfect  kind  was  thus 
obtained.' 

"These  words  'varying  strength'  are  also  added  to  assist  in 
floating  the  moribund  theory  of  sound,  and  have  no  significance 
whafever  as  the  words  a  'continuous  electric  current'  are 
sufficient." 

'It  will  be  needless  to  trace  the  successive  stages  in  the  discoveiy  of 
the  articulating  telephone,  as  they  have  already  been  frequently  dc^tsiled 
by  Professor  Bell  and  others.    We  will  confine  ourselves  to  the  descrip- 
tion of  the  last  and  highest  stage  in  the  process  of  evolntioa  of  this 
instrument    As  in  Reis'  telephone  a  membrane  is  caused  to  vibrate  by 
the  action  of  the  voice.    This  membrane  however  is  no  longer  of  skin^ 
but  consists  of  a  thin  disc  of  iron.     Behind  the  iron  disc  is  a  small 
straight  magnet;    round  that  pole  which  adjoins  the  disc  is  wound 
several  coils  ot  very  fine  insulated  wire,  and  the  ends  of  the  wire  are 
carried  to  screws  conveniently  placed  for  the  attachment  of  the  line 
and  return  wire  leading  to  and  from  the  distant  and  precisely  similar 
instrument.     As  is  usual  in  telegraphy  instead  of  a  return  wire,  connec- 
tion is  made  with  the  bar  magnet  that  must  be  made  to  slide  stiffly 
in  the  hole  in  the  lK)bbin.     The  ends  of  the  fine  wire  are  joined   to 
binding  screws,  which  can  be  procured  at  an  optician's  for  a  trifling 
sum  and  to  these  again  are  fastened  the  wires  leading  to  and  from  the 
distant  and  similar  instrument ;  or  a  gas-pipe  may  be  used  instead  of 
the  return  wire.     It  will  be  noticed  no  battery  is  in  circuit,  for  none 
is  required,  and  that,  unique  among  telegraphic  instruments,  the  sender 
and  the  receiver  are  identical  in  construction.      *     *     *     * 

*  And  now  in  conclusion  let  us  endeavor  to  understand  how  the  won- 
derful  doable  transformation  is  effected ;  first  of  the  voice,  into  electric 


WinSI'EKlNGS   OF   AN   OLH    VISE 


509 


pulsations,  and  then  how  these  electric  quivers  are  brought  back  into 
s|>eech  once  more.  Under  the  influence  of  the  neighboring  magnet  the 
iron  discs  become  themselves  magnetic.  When  a  magnet  is  made  to 
approach  a  coil  of  wire,  the  ends  of  which  are  united,  a  wave  of  elec- 
tricity flows  through  the  wire,  and  when  the  magnet  is  made  to  recede 
from  the  coil  another  electric  wave  is  set  up  in  a  reverse  direction. 
This  was  the  memorable  discovery  which  Faraday  gave  to  the  world,  a 
discovery  that  has  been  turned  into  enormous  practical  utility  and  upon 
which  vast  fortunes  have  been  reared  by  those  who  wisely  enough  have 
patented  some  of  its  various  practical  applications  which  their  ingenuity 
has  devised.  Professor  Bell's  patent  embraces  more  than  a  mere  appli- 
cation of  this  discovery,  it  is  virtually  a  new  discovery  in  itself ;  for  it 
re\*eals  the  fact  that  swift  and  subtle  as  are  the  vil>rations  of  the  iron 
disc  under  the  influence  of  the  voice  each  infinitesimal  motion  of  the 
disc  gives  birth  to  an  electric  wave  of  correspontling  strength  antl  dura- 
tion. These  waves  traverse  the  line  and  circulate  round  the  distant 
coil.  Then  they  create  proportional  variations  in  the  strength  of  the 
magnetic  regioii  adjoining  the  con  pan  ion  iron  disc.  At  each  fluctua- 
tron  of  magnetic  intensity  the  iron  disc  is  attracted  slightly  towards  or 
repelled  slightly  from  the  pole  of  its  magnet.  And  this  motion  can  take 
place  many  thousands  of  times  in  a  second,  so  that  even  if  one  disc 
quivers  to  and  fro  as  rapidly  as  the  wings  of  a  buz/Jng  gnat,  the  com* 
panion  disc  will  faithfully  imitate  the  motion  and  hence  give  forth  the 
sound  of  the  buzzing  gnat.  The  chief  point  of  interest  Is,  however,  • 
this:  not  only  the  rate  of  vibration  is  transmitted  and  reproduced  but 
the  mode  of  vibration  of  one  disc  repeats  itself  on  the  other.  But  as 
we  have  seen  in  the  early  part  of  this  article  if  we  can  transmit  any 
mode  of  vibration,  or,  what  is  the  same  thing,  any  peculiar  wave  form,  we 
can  transmit  speech  which  depends  on  the  peculiar  mode  of  vibration 
of  the  vocal  chords  in  the  speaker  and  of  the  tympanum  membrane  in 
the  listener.     Thtis  the  pitch  of  a  note  and  the  rpiality  of  a  note  are 


ELLEN    OK   THE 

oUuced,  the  two  chief  eJements  in  every  soimtL     Hence  not  onl>' 

1  musical  airs  electrically  transmitted  but  the  peculiar  lone  of  each 

jument,  whether  violtn,  harp^  jiianoforte,  tntmpet,  organ  or  %vhat 

I,     Speech  k  heard  and  the  mdividuality  of  the  speaker  is  recognized, 

::hanging  moods  are  even  discemibla  in  delicate  shades  of  expression 
.  all  this  though  the  speaker  may  be  in  London  and  the  listener 
Edinburgh  or  Aberdeen.' 

^*  Here  are  a  number  of  things  which  this  scientist  knows,  like 
most  of  his  class,— there  are  very  few  exceptions, — which  are 
not  so.  But  the  final  explanation  is,  and  it  is  impossible  to 
come  to  any  other,  unless  the  undidatory  theory  of  sound  13 
surrendered,  that  the  disk  at  the  receiving  station,  *  faithfully 
imitates  the  motion  oi  the  sending  disc  and  hence  gives  forth 
the  sound;'  which  in  plain  words  means  that  a  diafram  talks  or 
repeats  sound,  and,  as  Ellen  Has  shown,  it  does  not  and  cannot 
do  iL  It  is  noticeable,  too,  that  this  author  seeks  relief  from 
ignorance  by  eulogizing  Farada>'. 

"This  is  an  unusually  complete  illustration  of  drawing  upon 
imagination  for  facts.  Out  of  a  condition  of  ignorance  as 
dense  as  Egyptian  darkness  numerous  myths  are  evolved,  a 
sufficient  answer  to  which  is  that  the  sounds  could  be  heard 
equally  well  or  better  without  the  diafram  of  the  sending- 
instrument  which  this  scientist  has  made  responsible  for  them. 
So,  too,  a  wooden  diafram,  non-magnetic,  would  answer  the  pur- 
pose at  the  receiving  instrument,  by  which,  in  the  above,  all 
the  operations  supposed  to  be  performed  by  these  electric  waves 
would  be  elimnated. 

"  Certain  things  mentioned,  under  certain  conditions,  take 
place.     Thus  it  is  true  that  if  a  live  magnet  is  thruFt  into  a  bob* 


WHISPERINGS  OF  AN  OLD   PINE 

bin  of  wire  it  will  cause  aa  electric  current  to  flow  through  the 
wire,  and  if  withdrawn  the  current  will  be  reversed — thus  mim- 
icking the  gallant  excursion  of  the  king  of  Spain,  who,  with 
20,000  men»  marched  up  the  hill,  and  then  marched  down  again, 
*'(>iir  author  however  is  at  home  tn  anatomy  and  doubtless 
accurate,  and  also  appears  very  well  as  a  humorist.  Thus  he 
continues: 

*  The  mechanism  by  which  speeeh  is  produced  in  our  own  botlies 
naturally  suggested  the  first  melhod  of  making  a  speak ing-niathinc. 
Let  us  consider  for  a  uwineut  how  the  human  voice  originates.  If  we 
place  our  finger  on  the  lower  prirt  of  our  throat  we  shall  feel  the  car- 
tilaginous hoops  of  the  trachea  or  wind -pipe  ;  passing  upwards  we  reach 
a  grisdy  V-shaped  projei  tion,  the  point  of  the  V  being  in  fronts  consti- 
tuting what  is  commonly  called  Adam*s  apple  and  known  to  physiologists 
as  the  thyroid  cartilage.  This  is  the  front  portion  of  the  chamber  called 
the  larynx,  which  forms  the  summit  of  the  wind-pipe,  and  within  which 
chamber  is  the  seat  of  our  voice.  The  larynx  opens  into  the  mouth 
immediately  behind  the  tongue  by  an  aperture  called  the  glottis 
capable  of  being  closed  by  a  sort  of  lid,  the  e])iglottis,  or  by  the  shutting 
together  of  two  elastic  cushions  attached  to  the  larynx  immediately 
tjelow  the  epiglottis.  These  cushions  are  the  so-called  vocaJ  chords, 
which  when  at  rest  assume  a  V- shape,  but  can  be  drawn  parallel,  and 
more  or  less  stretched  by  appropriate  muscles.  When  in  this  state  of 
tension  a  current  of  air,  forced  from  the  lungs,  wiil  cause  the  vocal 
chords  to  quiver  with  a  rapidity  great  enough  to  generate  sonorous 
vibrations ;  the  range  of  a  person's  voice  depending,  in  fact,  on  the 
tlifference  of  tension  which  can  be  given  to  the  vocal  chords,  The 
greater  the  tension  the  more  swiftly  ihey  vibrate,  nnd  the  higher  the 
pilch  of  the  voice.  The  mere  vibration  of  the  chords  cannot,  however, 
produce  speech,  which  is  effected  by  the  modulation  of  the  voice 
through  the  agency  of  the  tonguei  lips,  and  cavity  of  the  mouth. 


5  I-  ELLEN   OR  THE 

*It  is  possible  to  make  a  rough  imitation  of  the  larynx  by  simply 
rolling  a  sheet  of  foolscap  into  a  narrow  tube,  and  over  one  end  tying 
side  by  side  a  couple  of  strips  of  thin  india-rubber ;  on  blowing  through 
the  tube  a  musical  note  is  obtained,  which  can  be  varied  in  pitch  by 
squeezing  the  tube,  and  so  altering  the  tension  of  the  india-rubber  vocal 
chords.  Nay,  more,  when  speech  has  been  lost  by  disease  or  removal 
of  the  natural  vocal  chords,  artificial  ones,  formed  of  a  vibrating  tongue 
for  "  reed  "  of  metal  or  ivory,  have  been  made,  and  inserted  in  the 
larynx  of  the  sufferer,  restoring  to  him  at  once  the  power  of  speech. 
In  fact,  so  successful  is  this  artificial  substitute,  that  the  only  difference 
noticeable  appears  to  be  the  peculiar  monotone  of  the  speaker ;  who, 
however,  has  the  advantage  of  having  a  variety  of  voices  at  command, 
for  by  selecting  a  grave  **reed"  to-day  he  can  roar  like  Bottom  the 
weaver,  and  by  using  a  high  pitch  to-morrow  speak  with  the  shrillness 
of  a  shrew.' 

**ln  speaking  of  the  phonograph  this  author  writes: 

'It  needed  the  ex|)erience  of  an  actual  trial  of  the  machine  to  con- 
vince the  ])rescnt  writer  tliat  its  (\a])al)i!ities  liad  not  been  grossly 
exaggerated.  rV)r  when  we  call  to  mind  the  extreme  eom|>lexity  of  the 
sonorous  waves  [sound]  generated  l)v  the  act  ot  speaking,  it  seemed 
hardly  ])ossil)le  that  the  subtle  movements  of  the  aerial  particles  could 
in- any  ade'iuate  manner  transcribe  the  nature  of  their  motion  upon  a 
^,hrr'.  o:  tin  foil,  so  that  the  foil  <(>ul(l  ai^ain  give  forth  the  words  it 
had  embalmed  :  and  thi>  dimply  through  the  instrumentality  of  a  disc  of 
metal  with  a  style  attached  to  onc.^  j)oinl  on  its  surface.' 

"Our  friend  is  entircl\' correct.  It  wouldn't  be  possible  for 
the  movement  of  aerial  particles,  subtle  or  otherwise,  to  do 
an}'thing  of  tlie  kind.  Hut  the  infinitesimal  particles  of  electri- 
cal matter  of  which  sound  is  composed,  can  do  it  most  success- 
full}'.     These  are  two  very  different  propositions." 


J-^'i-  NKW  YORK 


OLD    PINE 


XXXV. 


fc^nPHE  old  Pine  notices  again,"  I  said,  **that  this  author  uses 
^  the  words  sonorous  vibrations  instead  of  the  plain  word 
sound?" 

'*  Yes/'  she  replied,  **a  fraud  always  has  to  be  nursed  to  keep 
it  alive.  If  the  theory  was  sensible,  that  is,  if  it  was  true,  they 
would  be  called  sound.  Hut  the  theory  being  erroneous,  if  the\' 
were  habitually  called  sound,  it  would  kill  it,  because  constantl}' 
calling  attention  to  its  absurdities,  and  want  of  foundation.  And 
besides  it  is  asking  too  much  of  anyone,  however  devoted  he 
may  be  to  the  principles  or  want  of  principles  in  science,  to 
word  a  lie  in  plain  terms.  Sound  is  something  that  we  all 
have  ideas  about,  and  would  have  a  great  many  more  if  we 
were  not  misled :  but  sonorous  waves  are  entirely  mythical,  and 
therefore  a  good  refuge  for  those  considering  an  erroneous 
h\'pothesis. 

"Of  course  the  membrane  of  the  ear  has  nothing  to  do  with 
the  making  of  sounds.  Its  function  is  to  assist  in  their  deliver). 
The  membrane  of  the  ear  is  a  part  of  the  machinery  which 
digests  sound  as  the  stomach  does  food*  and  it  would  be  as 
sensible  to  say  that  the  stomach  makes  the  food  it  digests,  as 
that  the  membrane  makes  the  sound  it  helps  to  deliver.  But 
the  diafram  of  a  telephone  was  suggested  by  the  membrane  of 
the  car,  and  is  supposed  to  perform  the  same  functions, 

**Thc  making  of  the  graphophonc  record  is  thus  described: 


5l6  ELLEN  OR  THE 

'Speaking  into  the  mouth-piece  in  a  distinct  and  ddibcnitc  Yoioe^ 
and  at  the  same  time  turning  the  cylinder  by  clockwork  or  by  luhndt  Ae 
sonorous  vibrations  communicated  to  the  disc  record  tfaemaelnBS  od  die 
foil  in  the  shape  of  minute  indentations.  When  the  sentence  has  been 
spoken,  the  disc  and  style  are  drawn  aside,  the  cylinder  tmned  beck  to 
its  starting  point,  and  the  disc  and  style  again  placed  in  the 
they  first  occupied.  Once  more  rotating  the  cylinder,  the  wtylt 
and  falls  as  the  now  embossed  foil  passes  beneath  it,  and  the  motion 
given  to  the  style  is  communicated  to  the  disc  and  thence  to  the  air 
around.  The  air  is  thus  thrown  into  a  state  of  vibration  similar  to  that 
to  which  the  words  originally  gave  rise.' 

''The  whole  subject  of  the  graphophone  record  Ellen  will 
discuss  later.  We  recognize  that  the  sound  must  have  made  an 
indentation  or  record  of  itself,  very  possibly  whilst  in  motion. 
Such  record  is  one  of  excavation,  and  means  that  sound 
has  left  in  the  paraffin  and  wax  its  impression,  or  such 
a  path  as  it  makes  when  moving.  And  if  a  proper  instru- 
ment is  passed  through  this  record  the  record  will  repeat  the 
sounds  which  made  it.  It  is  perhaps  extraordinary  enough  that 
an  instrument,  following  the  line  of  indentation  made  by  this 
sound,  should  re-create  the  sound,  but  common  sense  would 
suggest  that  it  is  more  natural  to  think  that  it  might  do  it  by 
following  this  line  than  another  line  which  had  no  connection 
with  the  sound. 

*'But  common  sense  explains  more,  that  the  result  is  accom* 
plished  by  the  manufacturing  in  the  machiner}'  of  this  record 
the  sound,  infinitesimal  particles  of  matter,  the  same  as 
those  which  created  the  record.  And,  as  I^llen  thinks,  they  are 
always  made  in  large  quantity  with  a  remarkable  capability  of 


BRINGS   ()F 


b\A)    IIM-: 


SI7 


spreading.  For  sound  spreads  in  the  same  medium*  equally  in 
a!l  directions.  But  the  sound  of  the  second  second*  can  never 
overtake  that  of  the  first.     All  it  can  do  is  to  reduplicate  it 

**  Ellen  sa>'s  it  cannot  overtake  the  previous  sound,  because 
all  experiment  would  seem  t<>  prove  that  all  sound  has  the  same 
speed  in  the  same  medium. 

•*And,  as  Ellen  has  suggested  before*  the  production  of 
sound- producing  instruments  by  sound  is  vcr\'  suggestive  of 
the  methods  used  in  the  perpetuation  or  reproduction  of  each 
species  after  its  kind.  The  force  of  an  oak  is  so  concentrated 
in  an  acorn  as  to  make  the  nucleus  from  wliich  readily,  easily 
and  naturally  developcs  another  oak.  Ellen  cannot  .^ec  any- 
thing very  remarkable  about  ihis.  Ccrtainl)' not  more  remark- 
able than  that  the  oak  should  exist  at  all  And  indeed  there 
wouldn't  appear  to  be  any  sufficient  object  why  the  oak  should 
exist  at  all,  if  it  couldn*t  reproduce  its  kind.  And  if  the  oak, 
any  other  tree,  or  any  flower,  or  for  that  matter  the  material 
part  of  any  animal — the  body. 

•'One  thing  continues  another.  Hut  the  old  Pine  mustn't 
get  things  mixed,  sound  doesn't  re-create  sound,  but  a  record, 
that  h,  an  instrument,  which  will  reproduce  sound;  each  sound 
an  instrument  which  will  reproduce  itself.  There  is  a  marked 
distinction  here,  for,  with  another  instrument  there  are  two 
sound*producing  instruments*  where  before  there  was  but  one. 

**\Vhen  things  work  this  way  we  have  a  creation,  continuous 
and  eternal,  And  an\'  other  kind  of  creation,  as  Ellen  thinks, 
would  be  an  abortion.  The  light  would  hardly  be  worth  the 
candle.  It  would  be  so  soon  over,  and  nothing  left  but  the 
debris  of  a  dead  rreation. 


ause  of  a  theory   of  sound  v^hich  he  has  not  yet  learned   is 

I      Lse^     He  conlinaes: 

r'Once  more  rotating  the  cvlinder  the  sU^k  rmes  and  falls   as   the 
Eaiow  embossed  foil  passes  beneath  it,  and  the  molion  given  to  the  st>'Je 
is  communicateil  to  the  disc  and  thence  to  the  air  ;utmmt/ 

^^■^     **  Nothing  of  the  kind  takes  place* 

M  "What  takes  place,  as  we  have  seen,  is,  the  reproduction  or 

■       reappearance  of  the  original  sound,  with  all  ks  peculiarities  and 

I        characteristics.     And  this   is  jnBnitesimal  particles  of    matter, 

^^H  endowed  with  a  power  of  motion.  The  sounds  are  caused  by 
^^V  the  record  as  may  plainly  be  d em onj^t rated  by  listening.  They 
^^H  are  conducted  from  the  record  to  the  diafram,  and  through  this 
^^H  into  the  megaphone,  which  introduces  them  into  the  room 
^^H       where  they  are  heard* 

"  That  the  cause  of  reproduction  of  sound  in  a  graphophon 
is  entirely  connected  with  the  record,  may  be  tested  by  anyone. 
For  the  sound  can  be  heard  when  a  reproducer  is  passed  over 
the  record,  although  the  record  is  entirely  disconnected  from 
the  diafram.  Ellen  destroyed  the  diafram,  but  the  sounds 
were  reproduced,  the  style  being  pressed  down  upon  the  recbrd. 
All  any  diafram  can  do,  as  Ellen  has  shown,  is  to  assist  in 
collecting,  and  by  that  means  increasing  the  effect  of  sounds, 
made  by  some  sound-producing  instrument. 

'*ln  speaking  of  these  blunders  of  scientists,  Ellen  says  there 
are  but  few  exceptions.  By  which  she  means  that  those  who 
only  seek  truth,  and  for  the  love  of  it  work  assiduously  and  de- 
votedly, letting  go  all  other  considerations  are  very  few.      Mr. 


WHISPERINGS   OF  AN  OLD   PINE 


519 


Newton  went  straight  on  the  question  of  light,  into  which  he 
looked  more  carefully.  It's  the  men  of  smaller  caliber  and  the 
less  conscientious  that  make  or  perpetuate  gross  blunders,  those 
that  don't  know  and  think  they  do ;  or  worse  yet,  those  who 
care  nothing  at  all  whether  they  know  or  not,  if  they  can  make 
people  think  they  know.  Unfortunately  there  are  quite  a  good 
many  of  these  who  assume  to  lead,  riding  rough  shod  over  all 
truth  and  sometimes  escaping  detection  (or  quite  a  while.  It  is 
these  that  are  the  most  reckless  in  their  statements:  It  is  this 
class  that  in  the  undulatory  theories  bring  in  that  most  mon- 
strous of  lies  the  assumption  that  these  hypothetical  air  waves 
are  like  water-waves  or  ripples  upon  the  surface  of  a  pond* 
But  in  the  end  it  is  all  of  no  avail, 

*Tnuh  crushed  to  earth  will  rise  again. 

'The  eternal  years  of  God  are  hers,* 

'*  Ellen  will  mention  another  luyal  and  really  great  man, 
Huxley.  And  still  another,  who,  perhaps,  belonged  to  that 
class  of  whom  Christ  said : 

*  Blessed  are  the  meek,  for  they  shall  inherit  the  earth/ 

*'Ellen  refers  now  to  Mr.  Faraday,  whose  search  after  truth 
was  so  constant  and  sincere,  so  bright  and  perfect,  that  like  a 
touch  of  feeling,  it  made  the  world  akin, 

"  Faraday  was  remarkable  for  the  persistency  and  thorough- 
ness with  which  he  made  experiments  in  his  search  for  scien- 
tific truth.  Again  and  again  he  would  return^  without  result,  but 
he  never  gave  up  until  sickness  ami  death  closed  his  work  here, 
and  he  never  made  any  pretense  of  finding  anything  until  he  did 
find  it ;  and  constantly  he  discovered  valuable  facts. 


520  ELLEN  OR  THE 

«<From  'Michael  Faraday  His  Life  and  Woil^  1901/  by  Syl- 
vanus  P.  Thompson,  we  quote  the  following: 

'On  the  sand  of  September,  1791,  was  bom,  at  Neinogtan 
then  an  oadying  Surrey  village,  but  since  long  surrounded  and  1 
lowed  up  within  the  area  of  Greater  London,  the  boy  Michael  Faimd«f  • 
He  was  the  third  child  of  his  parents,  James  and  Maiguet  Fandaj^ 
who  had  but  recently  migrated  to  London  from  the  little  YoAahire 
village  of  Clapham.  Clapham  lies  under  the  shadow  of  Ing1eboIO^^g|^ 
on  the  western  border  of  the  county,  midway  between  Setde  and  Kirkby 
Lonsdale.  The  father,  James  Faraday,  was  a  working  bbcksmith  ;  the 
mother,  daughter  of  a  farmer  of  Mallerstang,  the  ronumtic  valley  iriiich 
runs  past  Pendragon  Castle  to  Kirkby  Stephen.  James  Famday  was 
one  of  the  ten  children  of  a  Robert  Faraday,  who  in  1756  had  married 
Elizabeth  Dean,  the  owner  of  a  small  homestead  known  as  Qapluuii 
Wood  Hall,  since  pulled  down.  All  Robert  Faraday's  sons  appear  to 
have  been  brought  up  to  trades,  one  being  a  shoemal^er,  another  a 
grocer,  another  a  farmer,  another  a  flaxworker,  and  another  a  ahcyp- 
keeper.     Descendants  of  some  of  these  still  live  in  the  district. 

'After  Michaers  birth,  his  parents  moved  to  the  north  side  of  the 
Thames,  living  for  a  short  time  in  Gilbert  Street,  but  removing  in  1796 
to  rooms  over  a  coach-house  in  Jacob's  Well  Mews,  Charles  Street, 
Manchester  Square,  where  they  lived  till  1809.  In  that  year,  young 
Michael  being  now  nearly  eighteen  years  old,  they  moved  to  18,  Wey- 
mouth Street,  Portland  Place.  Here  in  the  succeeding  year  James 
Faraday,  who  had  long  been  an  invalid,  died;  his  widow,  who  for 
some  years  remained  on  at  Weymouth  Street,  maintaining  herself 
by  taking  in  lodgers  until  her  sons  could  support  themselves  and  her, 
survived  till  1838.  Though  a  capable  w^oman  and  a  good  mother, 
she  was  quite  uneducated.  In  her  declining  years  she  was  wholly  sup- 
ported by  her  son,  of  whom  she  was  very  proud,  and  to  w^hom  she  was 
devoted.  *  * 


WHISPERINGS   OF   AN   OLD   PINE 


SSI 


*In  1804  he  went  on  trial  for  twelve  months  as  errand-boy  to  a  book- 
seller and  stationer  at  No.  2  Blandford  Street — N!r»  George  Riebau.  ♦  • 

'  Faraday  was  apprenticed  as  errand  boy  to  a  lx)oksel!er  in  London 
when  thirteen  years  old,  and  this  apprenticeship  lasted  seven  years*  *  • 

'Down  to  the  year  1830  Faraday  continued  to  undertake,  at  pro- 
fessional fees,  chemical  analyses  and  expert  work  m  the  law-courts, 
and  thereby  added  considerably  to  the  verj*  slender  emolument  of  his 
position  ;  but,  finding  this  work  to  make  increasing  demands  on  his 
time,  which  he  could  ill  spare  from  the  absorbing  pursuit  of  original 
researches,  he  decided  to  abandon  a  practice  which  would  have  made 
him  rich,  and  withdraw  from  expert  practice.     •     •     • 

*  He  might  easily  have  made  j£$,ooo  a  year  had  he  chosen  to  culti- 
vate ihe  professional  connection  thus  formed  ;  and  as  he  continued, 
with  little  intermission,  in  activity  till  i860,  he  might  have  died  a 
wealthy  man.  Hut  he  chose  otherwise ;  and  his  first  reward  came  in 
the  autumn  of  i8ji,  in  the  great  discovery  of  magneto-electric  cur- 
rents— the  principle  upon  which  all  our  mofiern  dynamos  and  trans- 
formers are  based,  the  foundation  of  all  Ihe  electric  lighting  and  elec- 
tric transmission  of  |>Dwer.     •     •     • 

'  But  the  immense  body  of  patient  scientific  work  thus  done  for  the 
love  of  science  was  not  accomplished  without  sacrifices  of  a  more  than 
pecuniary  kind.  He  withdrew  more  ami  more  from  society,  declined 
to  dine  in  company,  ceased  to  give  dinners,  withdrew  from  all  social 
and  philanthropic  organizations;  even  withdrew  from  taking  any  part 
in  the  management  of  any  of  the  learned  so  ieties/ 

*  In  a  letter  to  Prof.  G.  de  la  Rive  of  Geneva,  Faraday  wrote : 
"'You  partly  reproach  us  herewith  not  sufficiently  esteeming  Ampere's 

experiments  on  electroraagnetism.  Alow  me  to  extenuate  your  opin- 
ion a  little  on  this  point.  With  regard  to  the  experiments,  1  hope  and 
trust  that  due  weight  is  allowed  to  ihem;  but  these  you  know  are  few, 
and  theory  makes  up   the  great  part  of  what  M.  Ampere  has  published, 


S22 


ELLEN   OR  THE 


and  theory  in  a  great  many  points  unsupported  by  ex(>6rImeBts  when 

they  ought  to  have  been  addticed." 

'  And  in  same  letter  : 

' "  I  find  all  the  usual  attractions  and  repulsions  of  the  magnetic  needle 
by  the  conjunctive  wire  are  deceptions,  the  motions  being  not  aitxac* 
tions  or  repulsions,  nor  the  result  of  any  attractive  or  repulsive  forc^ 
but  the  result  of  a  force  in  the  wire,  which  instead  of  bringing  the  pole 
of  the  needle  nearer  to,  or  further  from  the  wire,  endeavors  to  make  it 
move  round  it  in  a  never  ending  circle  and  motion  whilst  the  battery 
remains  in  action.  I  have  succeeded  not  only  in  showing  the  existence 
of  this  motion  theoretically,  but  experimentally,  and  have  been  able  to 
make  the  wire  revolve  round  a  magnetic  pole,  or  a  magnetic  pole  round 
the  wire,  at  pleasure." 

^  And  again  same  letter  i 

"^Now  1  have  been  able,  experimentally,  to  trace  this  motion  into  its 
various  forms  as  exhibited  by  Ampere,  Nelice,  etc.,  and  in  all  cases 
to  show  that  the  attractions  and  repulsions  are  only  appearances  due  to 
this  circulation  of  the  pole,  to  show  that  dissimilar  poles  repel  as  well 
as  attract,  and  that  similar  poles  attract  as  well  as  repel,  and  to  make,  I 
think,  the  analogy  between  the  helix  and  common  bar  magnet  fiur 
stronger  than  before.  But  yet  I  am  by  no  means  decided  that  tiieie 
are  currents  of  electricity  in  the  common  magnet."     ♦    ♦    ♦ 

*With  the  year  1 831  begins  the  period  of  the  celebrated  **  Elxperi- 
mental  Researches  in  Electricity  and  Magnetism."  Dm-ing  the  years 
which  had  elapsed  since  his  discovery  of  the  electromagnetic  rotations 
in  1823,  Faraday,  though  occupied,  as  we  have  seen,  with  other  mat- 
ters, had  not  ceased  to  ponder  the  relation  between  the  magnet  and 
the  electric  current.  The  great  discoveries  of  Oersted,  Amp&re,  and 
Arago  had  culminated  m  England  in  two  results :  in  Faraday's  discxyr* 


WHISPERINGS   OF  AN   OLD    PINE 


S23 


ery  that  the  wire  which  carries  an  electric  current  tends  to  revolve 
around  the  pole  of  a  neighboring  magnet ;  and  in  Smrgeon*s  invention 
of  the  soft' iron  electromagnet,  a  core  of  iron  surrounded  by  a  coil  of 
copper  wire,  capable  of  acting  as  a  magnet  at  will  when  the  electric 
current  is  transmitted  to  the  coil  and  so  caused  to  circulate  around  the 
iron  core. 

*This  production  of  magnetism  from  electncity,  at  will,  and  at  a  dis- 
tance, by  the  simple  device  of  sending  the  electricity  to  circulate  as  a 
current  around  the  central  core  of  iron  was  then,  as  now,  a  cause  of 
much  speculation.  The  iron  core  which  is  to  be  made  temporarily 
into  a  magnet  stands  alone,  isolated.  Though  surrounded  outwardly 
by  the  magnetising  coil  of  copper  wire,  it  does  not  touch  it ;  nay,  must 
be  screened  from  contact  with  it  by  appropriate  insulation-  The  elec- 
tric current  entering  the  copper  coil  at  one  end  is  confined  from  leav- 
ing the  copper  wire  by  any  lateral  path  ;  it  must  circulate  around  each 
and  every  convolution,  nor  be  permitted  to  flow  back  by  the  return- 
wire  until  it  has  performed  the  required  amount  of  circulation.  That 
the  mere  external  circulation  of  electric  current  around  a  totally  dis- 
connected interior  core  of  iron  should  magnetise  that  core;  that  the 
magnetisation  should  be  maintained  so  long  as  the  circulation  of  elec- 
tricity is  maintained ;  and  that  the  magnetising  forces  should  cease  so 
soon  as  the  cunent  is  stopped,  are  facts,  familiar  enough  to  every 
beginner  in  the  science,  but  mysterious  enough  from  the  abstract  point 
of  view.  Faraday  was  firmly  persuaded  that,  great  as  had  been  these 
discoveries  of  the  production  of  magnetism  and  magnetic  motions 
from  electricity,  there  remained  other  relations  of  no  less  importance 
to  be  discovered,  Again  and  again  his  mind  recurred  to  the  subject. 
If  it  was  jx>ssible  to  use  electricity  to  prcKluce  magnetism,  why  should 
not  the  converse  be  true  ?  In  1822  his  notebook  suggestion  was,  as 
we  have  seen,  **  Convert  magnetism  into  electricity.'*     Yes,  but  how? 


$94  ELLEN  OR  THE 

'The  cause  of  aO  the  earlier. failures  was^.then,  that  hdtfi  magnet  and 
coil  were  at  rest  The  magnet  might .  lie  in  or  near  the  coQ  for  a  oeo- 
tuiy  and  cause  no  effect.  But  while  moving  towards  the  coO;  or  ftons 
it,  or  by  spinning  near  it,  electric  currents  were  at  once  indiioed.' 

"  Nothing  strange,  as  Ellen  thinks,  that  these  should  be'  pro- 
duced by  movement.  Thus,  air  in  motion  moves  the  ship, 
while  that  at  rest  does  not 

<We  here  come  upon  those  "lines  of  force"  which  plajred  ao 
important  a  part  in  these  and  many  of  Faraday's  later  inveatigatioiUL 
They  were .  known  before  Farady's  time — ^had,  in  &ct,  been  known  fiir 
two  hundred  years.  Descartes  had  seen  in  them  evidence  for  his 
hypothetical  vortices.  Musschenbroek  had  mapped  them.  But  it  was 
reserved  to  Faraday  to  point  out  their  true  significance.  To  the  TCiy 
end  of  his  life  he  continued  to  speculate  and  experin^ent  upon  them. 

'Mr.  Faraday  to  R.  Phillips,  Brighton,  November  29,  183 1 : 

* "  §  I.  When  an  electric  current  is  passed  through  one  or  two  parallel 
wires  it  causes  at  first  a  current  in  the  opposite  direction  through  the 
other,  but  this  induced  current  does  not  last  a  moment,  notwithstanding 
the  inducing  current  (from  the  Voltaic  battery)  is  continued,  all  seems 
unchanged  except  that  the  principal  current  continues  its  course,  but 
when  the  current  is  stopped  then  a  return  current  occurs  in  the  wire 
under  induction  of  about  the  same  intensity  and  momentary  duration 
but  in  the  opposite  direction  to  that  first  found.  Electrcity  in  currents 
therefore  exerts  an  inductive  action  like  ordinary  electricity  but  subject 
to  peculiar  laws  :  the  effects  are  a  current  in  the  opposite  direction  when 
the  induction  is  established  :  a  reverse  current  when  the  current  ceases 
and  2.  peculiar  state  in  the  interim.  Common  electricity  probably  does 
the  same  thing  but  as  it  is  at  present  impossible  to  separate  the  begin- 
ning and  the  end  of  a  si)ark  or  discharge  from  each  other,  all  the  effects 
are  simultaneous  and  neutralize  each  other — 


wmSI'ERINGS  OF  AN   OLIl    PINE 


S2S 


*"§  11.  Then  I  found  that  magnets  would  induce  just  like  voltaic  cur- 
rents, and  by  bringing  hcHccs  and  wires  and  jackets  up  to  the  poles  of 
magnets,  electrical  currents  were  produced  in  them,  these  currents 
being  able  to  deflect  the  galvanometer,  or  to  make,  by  means  of  the 
helixj  magnetic  needles^  or  in  one  case  even  to  give  a  spark*  Hence 
the  evolution  of  eiectridty  frt^m  magfutisntn  The  currents  were  not 
permanent^  they  ceased  the  moment  the  wires  ceased  to  approach  the 
magnet  because  the  new  and  apparently  quiescent  state  was  assumed 
just  as  in  the  case  of  the  induction  of  currents.  But  when  the  magnet 
was  removed j  and  its  induction  therefore  ceased,  the  return  currents 
appeared  as  before.  These  Ivvo  kinds  of  induction  I  have  distinguished 
by  the  terms  Valia-eiectnc  and  Magneio-eiectric  induction.  Their 
identity  of  action  and  results  is,  I  think,  a  very  powerfyl  proof  of  the 
truth  of  M.  Ampere's  theory  of  magnetism. 

***§  II L  The  new  electrical  condition  which  intervenes  by  induction 
between  the  beginning  and  end  of  the  inducing  current  gives  rise  to 
some  very  curious  results.  It  explains  why  chemical  action  or  other 
results  of  electricity  have  never  been  as  yet  obtained  in  trials  with  the 
magnet.  In  fact,  the  currents  have  no  sensible  duration.  The  rondi- 
tion  of  matter   1  have  dignified  by  the  term  Eitctrotomi\  The  Elkc- 

TKDTONIC  StA'I  E.      •       •       • 

* "  It  is  quite  comfortable  to  me  to  find  that  experiment  need  not  quail 
Ijefore  mathematics,  but  is  quite  competent  to  rival  it  in  discovery ; 
and  I  am  amused  to  find  that  what  the  high  mathematicians  have 
announced  as  the  essential  condition  to  the  rotation — namely,  that  time 
is  re^uired^has  so  little  foundation,  that  if  the  time  could  by  possi- 
bih"ty  be  anticipated  instead  of  being  required — i.f.  if  the  currents 
could  be  formed  /^e/ore  the  magnet  came  over  the  place  instead  of  after 
— the  effect  would  equally  ensue.*' ' 


*  These  currents,  it  is  evident,  are  a  result  of  increased  resist- 


k 


ELLEN   OR    TlIE 


r 


i^motion,  however  slight  it  may  be,  thus  caused.      Thus 
I  apparently  still  morning  if  we  drive  rapidly,  plenty  of  air 
sar  to  be  stirring. 

erefore,  the  words,  Electrotonic  State,  as  referring  to 
P^couuitions  of  matter  are  very  appropriate,  this  whole  mat- 
'nduced  currents  connecting  and  that  most  naturally  with 
i  electrical  action. 
^/  *'It  will  be  seen,  that  P^araday  rose  above  ^ny  fear  of  mathe- 
matics, although  he  had  never  studied  them*     He  was  thiiiker 
enough  to  hold  them  in  proper  place,  and  criticise  their  misuse, 
^  "  Returning   to   this   subject  oi   the  Electrotonic  State    Mr. 
mipson  says : 

'  Faraday,  to  whom  the  idea  of  mere  action  at  a  distance  was  abhor- 
rent^ if  no!  unthinkable,  conceived  all  these  force**  of  attraction  and 
repulsion  as  effects  taking  place  by  something  going  on  in  /ke  r>^r- 
vemng  mrdiumj  as  effects  propagated  from  point  to  point  continuously 
through  space.  Id  his  earlier  work  on  the  electromagnetic  rotations 
he  had  grown  to  regard  the  space  around  the  conducting  wire  as  being 
affected  by  the  so-called  current;  and  the  space  about  the  poles  of -a 
magnet  he  knew  to  be  traversed  by  curved  magnetic  lines,  invisible 
indeed,  but  real,  needing  only  the  simplest  of  expedients — the  sprink- 
ling of  iron  filings — to  reveal  their  existence  and  trend.  When,  diete<^ 
fore,  he  found  that  these  new  effects  of  the  induction  of  one  electzie. 
current  by  another  could  likewise  cross  an  intervening  space,  whe^ier 
empty  or  filled  with  material  bodies,  he  instinctively  sought  to  ascribe 
this  propagation  of  the  effect  to  a  property  or  state  of  the  medium^ 
And  finding  that  state  to  be  different  from  any  state  previously  knpwat^ 
different  from  the  state  existing  between  two  magnets  at  rest,  oc 
between  two  stationary  electric  charges,  he  followed  the  entirely  philo. 
sophical  course  of  exploring  its  properties  and  of  denoting  it  by  a  tuuoie 


"WHISPERINGS 


OLD    PINE 


527 


which  he  deemed  appropriate.     As  we  shall  see,  ihis  idea  of  an  elec- 

trotoDic  state  recurred  in  his  later  researches  with  new  and  important 
connections.'     •     •     • 

"Again  Mn  Thompson  says: 

'  Faraday's  mind  was  of  a  ver)*  individual  turn  ;  he  could  not  walk 
along  the  beaten  tracks,  but  must  pursue  truth  wherever  it  led  him. 
His  dogged  tenacity  for  exact  fact  was  accomp>anied  by  a  perfect  fear- 
lessness of  speculation.  He  %vould  throw  overboard  without  hesitation 
the  most  deeply-rooted  notions  if  experimental  evidence  pointed  to 
newer  ideas.  He  had  learned  to  doobt  the  ideas  of  poles ;  so  he  out- 
grew the  idea  of  atoms,  which  he  considered  an  arbitrary  conception. 
Many  who  heard  his  bold  speculations  and  his  free  coinage  of  new 
terms  deemed  him  vague  and  loose  in  thought  Nothing  could  be 
more  untnie.  He  let  his  mind  play  freely  about  the  facts  j  he  framed 
thousands  of  hj^otheses,  only  to  let  them  go  by  if  they  were  not  sui>- 
ported  by  facts.  *'  He  is  the  wisest  philosopher,"  he  said  in  a  lecture 
on  the  nature  of  matter,  "  who  holds  his  theory  with  some  doubt — who 
is  able  to  proportion  his  judgment  and  confidence  to  the  value  of  the 
evidence  set  before  hira,  taking  a  fact  for  a  fact  and  a  supixjsition  for  a 
supposition,  as  much  as  possible  keeping  his  mind  free  from  all  source 
of  prejudice;  or,  where  he  cannot  do  this  (as  in  the  case  of  a  theory), 
remembering  that  such  a  source  is  there,'* 

*  In  one  of  his  later  experimental  researches  he  wrote  :— 

"*  As  an  experimentalist,  I  feel  bound  to  let  experiment  guide  me  into 
any  train  of  thought  which  it  may  justify ;  being  satisfied  that  experi- 
ment, hke  analysis,  must  lead  to  strict  truth  if  nghtly  interpreted ;  and 
believing  also  that  it  is  in  its  nature  far  more  suggestive  of  new  trains 
of  thought  and  new  conditions  of  natural  power.      •     •     • 

***lt  puzzles  me  greatly  to  know  what  makes  the  successful  philos- 
opher.    Is  it  industry  and  perseverance  with  a  moderate  proportion  of 


f 


intelligence?     Is  not  a  moderate  assurance  or  earoest- 

ness  a  requisite?  Do  not  many  fail  because  they  look  rather  to  the 
renown  to  be  acquired  than  lo  the  pure  acquisition  of  knowledge,  and 
the  delight  which  the  contented  mind  has  in  acquiring  it  for  its  own 
sake?  I  am  sure  I  have  seen  many  who  would  have  been  good  and 
successful  pursuers  of  science,  and  have  gained  themselves  a  high  name, 
but  that  it  was  the  name  and  the  reward  they  were  always  looking  for- 
ward  to— the  reward  of  the  worldVs  j>raise.  In  such  there  is  always  a 
shade  of  envy  or  regret  over  their  minds,  and  I  cannot  imagine  a  man 
making  discoveries  in  science  under  these  feelings,*'  ^ 

*' Ellen  will  close  these  quotations  from  Mr.  Thompson's 
book, — who  throughout  the  whole  has  shown  his  own  excellent 
qualities  of  correct  perception  and  appreciation  of  hoiiest  \%'ork, 
and  fearless  thought  built  upon  it, — ^with  the  following,  which 
throws  light  upon  the  frailties  so  common  to  man,  and  which  go 
far  to  explain  the  errors  that  so  constantly  enter  scientfric 
work,  for  it  is  no  more  true  that  those  who  seek  will  find,  fhnn 
that  they  will  find  what  they  seek.  But  those  who  seek  for 
fame  are  not  in  the  lines  which  lead  to  Truth: 

'  Faraday  has  himself  left  on  record  that  when  he  Wrote  to  Davv 
asking  to  be  taken  into  his  employment,  his  motive  was  his  desire 
"  to  escape  from  trade,  which  I  thought  vicious  and  selfish,  and  to  enter 
into  the  service  of  Science,  which,  I  imagined,  made  its  pursuers  amia- 
ble  and  liberal."  Davy  had  smiled  at  this  boyish  notion,  and  had 
told  him  that  the  experience  of  a  few  years  would  correct  his  ideas. 
Years  afterwards  he  spoke  of  that  matter  to  Mrs.  Andrew  Crosse  in  an 
interview  which  she  has  recorded  : — 

'"After  viewing  the  ample  appliances  for  experimental  research,  and 
feeling  much  impressed  by  the  scientific  atmosphere  of  the  phure.  I 
turned  and  said, '  Mr.  Faraday,  you  must  be  very  happy  in  your  posi- 


WHISPERINGS   OF  .\N   OLD    P[NE 


529 


don  and  with  your  pursuits,  which  elevate  you  entirely  out  of  the  meaner 
aspects  and  lower  aims  of  common  life/ 

*"He  shook  his  head,  and  with  that  wonderful  mobility  of  coun*> 
nance  which  was  characteristic,  his  expression  of  joyousness  changed  to 
one  of  profound  sadness,  and  he  replied.  *  When  1  quitted  business  an  1 
took  to  science  as  a  career,  I  thought  1  load  left  behind  me  all  the  petty 
meannesses  and  small  jealousies  which  hinder  man  in  his  moral  prog- 
ress ;  but  I  found  myself  raised  into  another  sphere,  only  to  find  poor 
human  nature  just  the  same  everywhere — subject  to  the  same  weak- 
nesses and  the  same  self-seeking,  however  exalted  the  intellect.' 

"* These  were  his  words  as  well  as  I  can  recollect;  and,  looking  at 
that  good  and  great  man  I  thought  I  bad  never  seen  a  countenance 
which  so  impressed  me  with  the  characteristic  of  perfect  unwoildliness/*  * 

"Only  such  men  as  these  are  fit  to  kad  at  all,  or  to  write  text- 
books of  science,  and  their  number  is  exceedingly  small. 
Whilst  on  the  other  hand  the  least  reliable,  because  both  the 
least  conscientious  and  the  least  capable,  are  apt  to  forge  to  the 
front  both  in  text-books  and  writing.  Their  object  generally 
being  to  make  money,  or  vanity,  or  both,  whilst  that  of  such 
men  as  Faraday  or  Newton  is  simply  a  search  for  Truth. 

•*  If  the  work  done  on  sound  had  been  done  in  the  spirit  that 
Faraday  always  exemplified,  and  with  his  thoroughness.  FJlen 
might  have  been  taking  care  of  her  garden,  or  driving  her 
horses;  for  there  would  have  been  no  necessity  for  her  to  dis- 
cuss so  fully  with  the  old  Pine  this  theory  of  sound,  which 
she  does  wholly  to  correct  error  that  hangs  like  a  patl  over, 
and  retards,  indeed  largely  prevents,  the  advance  of  knowledge 
throughout  the  world. 


530  ELLEN   OR  THE 


XXXVI. 

^^nPHE  Popular  Science  Monthly,  in  an  article  headed  *The 
^  Telephone,  with  a  sketch  of  its  inventor,  Philip  Reis, 
by  Wm.  H.  Channing,  M.D.,'  Vol.  XXIII,  page  540,  gives 
a  short  biography  of  Johann  Philip  Reis,  born  Jan.  7,  1834, 
son  of  a  farmer  in  Cascl,  Germany.  Mr.  Reis  died  of  con- 
sumption Jan.  14,  1874. 

**The  article  thus  discusses  Mr.  Reis*  telephone: 

*The  description  of  Reis'  telephone  is  divided  naturally  into  two 
sections.  Here,  fully  illustrated  in  Professor  ITiompson's  booky  we 
have  ten  forms  of  transmitter,  all  imitating  the  mechanism  of  the  ear, 
and  applying  the  vibrations  of  an  artificial  tympanum  to  vary  or  modulate 
a  current  of  electricity,  by  varying  the  degree  of  contact  at  a  loose 
joint  in  the  circuit  one  or  both  of  the  members  at  this  point  of  contact 
having  an  elastic  bearing.  This  is  the  essential  principle  and  method, 
leaving  out  certain  adjuncts,  of  the  most  approved  modern  transmitters. 
In  the  very  first  transmitter  made  by  Reis,  in  1S60  or  1861,  a  little 
curved  lever  is  attached  by  one  end  to  the  center  of  an  elastic  tym- 
I)anum,  while  the  other  end  makes  varying  contact  with  a  delicate 
spring,  regulated  l)y  an  adjusting  screw — the  surfaces  of  contact  being 
of  platinum — and  the  lever  and  spring  included  in  a  telephonic  circuit 
e(iuipi)ed  with  a  galvanic  battery  and  receiver. 

*()f  the  receivers  four  forms  are  given.  The  first  receiver  made  by 
Reis  consisted  of  a  knitting-needle  wound  with  a  helix  of  silk-covered 
copj)er  wire,  rme  end  of  which  knitting-needle  was  thrust  into  the  bridge 
of  a  violin,  which  served  as  a  sounding  box.  This  instrument  was  given 
to  Reis  for  the  purpose  by  Herr  Peter,  the  music-teacher  of  Gamier 


WHISPERINGS   OF   AN    ULD    PINE 


533 


institute  and  it  is  now  preserved  with  other  relics  in  the  museum  of  that 
institution/ 

"Nature^  July  30,  1885,  page  29S,  says: 

'A  telephone  has  just  been  brought  to  this  country  from  America 
which  is  absolutely  independent  of  electricity  so  that  batteries,  coils, 
and  cells  are  quite  dispensed  with.  This  obviously  greatly  simplifies 
the  working  of  the  instrument.  In  this  "mechanical  telephone*'  which 
was  recently  subjected  to  a  severe  test,  simplicity  and  distinctness  are 
claimed  as  its  chief  characteristics.  The  instniment  consists  of  a 
diafram,  or  sounding  board  made  of  strips  of  willow  wood  which  has 
been  found  by  experiment  to  possess  remarkable  sensitiveness  to  &ound 
vibrations.  These  strips  of  wood  are  closely  woven  together  and  var- 
nished. In  the  centre  of  the  diafram  a  small  disc  of  metal  is  placedi 
from  which  the  wire  proceeds  to  any  point  desired  u})  to  two  miles.  In 
recent  trials  the  instrument  freely  answered  to  all  demands  upon  it,  the 
ticking  of  a  watch,  musical  sounds,  whispering,  etc.,  being  heard  with 
great  distinctness.* 

*' Nature,  Aug.  6,  1885,  says,  page  316: 

*  Having  observed  in  this  week*s  Nature  a  notice  of  a  "  mechanical 
ti-lephone"  said  to  be  brought  from  America,  I  may  state  that  as  far 
back  as  1S7S  I  experimented  on  the  transmission  of  stiunds  by  wires, . 
and  communicated  the  results  obtained,  from  a  large  number  of  experi- 
ments, to  the  Physical  Society  of  London  in  March,  1S78  ;  the  papet 
being  afterwards  published  in  the  Philosophical  Magazine  for  August, 
1878.  These  experiments  are  referred  to  by  the  Count  du  Moncel  in 
his  book  on  **  The  Telephone,"  published  in  1879.  I  found  no  difficulty 
in  carrying  on  a  conversation  through  wires  laid  in  various  wa>^  from 
room  to  room  of  a  house ;  and  musical  sounds,  breathing,  and  whistling, 
were  also  readily  transmitted,  and  through  most  unlikely  arrangements, 
such  as  a  common  wire  fence.     Various  materials  were  tried  for  th^ 


534  ELLEN   OR  THE 

transmitting  and  receiving  ends^-discs  of  card  board  set  in  deepish 
rims  being  found  to  give  excellent  results  with  a  No.  i6  copper  wire. 
In  one  of  my  experiments  I  found  that  the  discs  were  not  required,  the 
wire  itself  picking  up  and  transmitting  the  sounds.  The  results  obtained 
were  most  interesting ;  but  as  the  range  was  necessarily  limited,  it  did 
not  seem  to  me  that  there  was  much  scope  for  practical  application. 

W.  J.   Millar. 

loo  Wellington  Street,  Glascow,  July  31/ 

**The  above  is  a  very  complete  illustration  of  the  facility  with 
which  sound  enters  a  wire,  any  kind  of  wire,  and  can  be  heard 
by  it  much  fur.hcr  than  the  ordinary  voice  is  heard  through  the 
air. 

**  Ellen  would  call  especial  attention  to  the  fact  mentioned 
by  Mr.  Millar  that  he  found  disks  were  not  required,  the  wire 
itself  picking  up  and  transmitting  the  sounds.  As  Kllen  has 
said,  their  function  is  one  of  assistance,  not  of  necessity,  though 
under  certain  conditions  it  iiiii^ht  become  very  essential,  as  an 
car  trumpet  is  to  a  vcvy  deaf  person.  And,  as  Ellen  has  also 
said  she  thinks,  tliat  the  diafram  or  a  membrane  acts  to  collect 
sound,  as  a  clam  does  water,  and  thus  furnishes  an  increased 
suppl)'. 

"The  article  referred  to  above  by  Mr.  Millar,  headed  •  On 
the  Transmission  of  Vocal  and  other  Sounds  by  Wires,'  was 
published  in  the  Philosophical  Magazine,  Vol.  VI,  1 878,  as 
follows : 

OnjKt.  r    OK    PAI^ER. 

*  I.  The  object  of  the  present  paper  is  the  description  of  a  series  of 
experiments  made  by  the  author  ui)on  the  transmission  of  vocal  and 
other  sounds  by  wires,  and  the  results  obtained  from  these  experiments. 


WHISPERINGS    OF   AN    OLD    J'INE 


535 


*  2.  Transmission  of  Sound  in  Gekeral.^ — The  transmission  of  sound 
by  various  media  is  familiarly  illustrated  from  day  to  day ;  and  the 
readiness  with  which  these  media  are  affected  has  been  made  the  subject 
of  many  experiments. 

'One  familiar  illustralion  of  the  transmission  of  sound  from  air  to 
solids  and  thence  back  to  the  air  is  that  which  occurs  in  the  vertical  and 
horizontal  (lartiiions  between  roomn,  such  as  partition  walls  and  floor 
and  ceiling  spaces — the  sounds  originating  in  one  room  being  thus 
transmitted  to  the  adjoining  room  without  having  recourse  directly  to 
air  communication/ 

**This  is  a  practical  demonstration,  and  would  have  always 
been  accepted  as  such  but  for  the  ignorance  of  science,  that 
sound  is  an  entity  of  infinitesimal  size  which  readily  finds  its 
way  through  the  interstices  of  walls.  The  conceit  that  it  is  air 
waves,  some  of  them  seventy  feet  long,  and  many  of  them,  or 
most  much  longer  than  the  thickness  of  the  wall,  and  that 
these  swap  over  twice  in  going  through,  is  an  expression  of 
folly  that  it  wouldn't  be  supposed  any  sane  person  could 
make, 

*  From  a  consideration  of  the  latter,  as  also  from  other  phenomena, 
the  author  has  for  some  iiu;e  been  convinced  that  vocal  sounds  might 
be  transmitted  by  solid  bodies,  such  as  wires,  and  that  to  considerable 
distances, 

•After  several  unsuccessful  attempts,  the  author  during  the  month  of 
January  last,  having  orcasion  to  use  some  fine  copper  wire,  carried  a 
portion  of  it  out  from  the  house  to  a  distance  of  about  20  yards,  and 
attached  a  couple  of  pastelx)ard  disks  with  low  rims  to  the  ends  of  the 
wire:  the  transmission  of  vocal  sounds  was  then  found  to  be  easily 
effected,  conversation  being  readily  carried  on  through  this  length  of 
wire. 


^Mm 


c 


I 


Lce  that  time  the  author  has  made  marty  experitneots  with  vafioos 

Lbinations  and  under  various  circumstances.     The   principle  upon 

f  all  more  or  less  appear  to  depend,  so  far  as  the  rendermg 

the  sounds,  is  that  of  the  tuning-fork  and  sound  in g*box^  lo 

I      I        sound  from  the  vibratory  tnovetnents  of  a  metal  body  is 

£1        biy  intensified  when   the  body  is  placed  upon    a    sonoiotis 

e  affecting  the  air  in  its  vicinitv. 

*  J-  Notes  of  some  oE  the  more  mipor  ant  experiments, 

'(i).  No,  35  copper  wire  was  stretched  between  windows  outside  of 
a  house  and  attachments  at  right  angles  made  to  rooms  through  tbe 
windows.  Speaking  in  one  room  was  then  heard  in  the  other»  the 
dislance  was  about  ao  yards.  Pianoforte  music  was  easily  traiisniitted 
by  placing  an  ear-piece  inside  the  instrument  and  carrying  the  other 
end  of  the  wire  outside  the  house, 

*  (2).  No.  40  copper  wire  fitted  up  in  a  building  passing  from  room 
to  room*     Six  attachments  and  angles. 

*  Distance  about  50  yards.  Conversation,  singing,  whistling,  breathing, 
and  the  sound  of  a  light  C  tuning-fork  (2j^  inches  in  fork)  readily 
transmitted. 

'Various  similar  arrangements  were  also  made  in  house  from  zoom  to 
room,  and  finally  carried  to  a  distance  outside,  where  all  the  above 
effects,  as  also  the  transmission  of  whispering,  were  clearly  demonstrate^ 
the  persons  at  either  end  being  quite  out  of  hearing  in  the  oidinazy 
manner. 

'The  communication  was  not  limited  to  the  persons  at  either  end  oi 
the  wire ;  additional  connections  were  occasionally  made,  where  tfuee 
or  more  individuals  could  communicate  with  each  other. 

*(3).  Carried  about  7  yards  of  No.  23  copper  wire  from  one  room 
through  an  adjoining  one  to  a  room  beyond,  the  wire  in  its  comse 
passing  below  two  doors  shut  above  it,  and  for  the  most  part  in  .oonttf^ 
with  the  carpet,  but  fastened  at  the  ends  so  as  to  produce  some  tetisiofu 


WHISPERINGS  OF  AN  OLD   PINE 


537 


Made  two  connections  of  No.  40  copper  wire  at  angles  with  the  main 
wire ;  conversation  was  then  readily  c:arriefl  on  to  all  the  phenomena 
already  descrilied  produced.  Subsequent  experiments  with  No*  16 
copper  wire  arranged  as  above  were  found  to  yield  better  results, 

*A  somewhat  similar  and  equally  Spuccessful  experiment  was  made  by 
carrying  the  same  size  of  wire  down  stairs^  passing  below  two  doors  and 
partly  resting  on  carpet  and  wood,  A  positive  advantage  is  gained  by 
resting  the  heavy  wire  in  this  manner,  the  words  being  clearer  and  more 
distinct,  and  free  from  the  rumbling  sound  occurring  with  a  suspended 
IV ire  free  to  move  about. 

*(4).  Fastened  No,  23  copper  wire  to  telegraph  wire,  made  another 
and  similar  attachment  75  yards  further  on,  but  within  two  posts* 
Breathing,  whistling,  and  tuning-fork  sounds  readily  transmitted. 

'(5).  Carried  the  latter  attachment  to  150  yards^  thus  passing  one 
post.  Breathing,  whistling,  singing,  and  the  sound  of  the  light  C 
tuning-fork,  formerly  mentioned  readily  transmitted.  No  apparent  loss 
though  passing  the  support  (the  latter  was  of  the  usual  china*ware  cup 
with  l)inding-wire).  The  speaking  was  not  so  distinct,  although  the 
different  wonl-sounds  were  discernible.  This  can  be  accounted  for  by 
the  fact  that,  as  the  poles  were  about  14  feet  high,  the  attachment  ends 
were  free  to  swing  about,  which,  combined  with  the  exposed  situation  of 
the  main  line,  gave  rise  to  a  considerable  vibratory  action  due  to  other 
causes  than  the  vo<al  sounds. 

'(6).  About  50  yards  of  No.  23  copper  wire  was  laid  out  so  as  to 
rest  partly  on  grass,  and  fastened  up  at  the  ends  to  pins ;  attachments 
were  made,  and  vo<?al  sounds  transmitted ;  whistling  and  the  tuning- 
fork  sounds  very  clearly  heard,  although  a  high  wind  was  blowing  at  the 
time. 

'4.  The  MntrrH  and  Ear  Pieces. — The  mouth  and  ear  pieces  used 
in  these  experiments  have  been  of  various  materials  and  forms.  The 
materials  tried  have  been  pasteboard,  wooil,  gutta-percha,  india-rubber, 
parchment,  iron,  tin<  and  zinc.    ITiesc  have  generally  been  arranged  as 


S38 


ELLEN    OR   TlIE 


disea  or  dnims,  having  a  more  or  less  extended  rim  around   thetB  to 

confine  the  sounds.     This  rim  has  been  of  cyliiidrical,  conical >  andoUier 

forms, 

'In  general,  greater  volurae  of  sound  accompanied  increased  depth 

of  rim  ;  but  the  sounds  were  hardly  so  distinct  as  when    the  rim  was 

kept  shallow. 

I      *The  wire  was  usually  attached  to  the  centre  of  disc  ;  but  in   some 

cases  good  results  were  got  where  the  wire  was  led  through  a  cylindric^ 

hollow  piece  of  wood  and  terminated  close  to  the  disc  ;  indeed  a  hollow 

piece  of  wood  without  a  disc  did  very  well 

*  As  a  rule,  the  effects  seemed  better  where  the  wire  was  let!  oiit&ule 
of  the  house, 

*  High-pitched  voices  are  more  easily  heard  than  deep  strong  \^oices* 
*ln  the  experiments  with  the  telegraph  wire  one  of  the  discs   used 

was  of  thin  sheet  iron  5J4  inches  in  diameter.  Set  in  a  wooden  rim 
about  J4  inch  deep,  the  wire  was  fastened  into  a  small  piece  of  wood, 
which  in  turn  was  cemented  down  to  centre  of  disc.  The  tun  in  g- fork 
smin-rls  were  very  w<^l!  heni-'l  with  thi^  armiu^^^^men^  :  r^n<l  on*>  l^eruHariiy 
was  that,  on  the  wooden  fastening  accidentally  breaking  aw/  ftom  the 
iron,  the  sounds  could  again  be  heard  by  holding  the  disc  in  Oi?e  hand 
and  pressing  the  wooden  termination  of  the  wire  upon  the  disc  with 
the  other. 

*5.  Wires. — The  wires,  as  a  rule,  require  to  be  more  or  less  tightened 
up ;  but  this  varies  with  the  heaviness  of  the  wire. 
.  *The  sound  is  increased  with  a  tight  wire. 

'The  volume  of  sound  appears  to  be  increased  with  a  heavy  wiie. 
Thus  in  the  telegraph  wire  about  one-eighth  inch  thick,  probably  No*  S» 
the  sounds  were  stronger  and  fuller  than  in  the  thinner  wires  andL 
probably  owing  to  the  high  tension  of  the  former,  faint  sounds 
more  readily  transmitted  :  thus  the  accidental  or  intentional 
of  the  tuning-fork  with  the  rim  of  the  mouth-piece,  causing  a  sludit 
clicking  soimd,  was  distinctly  heard  through  the  ear-piece  at  a  ^jjgf^np^ 


WHISPERINGS   OF  AN    OLD    PINE 


539 


of  ISO  yards — and  this,  even  although  the  two  attachments  of  copper 
wire  were  practically  at  right  angles  to  the  main  »viie,  whereby  part  of 
the  sountl  would  pass  away  onwards  up  and  down  the  line. 

*6.  The  great  delicacy  of  the  action  may  be  inferred  "^om  the  fact 
that  fine  sand  strewn  upon  the  disc  of  the  ear-piece  is  unaffected  by 
conversation  thrcnigh  lengths  of  about  seven  yards*  The  sensitiveness 
also  of  the  mouth-piece  was  shown  by  sounds  not  spoken  into  it  being 
readily  transmitted,  such  as  coughing,  laughing,  or  remarks  made  by 
persons  standing  beside  the  instrument  Indeed,  in  some  cases  an 
advantage  is  obtained  by  keeping  back  from  the  mouth  or  ear-piece : 
and  the  author  has  sometimes  thought  an  improvement  was  obtained 
by  holding  the  ear-piece  slightly  inciinet^  to  the  ear, 

*  In  all  cases  the  individual  voice  could  easily  be  distinguished 
though  modified  more  o^  le»i  by  the  structure  and  material  of  the 
niouth  and  ea  ^pieces. 

*The  mouth  and  ear-pieces  were  usually  of  the  same  form  and 
material,  and  were  therefore  used  for  either  speaking  or  hearing.  Some 
forms,  however,  do  better  as  ear* pieces,  others  as  mouth-pieces. 

•In  conclusion,  the  author  believes  that  many  interesting  physical 
questions  may  be  st tidied  by  means  of  these  arrangements,  and  that 
practical  application  may  be  made  where  communication  of  this  nature 
is  required/ 

'*  *  Practical  Telephony,'  by  James  Bell,  1898,  says: 
'  M,  Monadier  made  a  large  number  of  experiments  with  various 
kinds  of  disks,  from  which  he  concludes  that  telephones  with  iron  disks 
are  much  louder  than  others,  and  that  the  effect  is  chiefly  due  to  mag- 
netic induction.  Copper  and  aluminum  disks  reproduce  the  timbre 
very  much  better  than  those  of  iron.  Iron  disks  an  inch  thick  reduce 
the  intensity,  but  do  not  affect  the  clearness  of  speech.  Discs  made  of 
thick  pieces  of  lead,  zinc,  glass,  and  steel  have  also  been  tried,  and  all 
these  substances  act,     Wood    also    reproduces   the  sound,  and  the 


540  ELLEN    OR  THE 

intensity  increases  with  its  thickness  up  to  one  and  one-half  inches. 
A  half- inch  cork  has  been  used,  also  an  empty  wooden  box,  also  a 
razor-stone  t\^'0  inches  thick.  By  dispensing  with  the  disk  and  apply- 
ing the  ear  very  close  to  the  pole  of  the  magnet  a  faint  sound  has  been 
heard.  Messrs.  Edison,  Blythe  and  Preece  have  also  shown  that  sound 
may  be  reproduced,  although  the  disk  [at  receiving  telephone]  is  non- 
magnetic. Du  Moncel  tried  water  and  mercury  on  the  disks  to  provi 
whether  the  disks  really  vibrated  at  all  or  not.  He  was  unable  to  dis- 
cover any  signs  of  vibration  even  when  luminous  reflections  were  em- 
ployed to  detect  them ;  but  the  more  sensitive  photographers'  plates 
have  shown  that  vibrations  are  really  produced  in  the  disk  of  the 
receiving  telephone.     *     ♦     * 

'  It  has  been  found  that  a  small  flat  lx)x  filled  with  coke,  with  t^-o  tin 
electrodes  fixed  to  the  ends,  is  one  of  the  best  arrangements  for  a 
microphone,  and  that  even  a  single  piece  of  cork  will  make  a  micro- 
phone capable  of  transmitting  speech.  The  microphone  can  not  onlv 
transmit  speech,  but  it  can  also  under  certain  conditions  repro<iuce  it, 
and  consequently  supply  the  place  of  the  receiving  telephone  •  but 
experiments  in  this  direction  have  not  been  very  successful.  A  micro- 
phone conii)osed  of  two  pieces  of  lead  pencil  placed  in  a  watch  case. 
and  connected  by  a  piece  of  money,  was  exhibited  at  Rouen  in  1878.' 

"  I'^llcn  would  call  attention  here  to  the  statement  that  a 
microphone  can  under  certain  conditions  reproduce  speech 
and  supply  the  place  of  the  receiving  telephone.  Undoubtedly 
experiments  were  tried  in  which  the  particles  of  sound  came 
through  the  wire  and  were  delivered  by  a  microphone.  Ellen 
calls  attention,  too,  to  the  fact  that  sound  was  heard  at  the 
receiver  although  the  disk  (diafram)  was  not  magnetic,  and  also 
when  there  was  no  disk,  as  disk  and  magnetism  had  been  largely 
relied  upon  previously  to  explain  the  phenomena. 


WHISPERINGS   OF   AN    OLD    I'INE 


541 


• 


"  It  also  appears,  as  in  other  accounts,  that  the  vibrations  of 
the  diaframs  under  ordinary,  or  even  extraordinary  conditions^ 
are  imperceptible.  Against  this  is  the  statement,  giving  neither 
names,  dates,  or  places,  that  the  more  sensitive  photographers' 
plates  have  shown  that  vibrations  are  produced,  Ellen  has 
seen  this  same  statement  elsewhere,  but  in  tliis  indefinite  form. 
That  is,  it  is  the  worst  kind  of  hearsay  evidence,  which  would 
not  be  admitted  m  law,  although  it  would  appear  to  be  satis- 
factory to  science. 

**In  *Thc  Problem  of  Human  Life,*  Mr,  Hall  says: 

*  Some  of  our  greatest  physical  investigators  do  not  hesitate  to  claim 
that  even  the  more  delicate  telephonic  effects  i>ro(Juced  through  the 
Bell  diafram  can  not  be  attributed  to  its  mechanical  or  l>OLlilv  vibra* 
tions  toward  and  from  the  pole  of  the  magnetized  bar*  The  eminent 
Scotch  physicist,  R.  \L  Ferguson,  Ph.  D.,  F.  R.  S.  E.,  distinctly  takes 
this  position  in  a  lecture  on  the  telephone  recently  delivered  before  the 
Royal  Scottish  Society  of  Arts,  as  copied  into  the  ** Scientific  Aoierican 
Supplement,"  No,  tao. 

*  Dr,  Ferguson  shows,  by  the  most  convincing  arguments,  that  the 
merhauiral  oscillation  of  this  iron  disc  is  wholly  insufficient  to  account 
for  some  of  the  effects  produced  in  the  transmission  of  articulate 
speech ;  though  he  admits  that  these  bodily  movements  of  the  mem* 
brane  add  to  the  loudness  and  distinctness  of  the  message.  As  a 
proof  that  but  a  portion  of  these  effects  can  come  from  the  vibra- 
tory motion  of  the  transmitting  membrane,  he  notes  the  fact  that  a 
solid  iron  plate,  an  ifuh  thick^  in  place  of  the  membrane,  has  produced 
distinct  transmissions  of  speech^  and  that  even  the  naked  end  of  the 
magnetized  bar  has  done  the  same  thing  without  the  intervention  of 
any  kind  of  diafram  or  plate.  •  •  •  In  speaking  of  the  common 
explanation  tl  the  telephone,  as  given  by  all  writers  on  the  subject, — 


542  ELLEN  OR  THE 

that  is,  that  the  transmission  of  speech  depends  entireljr  upon  the  me- 
chanical vibration  of  the  transmitting  membnmei— the  Doctor  lemaika: 
* "  This  explanation  is  beautiful  and  simple,  and  one  ivould  wish  it 
true ;  it  must  always  remain  the  popular  one.  Undoabtedlj,  however, 
when  narrowly  examined,  it  is  found  to  be  a  mere  hjrpodiesii^  and  to 
have  as  yet  no  experimental  confirmation.  *  *  *  I  would,  in  the 
first  place,  take  exception  to  the  vibratory  theory  of  Bell,  vis,,  that  it  is 
the  vibrations  of  the  disc  to  and  from  the  pole  of  the  noa^gnet,  m  exntr- 
sions  proportionate  to  the  intensity,  pitch,  and  quaHty  e^  tike  vpcal 
sounds,  that  electrically  affect  the  instrument ;  and  in  so  doing  I  only 
express  the  dissatisfaction  with  it  of  almost  every  one  wbo  deals  with  the 
telephone." ' 

"  From  the  facts  as  here  stated  it  is  Very  plain  that  the  sounds 
go  through  the  wire.  The  Doctor's  idia,  that  the  sound  heard 
was  that  repeated  by  the  diafram,  would  always  remain  the 
popular  explanation  was  entirely  gratuitous ;  for  with  a  very  lit- 
tle intelligent  examination  of  the  subject  it  won't  remain  at  all. 


WHISPERINGS   OK   AN    OLD    PINE 


545 


XXXVII. 


^^T^HE  following  experiments,  with  a  telephone,  Ellen  has 
^     tried  herself: 

**If  one  speaks  close  to  the  mouth-piece  of  the  transmitter^ 
the  sound  will  be  much  louder  at  the  receiver  (evidently  because 
more  of  the  sound  goes  through),  but  not  so  distinct  (appar- 
ently because  not  so  well  arranged  for  effect). 

'*  The  louder  one  talks  at  the  transmitter  the  louder  is  the 
sound  heard  at  the  receiver »  but  the  difference  would  appear  to 
be  not  nearly  so  great  at  the  receiver  as  it  is  where  the  sounds 
are  made.  Experiments  showed  that  the  ordinary  voice  at  the 
transmitter  would  not  produce  a  graphophone  record  at  the 
receiver,  although  a  megaphone  at  the  receiver  was  used  to 
assist;  but  a  graphophone  record  was  made  with  a  loud 
whisper  spoken  directly  into  the  megaphone.  The  sound  of 
a  dinner  bell  rung  loudly  at  the  transmitter  produced  a  grapho- 
phone record  at  the  receiver,  but  not  a  loud  one.  In  all  these 
cases  the  transmitter  was  twelve  miles  distant  from  the  receiver. 

"Two  persons,  or  more,  speaking  at  the  same  time  near  the 
transmitter  can  be  heard  at  the  receiver,  which  illustrates  how  in 
a  graphophone  record  each  voice  uttered  into  the  instrument 
makes  an  independent  record. 

"And  this  acts  precisely  as  the  different  notes  of  a  piano 
lowing  into  a  sounding-board,  each  retaining  through  its  exist- 
'  cnce  its  individuality.     This  is  a  quality  that  all  sound  always 


546  ELLEN  OR  THE 

has ;  it  never  mixes.    And  Ellen  thinks  the  old  I^ne  will 
that  it  never  mixes  because  its  maker  designed  that  it  shouldn'L 

''The  idea  of  those  who  believe  in  the  diafram  talking  is  that 
it  can  talk  for  two  or  many,  or  play  on  fifty  instruments,  more 
or  less,  at  the  same  time." 

"The  graphophone  record  does  that,  does  it  not,  Ellen?*' 
I  asked. 

''  It  does,  indeed/'  she  answered,  **  because  it  is  composed  not 
of  one  but  of  many  indentures,  each  representing  a  sound 
uttered  into  the  gpraphophone,  many  of  which  may  be  uttered 
at  the  same  time,  and  these  are  repeated  at  the  same  time. 
That  is,  a  graphophone  record  will  repeat  the  sounds  uttered 
into  it,  and  in  the  order  uttered.     The  diafram  can  repeat  none. 

"  Did  the  old  Pine  suppose  that  a  graphophone  record  could  do 
anything  more  or  different  than  what  it  had  been  made  to  do,  the 
same  as  a  piano  or  any  other  musical  instrument  made  by  man/* 

"But  did  man  make  this  instrument?"  I  asked. 

"Surely  the  old  Pine  didn't  think  it  made  itself/'  she  answered. 
"  If  it  could  make  itself  perhaps  a  diafram  might  talk,  because 
anything  might  happen." 

"Sound  makes  it,  does  it  not  Ellen?"  I  asked. 

"With  the  assistance  of  man,  and  not  without,"  she  answered. 
'*For  sound  could  not  make  this  record  without  such  assistance, 
any  more  than  a  diafram  could  talk." 

"Then  Ellen  thinks  the  diafram  can't  talk?" 

"  She  knows  it  can't  talk,  any  more  than,  of  its  own  movement, 
it  could  fly,  or  build  a  house,  or  set  up  in  business  for  a  wholesale 
grocer.  Surely  the  old  Pine  didn't  suppose  the  diafram  could 
do  everything,  did  he ;  chop  wood,  for  instance,  and  get  out  ice  ?" 


WHISPERINGS    OF   AN    OLD    PINE 


547 


**No/*  I  said,  '*and  the  old  Pine  begins  to  think  that  the 
diafram  cannot  do  anything  except  play  the  part  of  a  diafiam. 

•*And  the  old  Pine  thinks  if  man  makes  the  graphophone 
record  there's  certainly  no  such  record  in  the  diafram." 

"  Indeed  there  is  not/'  she  answered » **  or  any  power  whatever 
to  repeat  any  sound  except  that  made  by  its  normal  vibration. 

''Ellen  will  now  return  to  the  experiments.  In  making  a 
graphophone  record  many  voices  or  sounds  can  be  recorded  at 
the  same  time.  And  this  means  that  each  particle  of  sound 
acts  independently.  Whether  vocal  or  instrumental  it  is 
created  independently,  enters  the  graphophone  independently 
and  emerges  from  it  independently. 

**But  beyond  this  it  means  that  the  universal  explanation  of 
the  manner  in  which  a  graphophone  record  is  made  is  another 
oi  those  things  which  the  scientists  know  that  arc  not  so. 

*'The  explanation  is  that  the  diafram,  itself  moved  by  the 
different  sounds,  causes  the  stylus,  which  is  fastened  to  it,  to 
make  the  indentures  in  the  paraflfin  and  wax.  If  it  was  possible 
for  the  diafram  to  vibrate  synchronously  with  every  vibrating 
body  it  might  perhaps  consecutively  make  the  record  of  every 
conceivable  sound.  But  we  know  it  cannot  so  vibrate*  And  in 
addition  to  this,  if  directly  or  indirectly  it  made  the  record  of 
a  graphophone.  it  would  have  often  to  vibrate  at  the  same  time 
with  a  hundred  more  or  less  instruments,  all  having  different 
vibrations.  Ellen  knows  that  those  who  believe  in  undulatory 
theories  can  swallow  this  and  a  good  deal  more,  but  no  sensible 
person  will  whose  attention  is  called  to  it. 

**  For  if  different  forces  affected  it  at  the  same  time,  its  move* 
mcnt  would  be  that  of  the  resultant  of  these  forces. 


^^^Sm 


548  ELLEN   OR   THE 

**It  follows,"  as  Ellen  has  said,  *'that  graphophone  records 
are  not  made  by  the  diafram  influenced  by  sound,  and  therefore 
must  be  made  by  the  sounds  themselves, — infinitesimal  particles 
of  electrical  matter. 

"In  experiments  with  different  diaframs  at  the  receiver  it 
was  found:  first,  that  with  a  thin  piece  of  sheet  iron  tinned  on 
the  outside  placed  directly  against  the  pole  of  the  magnet,  the 
conversation  was  plainly  audible,  not  quite  as  loud  but  other 
wise  very  like  that  heard  with  the  usual  diafram ;  second,  that 
with  a  pine  diafram  seven-eighths  of  an  inch  thick  placed  in  the 
usual  position  of  the  diafram,  sound  was  heard.  With  a  spruce 
diafram  one-third  of  an  inch  thick,  it  was  also  heard,  but  not 
quite  as  well.  A  twenty-penny  nail  held  with  the  head  against 
the  pole  of  the  magnet  and  the  other  end  between  the 
teeth,  gave  no  sound  when  held*  stationary,  but  when  the 
nail  was  moved  so  as  to  vary  its  contact  with  the  magnet, 
sounds  at  the  transmitter  were  plainly  heard.  This  was  one 
of  the  most  remarkable  experiments  that  Ellen  tried.  At 
times,  whilst  moving  the  nail,  the  words  would  be  very  distinct, 
and  then  would  be  entirely  lost.  One  or  two  experiments  in 
which  the  teeth  were  held  against  the  poles  of  the  magnet, 
gave  no  sound.  A  tuning  fork  E  (320  vibrations),  when 
sounded  at  the  transmitter,  was  distinctly  heard  at  the  receiver. 

"In  the  later  Bell  instrument  what  is  called  a  microphone 
was  used  ;  it  was  without  a  diafram,  and  gave  better  results 
than  did  the  old  transmitter  with  diafram.  In  this  microphone 
transmitter  there  is  no  magnet,  but  an  arrangement  of  carbon 
rods  forming  a  part  of  the  circuit  through  which  the  current  of 
electricity  passes. 


WHISPERINGS   OF  AN    OLD    PINE 

** There  is  this  distinction  in  the  supposed  results  obtained 
with  these  two  transmitters :  in  the  one  duplicate  vibrations  of 
a  diafram  are  supposed  to  be  produced  at  the  receiver;  in  the 
other  duplicate  vibrations  of  pieces  of  carbon* 

'*In  either  case  or  in  any  case  if  vibrations  were  reproduced 
at  the  receiver,  and  any  sounds  made  by  them,  they  must  first 
be  made  by  a  vibrating  body  at  the  transmitter;  that  is,  by  the 
body  whose  vibrations  are  supposed  to  be  reproduced.  I*'or 
nothing  can  be  more  certain  than  that  if  a  transmitting  diafram 
does  not  make  sound,  the  repeating  of  its  vibrations  by  another 
similar  diafram  will  not  make  sound.  And  so  if  the  vibration 
of  carbon  rods  or  anything  else  at  the  transmitter  does  not 
produce  sound,  the  reproduction  of  these  vibrations  at  the 
receiver  will  not  produce  sound.  Kllen  calls  attention  to  this 
necessary  sequence  to  show  the  absurdity  of  the  whole  concep- 
tion. 

**The  following  paper  upon  the  'Transmission  of  Sound  by 
Loose  Electrical  Contact  *  was  read  before  the  Royal  Society  of 
Edinburgh  by  James  Blythe,  M.  A.,  July  27,  1879: 


*  In  a  paper  published  in  the  Transactions  of  this  Society  for  Session 
1877— 7 tS,  I  described  an  experiment  which  showed  that  if  a  moder* 
ately  strong  current  stich  as  that  from  four  or  five  Bimsen  cells  be  led 
through  two  jam-pot^s  filled  with  fragments  of  carbon,  and  if  any  sound 
be  uttered  strongly  in  the  one  jam-pot  it  will  be  reproduced  distinctly, 
although  faintly*  in  the  other.  In  this  experiment  it  has  been  found 
that  the  fragments  of  carbon  may  be  replaced  by  any  kind  of  loose 
contact,  such  as  microphones,  or  a  handful  of  screw-nails  put  into  each 
jam-pot,  or  vibrating  springs  beating  against  metallic  stops,  or  nails  laid 


^SiggSSg^mmMm 


^^s^gi 


5 so  ELLEN   OR   THE 

across  each  other  in  log-hut  fashion,  and  that  in  each  case  an  effect 
similar  in  kind,  although  it  may  be  differing  greatly  in  degree,  is  pro- 
duced. Hence  it  may  be  almost  laid  down  as  a  general  experimental 
result,  that  if  an  electric  circuit  conveying  a  tolerably  strong  current 
contain  two  places  of  loose  contact,  A  and  B,  and  if  any  sound  be  pro- 
duced loud  enough  at  A  a  similar  sound  will  be  heard  proceeding 
from  B. 

*  To  all  appearance  this  phenomenon  can  only  arise  from  the  altered 
resistance  produced  at  A  by  the  sound  waves,  and  it  becomes  a  problem 
to  explain  how  this  altered  resistance  at  A  so  affects  the  materials  in 
contact  at  B  as  to  make  them  give  forth  waves  which  convey  a  similar 
sound  to  the  ear.  No  satisfactory  solution  of  this  problem  has  as  yet 
been  given,  and  it  was  in  hopes  of  getting  some  information  on  the  sub- 
ject that  I  made  the  following  experiments. 

*  Experiment  i  . — Four  strong  Bunsen  cells  were  included  in  the  cir- 
cuit, and  the  loose  contacts  A  and  B  placed  in  different  rooms,  so  that 
the  sound  uttered  g-t  A  could  not  be  directly  heard  at  B.  (Throughout 
we  shall  understand  by  A  the  sending,  and  B  the  receiving  station.)  In 
order  to  make  tlie  alteration  of  resistance  at  A  as  great  as  j)Ossible, 
an  actual  make-and-break  was  there  inserted.  A  toothed  wheel  driven 
round  against  a  s])ring  or  any  one  of  the  ordinary  loud-sounding  auto- 
matic kinds  would  do ;  but  what  served  my  purpose  best  in  this  experi- 
ment was  made  in  the  following  way  :  One  of  the  terminal  wires  of 
the  circuit  was  firmly  attached  to  a  tin  can  and  the  other  to  a  common 
round  file.  A  hole  was  then  pierced  through  the  bottom  of  the  can  at 
its  center,  and  the  file  driven  backwards  and  forwards  in  the  hole  as  if 
for  the  purpose  of  making  it  larger.  At  the  receiving  end  B  a  precisely 
similar  can  and  file  were  used,  and  the  file  allowed  to  rest  lightly  in  the 
hole.  Every  to-and-fro  rasp  of  the  file  at  A  was  distinctly  heard  at  B, 
even  when  the  can  was  at  some  distance  from  the  ear.  The  same 
sound  was  heard  when  the   file  at  A  was   laid  against  any  part  of  the 


WHISPERINGS   OF   AN    OLD    PIKE 


551 


can,  hot  most  loudly  when  it  happened  to  he  against  a  comer  or  other 
sharp  edge.  It  was  remarkable  also,  that  the  sound  was  heard  dis- 
tinclly  even  when  the  fate  did  not  touch  the  can  at  all,  but  was  merely 
laid  against  the  wire  attached  to  it,  so  as  to  complete  the  electric  cir- 
cuit without  including  the  can  in  it.  It  would  seem  from  this  that 
some  mechanical  tremor  is  set  up  at  the  loose  contact  of  the  file  with 
the  wire  which  is  transmitted  along  the  wiit  to  the  can.  As  a  variety 
of  this  experiment,  I  removed  the  can  from  the  wire,  and  substituted  in 
its  place  a  poker,  having  the  circuit  wire  firmly  attached  to  its  point. 
When  the  other  end  of  the  poker  w^as  put  to  the  ear,  and  the  file 
applied  to  the  jKjker  at  any  point,  the  sound  of  the  distant  rasping  was 
distinctly  heard.  The  same  was  the  case  when  a  long  brass  tube  was 
substituted  for  the  poker,  all  which  very  strongly  suggests  the  idea  of 
a  mechanical  tremor  transmitted  through  the  metal  from  the  point  of 
loose  contact. 

*  Experiment  2. — In  this  experiment  a  common  automatic  make-and- 
break,  consisting  of  a  vibrating  spring  worked  by  a  small  electro-magnet, 
was  introduced  into  the  circuit  at  A,  and  a  similar  spring,  only  without 
the  electro- magnet,  at  B.  At  B  the  sound  of  the  vibrations  of  the 
springs  at  A  was  so  distinctly  heartl,  as  to  at  once  suggest  the  idea  that 
the  spring  at  B  was  itself  vibrating.  However,  I  was  unable  to  detect 
any  such  vibration,  either  with  the  aid  of  a  microscope,  or  by  attaching 
a  small  polished  bead  to  the  spring  and  observing  in  it  the  reflection  of 
a  light.  Still  it  would  be  rash,  I  think,  to  assert  that  such  vibrations 
were  not  present,  and  it  is  possible  that,  by  more  refined  experimental 
means,  they  may  yet  be  manifest.  It  was  very  noticeable  in  this 
experiment  that  the  sound  at  B  got  less  and  less  loud  as  the  pressure 
on  the  vibrating  spring  was  increased,  until  it  ceased  altogether  when 
the  contact  was  made  perfectly  tight. 

*  Experiment  j, — ^The  sound  from  the  poker  in  Experiment  i  was  so 
like  that  produced  by  the  Trevelyan  rocker,  that  it  immediately  sug- 


552  ELLEN    OR   THE 

gested  the  employment  of  that  apparatus  as  the  loose  contact  at  B. 
For  this  purpose  the  current  was  led  through  the  lead  block,  the  rocker, 
and  a  brass  plate,  on  which  the  ball  at  the  end  of  the  rocker  rested. 
When  this  was  done,  and  the  make-and-break  set  agoing  at  A,  a  dis- 
tinct sound  was  heard  at  B,  suggesting  very  strongly  the  idea  that  the 
rocker  was  in  actual  vibratory  motion.  To  test  this  in  some  measure,  I 
heated  the  rocker  and  laid  it  on  the  lead  block,  when  two  sounds  were 
distinctly  heard,  one  due  to  the  make-and-break,  and  the  other  to  the 
heat  effect.  The  one  did  not  seem  in  the  least  to  interfere  with  the 
other.  Still  farther  to  test  the  idea  of  actual  vibration,  it  occurred  to 
me  to  try  if  one  rocker  could  not  be  made  to  act  as  the  make-and- 
break  to  agitate  the  other.  For  this  purpose  two  precisely  similar 
rockers  were  taken,  consisting  of  two  long  flat  files.  These  were  put 
edgewise  on  the  lead  blocks,  with  their  tails  resting  on  the  edges  of 
three- cornered  files.  The  current  was  sent  through  the  rockers  by 
means  of  these  lead  blocks  and  three  cornered  files.  One  of  these 
rockers  was  placed  at  A  along  with  the  automatic  make-and-break, 
while  the  other  was  placed  at  B.  An  arrangement  was  provided 
whereby  the  make-and-break  could  be  at  any  moment  shunted  out  of 
the  circuit  without  interrupting  the  current.  The  make-and-break  was 
then  started,  and  having  asccrLiincd  that  the  rockers  at  A  and  B  were 
both  sounding,  the  make-and-break  was  shunted  ofT  in  hopes  of  hearing 
A  and  B  still  continuing  to  sound  from  the  one  acting  as  make-and- 
break  to  the  other.  These  hopes,  however,  were  doomed  to  disap- 
pointment, as,  after  many  trials,  I  failed  to  hear  any  sound  after  the 
shunt  was  made. 

'ExPKRiMENr  4. — Being  still  not  satisfied  that  there  was  not  an 
actual  vibration  at  B  in  these  experiments,  I  determined  to  test  for  it 
in  another  way.  This  time  I  took  a  tin  can  and  riveted  into  the  center 
of  its  bottom  a  pointed  i)iece  of  steel  wire.  The  can  was  fixed  to  a 
wooden  board,  and  an  arrangement  made  whereby  another   pointed 


WHISPERINGS   OF   AN   OLD    PINE 


553 


piece  of  steel  wire  could  be  moved  up  opposite  to  the  former  piece, 
and  as  close  to  it  as  might  be  desired.  The  current  was  now  led 
through  the  can  and  these  pieces  of  steel,  and  the  make-and-break 
started  as  usual,  when  %'ery  minute  to-and-fro  vibrations  of  the  can 
were  observable,  especially  when  the  steel  |>oints  were  not  pressing  hard 
against  each  other  but  loosely  m  contact,  so  that  little  sparks  could  be 
seen  l>etween  them.  To  make  ijerfectly  certain  of  this  obser\'ation,  I 
hope  to  repeat  the  experiment  w*ith  still  greater  care, 

'  From  this  experiment,  notwithstanding  the  negative  evidence  of  the 
others,  it  seems  not  unlikely  that  when  a  strong  interrupted  current  is 
sent  through  a  circuit  where  there  is  a  loose  contact,  more  or  less  of  an 
actual  separation  of  the  surfaces  there  takes  place,  so  as  to  make  some- 
thing of  a  make-and-break  similar  to  the  original  make-and-break 
which  causes  the  interrupted  current.  Should  this  suggestion  be  estab- 
lished, it  will  follow  that  it  is  something  of  the  same  kind,  but  only 
differing  in  degree,  which  sends  the  undulatory  currents  which  transmit 
musical  sounds  and  articulate  speech  from  any  form  of  microphone 
transmitter  to  a  similar  form  of  microphone  receiver* 

*  As  to  the  cause  or  causes  of  this  separation  of  the  surface  at  the 
loose  contact  B,  or  of  whatever  agitation  else  it  may  be  which  gives 
forth  the  sound,  it  is  impossible  in  the  present  state  of  knowledge  to 
speak  with  confidence,  I  am  inclined^  however,  to  look  for  one  cause 
at  least  in  that  produced  by  the  current  at  the  loose  contact.  There 
the  resistance  and,  in  consequence,  the  rise  of  temperature  produced 
by  the  current  is  greatest,  and  an  effect  similar  to  the  Trevelyan  rocker 
will  be  set  up,  although  immensely  smaller  in  amount. 

'  Experiment  5. — This  experiment  has  reference  to  the  sounds  heard 
in  a  telephone  by  means  of  a  microphone  transmitter.  It  is  well 
known  that  these  can  be  heard  with  a  very  weak  battery  in  the  circuit, 
and  even  with  no  battery  at  all,  provided  the  points  of  the  microphone 
carbon  be  a  little  moist,     I  find  that  sounds  can  be  heard  in  the  tele- 


554  ELLEN  OR  THE 

phone  without  a  battery,  and  with  the  carbons  apparently  qmte  diy,  if 
we  rub  the  carbons  hard  together.  This  rubbing  is  distinctly  heard,  axid 
it  seems  that  it  must  arise  in  part  at  least  from  thermo-electric  currents 
produced  by  the  friction.  That  such  are  produced  is  readily  shown  by 
attaching  two  wires  to  the  terminals  of  a  Thomson's  reflecting  gahanom- 
eter,  and  to  the  ends  of  these  wires  any  two  conducting  substancesu 
When  these  substances  are  rubbed  against  each  other  the  movements  of 
the  spot  of  light  clearly  indicate  the  production  of  currents.  I  have 
roughly  tested  these  currents,  and  find  that  they  are  stronger  in  pro- 
portion as  the  metals  rubbed  are  wider  apart  on  the  thermo-electric 
scale ;  but  I  have  found  no  two  substances,  even  of  the  same  kind, 
which  do  not  give  them  slightly.  It  is  just  possible,  however,  that  sach 
currents  may  not  be  wholly  thermo-electric,  but  that  some  may  be  due* 
as  I  mentioned  in  a  recent  paper  to  the  society,  to  the  currents  sug- 
gested by  Sir  ^Uiam  Thomson  as  the  cause  of  friction.' 

"All  of  which  is  suggestive  that  sound  is  carried  by  the  elec- 
tric current 

"Sound  is  distributed  in  all  directions,  usually  only  by  the 
air.  But  if  solid  bodies  come  in  contact  with  the  sounding 
body  they  are  also  used  for  carrying  away  the  sounds. 

"To  illustrate,  strike  a  tuning  fork.  The  result  of  the  blow 
is  sound  and  vibration.  And  however  the  sound  is  caused 
it  spreads  into  the  air.  But  if  the  end  of  the  fork  is  placed 
upon  a  table  or  board,  the  sound  is  rapidly  conducted  from 
the  fork  to  the  board  and  thence  more  freely  passes  into 
the  air.  And  so  if  this  end  is  placed  against  any  solid  body, 
the  sound  is  conducted  more  or  less  quickly,  and  generally 
also  more  or  less  of  it  passes  to  the  air.  Ellen  finds  in 
'Silliman's  Journal/  Vol.  105,  page  125,  a  statement  of  Prof. 
A.  M.  Mayer,  as  follows: 


WHISPERINGS    OF   AN   OLD   PINE 


sss 


*In  the  SmithsoDian  Report  for  1S57  will  be  found  an  account  of 
very  interesting  and  valuable  experiments  by  Prof.  J.  Henry,  bearing  on 
"Acoustics  Applied  to  Public  Building^/'  In  these  investigatons  Prof, 
Henry  determined  the  relative  powers  of  various  substances  to  reflect, 
transmit,  and  absorb  sonorous  vibrations,  by  placing  on  the  bodies  the 
foot  of  a  tuning  fork,  and  comparing  the  duration  of  its  sound  when 
thus  placed  with  that  given  when  the  fork  was  suspended  in  the  free  air 
by  a  fine  cambric  thread.  Thus  suspended  the  fork  vibrated  during 
252  seconds.  Placed  on  a  large  thin  pine  board  its  vibrations  lasted 
about  10  seconds.  In  this  case  "the  shortness  of  duration  was  com- 
pensated for  by  the  greater  intensity  of  effect  produced."  The  fork 
having  been  placed  successively  on  a  marble  slab»  a  solid  brick  wall,  and 
on  a  wall  of  lath  and  plaster  its  vibrations  lasted  respectively  115,  88 
and  18  seconds,  FHaced  on  a  cube  of  india-rubber,  the  sound  emitted 
by  the  fork  was  scarcely  greater  than  when  it  was  suspended  from  the 
cambric  thread,  but  its  duration  was  only  40  seconds.  What  became 
of  the  impulses  lo^?t  by  the  tuning  fork?  They  were  neither  transmitted 
through  the  rubber  nor  given  off  to  the  air  in  form  of  sound  :  but  prob- 
ably produced  a  change  in  the  matter  of  the  rubber,  or  were  changed  to 
heat,  or  both/ 

•*  Ellen  has  seen  no  explanation  by  scientists  why  the 
vibrations  of  the  fork  should  be  thus  differently  affected. 
These  experiments  prove  that  this  is  not  because  of  the  resist- 
ance of  these  bodies.  For  contact  with  marble  or  brick,  if  this 
was  the  cause,  should  obstruct  the  fork  as  much  as,  or  more 
than,  contact  with  the  board.  And  therefore,  the  stoppage 
of  vibration  in  the  fork  is  not  principally  due  to  resistance 
of  the  body  in  contact.  It  must  then  be  due  to  the  conducting 
away  from  the  fork  of  the  force  or  forces  which  make  it  vibrate. 
Rut  it  is  sound   that  is  conducted  away,  and  hence  it  must  be 


556  ELLEN   OR  THE 

sound  that  causes  the  vibrations.  And  this,  that  sound  causes 
the  vibrations,  is  the  great  secret  of  sound,  explaining  all  its 
phenomena,  including  the  remarkable  one  of  sympathetic  vibra- 
tion never  before  explained.  For  it  is  evident  that  whatever 
would  cause  one  body  to  vibrate,  should  make  vibrate  all 
bodies  having  the  same  vibration. 

"  A  condition  similar  to  this  spoken  of  by  Mr.  Henry  is  con- 
nected with  the  telephone.  Thus  *  The  Dynamic  Theory,'  by 
James  B.  Alexander,  page  1026,  says: 

*  Dr.  Konig  showed  that  if  the  diafram  be  removed  and  a  tuning 
fork  set  in  vibration  near  the  end  of  the  magnet,  the  disturbance  of  the 
lines  of  force  took  place  the  same  as  with  the  vibratory  disc,  and  a  fork 
of  the  same  pitch  or  differing  by  octaves,  when  placed  near  the  magnet 
of  the  receiving  instrument,  whose  disc  was  also  removed,  took  up  the 
vibration  and  gave  its  fundamental  sound.' 

"  It  is  evident,  here,  that  the  particles  of  sound  arc  carried 
from  the  transmitting  to  the  reccivini^  instrument." 

''And  does  l^llcn  think  that  sound  can  make  vibration,  and 
vibration  sound  ?  " 

''  She  thinks  sound  can  make  vibration  and  vibration  help 
define  the  character  of  sound.  Thus  from  a  cloud  falls  rain, 
hail  or  snow,  but  the  character  of  the  drops,  or  of  the  pretty 
snowflakcs  wliich  have  a  million  different  forms  and  all  of  them 
as  perfect,  beautiful,  and  wonderful  as  that  of  a  tree,  or  of  a 
flower,  is  determined  by  temperature,  in  part,  if  not  entirely. 
And  they 

'  Fall  as  the  leaves  fall  when  Summer  is  ended.' 

*'  And  here  where  the  old  Pine  and  Ellen  are,  they  are  every 


WHISPERINGS   OF   AN   OLD    PINE 


557 


bit  as  plenty  as  sounds,  and,  as  Ellen  thinks,  just  as  wonderful 
in  their  conformations.  And  thus  great  clouds  of  sound  are 
formed  within  bodies  by  shock,  and  its  character,  in  part  at 
least,  is  defined  by  vibration.  Thus  sound,  if  properly  con- 
fined,  may  vibrate  in  air.  And  so  the  material  of  which  any 
particular  sound  is  made  is  always  the  same,  combined  or  set 
into  action  by  shock. 

'*  Similarly,  as  KUen  has  quoted,  Mr.  Newton  suggested  that 
the  action  of  electric  bodies  was  due  to  an  elastic  fluid,  and 
the  emission  of  it  to  the  vibratory  motion  of  the  parts  of  the 
excited  bodies.* 

**  This  great  principle,  that  vibration  is  made  by  sound,  is 
illustrated  again  in  the  operations  of  resonance.  Thus  take  a 
tumbler,  (a  larger  vessel  perhaps  would  do  better),  and  partly 
cover  its  opening  so  that  when  a  vibrating  fork  is  held  ov^er 
this  opening  the  loudest  resonance  is  obtained.  Changing  now 
the  capacity  of  air  in  the  vessel  by  pouring  in  water,  resonance 
may  still  be  got,  and  by  the  same  fork,  but  the  opening  must 
be  lessened ;  and  by  repeated  experiments  it  becomes  evident 
that  for  best  results  the  opening  must  be  proportional  to  the 
space  in  which  the  air  vibrates ;  and  this  means  that  a  fixed 
amount  of  sound  is  necessary  for  the  purposes  of  resonance — 
always  a  fixed  amount,  and  that  amount  proportional  to  the 
space  where  the  resonance  takes  place, 

*  See  page    192. 


558  ELLEN    OR   THE 


XXXVIII. 


^^T^HE  following   experiments,  reported  by   Mr.    T)nidall, 
•1        illustrate    further  the  remarkable  action  of    sounding 
boards : 

*  The  transmission  of  musical  sounds  through  solid  bodies  is  also 
capable  of  easy  and  agreeable  illustration.  Before  you  is  a  wooden  rod, 
thirty  feet  long,  passing  from  the  table  through  a  window  in  the  ceih'ng, 
into  the  open  air  above.  The  lower  end  of  the  rod  rests  upon  a 
wooden  tray,  to  which  the  musical  vibrations  of  a  body  applied  to  the 
upper  end  of  the  rod  are  to  be  transferred.  An  assistant  is  above,  with 
a  tuning  fork  in  his  hand.  He  strikes  the  fork  against  a  pad ;  it 
vibrates,  but  you  hear  nothing.  He  now  applies  the  stem  of  the  fork 
to  the  end  of  the  rod,  and  instantly  the  wooden  tray  upon  the  table  is 
rendered  musical.  The  pitch  of  the  sound,  moreover,  is  exactly  that 
of  the  tuning  fork;  the  wood  has  been  passive  as  regards  pitch. 
With  anolher  fork  a  note  of  another  pitch  is  obtained.  Thus  fifty  forks 
might  be  employed  instead  of  two,  and  ^^oo  feet  of  wood  instead  of 
thirty  ;  the  rod  would  transmit  the  precise  vibrations  imparted  to  it, 
and  no  other. 

^  We  are  now  prepared  to  ap|)reciate  an  extremely  beautiful  experi- 
ment, for  which  we  are  indebted  to  Sir  Charles  Wheatstone.  In  a 
room  underneath  this,  and  separated  from  it  by  two  floors,  is  a  piano. 
Through  the  two  floors  passes  a  tin  tube  two  and  one-half  inches  in 
diameter,  and  along  the  axis  of  this  tube  jkisscs  a  rod  of  deal,  the  end 
of  which  emerges  from  the  floor  in  front  of  the  lecture  table.     The  rod 


WHISPERINGS   OF  AN   OLD    PINE 


S6l 


is  clasped  by  India  rubber  bands,  which  entirely  close  the  tin  tube. 
The  lower  end  of  the  rod  rests  upon  the  sound  board  of  the  piano,  its 
upper  end  being  exposed  before  you.  An  artist  is  at  this  moment 
engaged  at  the  instrument,  but  you  hear  no  sound.  When,  however,  a 
violin  is  placed  upon  the  end  of  the  rod,  the  instrument  becomes 
instantly  musical,  not,  however,  with  the  vibrations  of  its  own  stnngs, 
but  with  those  of  the  piano.  When  the  violin  is  removed,  the  sound 
ceasec  ;  putting  in  its  place  a  giu'tar.  the  music  revives.  For  the  violin 
and  guitar  we  may  substitute  a  plain  wooden  tray,  which  is  also 
rendered  musical.  Here,  finally,  is  a  harp,  against  the  sound  board  of 
which  the  end  of  the  deal  rod  is  caused  to  press ;  every  note  of  the 
piano  is  reproduced  before  you.  On  lifting  the  harp  so  as  to  break  the 
connection  with  the  piano,  the  sound  vanishes ;  but  the  moment  the 
sound  board  is  caused  to  press  upon  the  rod  the  music  is  restored. 
The  sound  of  the  piano  so  far  resembles  that  of  the  harp  that  it  is  hard 
to  resist  the  impression  that  the  music  you  hear  is  that  of  the  latter 
instrument.  An  uneducated  ear  might  well  believe  that  witchcraft  or 
"spiritualism"  is  concerned  in  the  production  of  this  music* 

'*  The  violin,  or  guitar,  or  tray  performs  precisely  the  same 
office  in  these  experiments  that  a  sounding  board  docs  upon 
which  the  bottom  of  a  vibrating  tuning  fork  rests.  That  is,  the 
sounds  flow  from  the  piano,  each  different  sound  by  a  separate 
stream,  into  these  instruments  and  thence  pass  into  the  air. 

'*  Ellen  illustrated  this  as  follows:  She  placed  the  stem  of  a 
vibrating  tuning  fork  upon  a  smooth  spruce  board  of  moderate 
size  She  then  took  a  small  spruce  rod  about  one  foot  in  length, 
and  having  a  cross  section  about  one-half  by  one-fourth  inch. 
She  held  one  end  between  her  teethe  and  let  the  other  approach 
very  near  but  not  touch  the  sounding  board.  No  sound  was 
heard  through  the  stick;  but  when  one  end  of  the  stick  rested 


S62  ELLEN    OR  THE 

upon  the  board,  the  sound  was  immediately  conducted  by  the 
stick  and  teeth  to  the  auditory  nerve.     Ellen  now  placed  two 
and  then  three  vibrating  forks  upon  the  board,  plainly  hearing 
and  distinguishing  the  three  by  the  stick  and  teeth  when  the 
stick  rested  upon  the  board.     Then  she  put  a  small  nail  in  one 
end  of  the  stick,  filed  it  to  a  point,  and  placed  the  point  upon 
the  board.     The  sound  of  the  three  forks  was  plainly  heard 
and  distinguished  as  before.     She  then  fastened  a  pin,  smaller 
and  sharper  than  the  nail,  in  another  similar  stick,  and  placed 
the   point  lightly  upon   the    board.     The  sound  of   the  three 
forks  was  again  plainly  distinguishable  but  less  loud,  evidently 
because  of  the  smaller  dimensions  of  the  pin    point  and    pin. 
She  then  tried  a  third  stick,  with  a  fine  cambric  needle  smaller 
and  sharper  than  the  pin,  and   placed   the  point  of  the  needle 
lightly  upon  the  board.     All    the  sounds  were   again   plainly 
heard,  but  still  less  loud,  and  it  was  evident,  first,  that  no  sound 
passed  through  the  stick  unless  it  or  the  needle  came  in  con- 
tact with    the   board;    second,   that  although    a    small    needle 
was  sufficient   to   carry  all  the   sounds  from  the  board   to   the 
stick,  the    amount  of  sound   thus   carried   was   proportional    to 
the    size   (^f    such    needle.      In    all    cases    it    made    no    appre- 
ciable  difference    in   the   sound   upon   what   part   of  the  board 
the   needle   was   placed.     And    this   shows   that  sounds  spread 
in  all  directions  upon  a  board,  as  they  do  in  the  air. 

*'Nor  do  they  in  the  slightest  degree  mix  any  more 
than  the\'  do  in  air.  And  this  is  one  of  the  most  remarkable 
things  in  connection  with  sound,  that  sound  is  a  fluid,  every 
sojnd  at  times  moving  in  a  channel,  antl  they  will  all  tumble 
along    close    together,     spreading    like    water    over    a     large 


WHISPERINGS   OF   AN   OLD    PINE  563 

surface,  but  they  never  mix,  whether  on  the  surface  or  in  the 
air. 

'*They  mix  no  more  than  the  spheres  of  heaven  mix,  or 
animals,  or  plants,  or  grains  of  sand,  or  the  lovely  shells  which 
gather  within  them  the  sounds  of  ocean.  Nothing  mixes  ever 
in  this  vast  universe  that  wasn't  made  to  mix,  but  lives  out  its 
individual  existence,  ever  ready  to  perform  the  part  for  which 
it  was  created. 


564  ELLEN    OR   THE 


XXXIX. 

^^IN  order  to  still  better  perceive  what  happens  in  sound, 
^  let  us  consider  the  laws  that  have  to  do  with  the  manu* 
facture  and  distribution  of  things.  And  in  the  first  place  the  old 
Pine  must  remember  that  all  things  are  made  by  machinery. 
For  it  would  be  impossible  for  things  to  come  into  existence 
without  a  cause.  First,  then,  always  is  the  machinery,  or  cause, 
by  which  things  are  made,  and  always  in  the  material  universe 
this  machinery  is  material.  For  all  material  things  are  com- 
posed of  this  wonderful  thing,  matter,  whose  possibilities  for 
results  would  seem  to  be  limitless.  For  from  it  is  constructed 
equally  the  large  and  the  small,  the  beautiful  and  the  plain,  the 
sweet  and  the  sour,  the  pleasant  and  the  disagreeable,  the  health- 
ful and  the  poisonous,  the  fragrant  and  the  odorless,  the  bois- 
terous and  the  still. 

"Here  is  our  first  knowledge;  and  the  second  is  the  manner 
of  production,  that  all  these  things  are  made  from  this  matter 
by  one  and  only  one  method  or  law, — that  of  its  combination 
in  different  elements  and  different  proportions. 

"Then  comes  the  places  of  manufacture  and  the  laws  of  dis- 
tribution. Things  are  variously  distributed.  Some  things,  as 
the  air  or  earth  or  water,  are  distributed  very  widely,  and 
others,  as  different  families  or  species  of  animals  and  plants,  in 
more  limited  spaces.  And  so  a  particular  rain-storm  or  snow- 
storm is  limited  in  its  extent 


■ 

THE  HEW  YORK 
PUBLIC  LIBRARY 

^H 

, 

WHISPERINGS   OF  AN  OLD    PINE 


567 


*'Not  only,  too,  are  things  made  m  different  ways,  but  the 
shops  where  they  are  made  are  differently  placed.  Some  are 
fixed  and  cannot  be  moved.  There  are  many  things,  some  of 
which  are  widely  spread,  which  are  made  at  stationary  mills. 
Seeds  arc  thus  made,  and  they  are  scattered  in  many  different 
w*ays,  though  always  in  some  form  carried,  for  they  cannot 
walk  or  run  as  Ellen  can.  But  there  may  be  a  great  many 
different  factories  for  their  manufacture,  placed  at  a  great  many 
different  points.  Odors,  too,  are  so  made,  and  are  carried  or 
move  for  a  certain  distance. 

**  Other  things  are  made  by  moving  mills,  as  rain  or  snow  or 
hail.  And  these  things  themselves,  after  being  produced,  do 
not  move  as  much,  for  it  isn't  necessary.  The  snowflakes  sail 
about  some,  but  the  rain  drops  come  pretty  straight  down, 
tlie  clouds  move  and  distribute  the  rain  and  the  snow  where 
they  are  needed,  so  that  they  may  accomplish  the  purposes 
for  which  they  are  made.  For  Ellen  has  told  the  old  Pine 
before  that  there  is  nothing  made  except  for  a  purpose.  The 
old  Pine  will  see  that  either  of  these  systems  of  distribution 
may  be  used. 

**In  certain  cases  the  mills  of  production  are  close  together 
and  in  otliers  quite  a  distance  apart.  Where  they  are  close 
together  the  things  produced  naturally  do  not  extend  or  spread 
far,  for  it  isn't  necessary.  These  are  the  methods  for  manu- 
facture and  distribution,  and  the  mills  of  sound  sometimes  move, 
and  at  others  arc  stationary." 

**But  how  would  Ellen  account  for  the  echoes?'*  I 
asked. 

**By  reflection,**  she  said. 


568  ELLEN  OR  THE 

*'  And  would  there  not  be  the  same  objection  that  Ellen  found 
with  the  reflection  of  waves?  " 

"Not  at  all,"  she  replied.  "The  difficulty  then  was,  and  it 
was  fatal  to  the  theory,  that  waves  constituted  the  correlative 
of  sound.  And  they  could  be  reflected  only  in  reverse  or 
broken  form,  when  the  correlative  would  be  destroyed*  and 
with  it  the  sound.  3ut  in  this  theory  the  reflection  would  be 
of  a  solid  substance,  subject  to  the  laws  of  reflection." 

"And  how  does  Ellen  explain  the  speed?" 

"That  it  is  inherent.  For  a  Substance  maybe  imagined 
which  carries  its  own  energy.  Or,  as  Ellen  thinks,  motion, 
being  an  attribute  of  matter,  varies  as  other  attributes.  Thus, 
some  bodies  are  far  more  elaistic  than  others,  some  harder, 
some  more  dense,  and  others  more  porous.  And  so  this  qual- 
ity of  motion  varies,  but  enters  into  the  composition  of  all  mat- 
ter, as  illustrated  by  the  flnal  disintegration  of  matter.  But 
in  all  of  these  qualities  the  difference  is  that  between  extremes, 
and  may  therefore  be  very  great.  Thus  in  elasticity  it  is  from 
the  extremely  elastic  to  the  inelastic.  Hardness  varies  from 
the  very  hard  to  the  soft.  And  so,  in  the  quality  of  motion, 
conditions  exist  so  marked  in  their  action  that  matter  would 
seem  to  be  rather  a  property  of  energy,  than  energy  of  matter. 
This  is  not  at  all  the  condition  of  sound.  And  yet,  as  Ellen 
thinks,  its  speed  is  one  of  its  properties." 

"  It  is  thus  in  the  kinetic  theory  of  gases  that  particles  are 
supposed  to  move,  is  it  not,  lilllen?"  I  asked. 

**  Ellen  does  not  care  to  be  responsible  for  the  kinetic  theory 
of  gases,"  she  replied,  "and  so  must  refer  the  old  Pine  to  the 
scientists  for  an  answer  to  this  question  or  others  regarding  it. 


WHISPERINGS   OF   AN   OLD    TINE 


569 


**An  animal  may  b€  supposed  to  control  its  speed,  A 
locomotive  may  maintain  practically  the  same  rate  of  speed  for 
some  time,  though  finally  left  to  itself,  the  force  driving  it 
being  expended,  it  will  gradually  stop.  Motion,  constant,  rapid, 
and  long  continued,  would  appear  to  be  the  characteristic  of 
radiant  matter,  and  sound  belongs  to  this  class  of  matter* 
Light,  electricity,  heat,  are  other  members  of  the  class,  all 
notably  endowed  with  a  power  of  speed  that,  certainly  for  a 
time,  is  both  constant  and  remarkable,  And  so  sound  moves 
with  a  speed  of  uniform  character,  but  at  different  rates,  accord- 
ing to  the  path  over  which  it  moves. 

"Sound,  then»  like  everything  else,  is  an  'entity,  made  out  of 
matter  by  the  universal  law  of  its  combination  in  certain  pro- 
portions. 

"This  entity  is  furnished  in  great  quantities  and  great 
variety,  In  this  respect  it  is  similar  to  other  things  furnished  by 
naturet  as  the  different  varieties  of  trees  and  plants,  or  the  differ- 
ent varieties  of  animals  or  insects,  or  those  of  stones  or  shells. 

'* These  varieties  of  sound,  as  well  as  of  trees,  or  plants,  or 
animals,  or  insects,  or  stones,  or  shells,  arc  the  material  forms 
of  sensations;  and,  as  such,  include  in  their  forms  every 
possible  change  or  variety  which  the  soul  is  capable  of  receiv- 
ing from  the  phenomena  of  sound.  And  as  always,  if  the 
material  form  of  sensation,  as  of  a  tree,  or  plant,  or  shell,  or 
flower,  is  injured  in  the  slightest  degree,  the  sensation  pro- 
duced by  it  will  be  similarly  injured ;  so  if  the  material  form  of 
sound  is  injured,  the  sensation  from  it  will  be  similarly  incom- 
plete. And  thus  it  is  that  the  soul  distinguishes  the  character 
of  speech,  its  intonations  and  inflections.     And  thus,  too,  it  is 


570  ELLEN   OR  THE 

evident  that  the  matter  from  which  sound  is  formed,  although 
in  its  nature  short-lived,  has,  while  it  lasts,  a  wonderful  tenacity 
of  form." 

*'But,  Ellen,"  I  asked,  *'do  not  the  different  sensations  of 
sound,  flavor,  odor,  and  touch,  come  from  the  quality  rather 
than  the  form  of  the  material  used?" 

'That  is  very  possible,"  she  replied,  ''perhaps,  indeed,  most 
probable.  Certainly  it  is  true  of  all  things  which  we  see. 
That  is,  the  sensations  of  sight  come  from  both  form  and  sub- 
stance. This,  too,  is  true  of  taste,  and  perhaps  Ellen  would 
say  unquestionably  also  of  hearing. 

"The  peach  and  the  meat  of  the  walnut  are  composed  of 
very  different  combinations  of  matter;  hence  their  different 
taste.  Whether  any  particular  form  enters  into  this  result  or 
not,  Ellen  docs  not  know.  She  cannot  see  why  it  necessarily 
should,  nor  does  she  know  that  it  certainly  does  not.  But  she 
docs  know  that  form  of  some  kind  it  must  have,  as  well  as  sub- 
stance, and  she  is  willing  to  believe  that  always  the  form,  as 
well  as  the  substance,  chosen  in  nature,  is  tlic  best  possible  for 
the  result  sought. 

"Sound  enters  or  is  poured  into  the  ears  like  grain  into  a 
hopper,  and  thus  carried  to  the  seat  of  the  soul.  In  what 
manner  it  affects  the  soul  Ellen  does  not  know,  any  more  than 
she  does  how  the  other  sensations, — all  of  which  are  brought 
in  some  similar  way  before  its  presence, — may  affect  it ;  ex- 
cepting that  it  would  appear  to  be  done  in  each  case  by  the 
great  law  of  contact,  apparently  the  universal  law  of  nature  in 
the  creation  of  its  phenomena. 

"Nor,  in  the   nature  of  creation,  does  it  seem  to  Ellen  at  all 


WHISPERINGS   OF   AN    OLD    PINE 


57i 


extraordinary,  that  there  should  be  a  thinking  substance  suscep- 
tible to  every  possible  change  in  matter  which  comes  in  con- 
tact with  it. 

**  For  the  intimate  relation  of  every  particle  of  matter  to  every 
other  particle  is  very  evident.  That  it  should  have  the  same 
relation  to  another  substance,  and  that  a  thinking  substance,  is 
no  more  remarkable,  as  far  as  Ellen  can  see,  than  that  it  should 
be  thus  intimately  related  with  itself.  And  this,  especially 
when  she  believes  that  the  thinking  substance  was  created  by, 
or  derived  from,  a  higher  intelligence,  and  that  matter  was 
created  for  the  use  of  this  thinking  substance,  and  other  intel- 
ligences. 

** There  is  such  a  thinking  substance^  and  when  by  sensation 
the  different  conditions  of  matter  are  brought  in  contact  with 
it,  they  affect  it  in  these  different  ways,  and,  so  far  as  Ellen 
knows,  it  is  not  affected  in  any  other  way, 

'*Thu5  all  the  sensibilities  of  souls  which  dwell  in  material 
conditions,  whether  of  feeling  or  intelligence,  would  appear  to 
be  produced.  If  the  old  Pine  can  imagine  any  better  method 
for  the  instruction  of  individual  existences,  Ellen  will  be  very 
much  pleased  to  hear  it. 

'*  It  seems  to  Ellen  that  the  method  which  exists  is  exceed- 
ingly comprehensive,  producing,  in  infinite  variety,  both  feeling 
and  thought, 

•'And  therefore  again  would  it  appear  that  it  is  as  well 
devised  for  the  purposes  of  creation  in  material  conditions  as  it 
can  be/' 

'•But  Ellen  thinks,"  I  said,  "that  beyond  these  material 
conditions  there  is  a   more  glorious  state   of   existence;    and 


572  ELLEN   OR  THE 

beyond  the  intelligences  with  which  we  are  acquainted,  there 
are  other  intelligences  with  far  greater  powers  both  of  knowl- 
edge and  feeling?" 

'*  She  has  no  doubt  of  it,"  she  replied. 

"  Culminating,"  I  continued,  **  in  the  highest  Intelligence,  by 
Whom  all  others  have  been  created  ?  " 

"It  must  culminate,"  she  replied  "in  such  an  Intelligence. 
Without  such  this  universe  could  never  have  been ;  without  such 
it  could  not  continue. 

'From  Eternity  to  Eternity  Thou  art  God.' 


WHISPERINGS   OF   AN    OLD    PINE 


57S 


XL. 


^^f    ITTEL'S  Living   Age,  1878,  pages   761,    762,   763,   m 
^     an  article  on  The  Telephone,  taken  from  the  Westmin- 
ster Review,  says ; 

'Of  all  modern  inventions  coivnected  with  the  transmission  of  tele- 
graphic signals,  the  telephone,  devised  by  Mr*  Alexander  Graham 
Bell,  has  excited  the  most  widespread  interest  and  wonder.  Wherever 
Mr.  Bell  has  appeared  before  the  public  to  give  an  account  of  his 
invention  and  the  researches  w^hich  have  led  up  to  it,  crowds  have 
assembled  to  hear  him.  Nor  is  this  astonishing;  for  the  telephone 
professes  not  only  to  convey  intelligible  signals  to  great  distances 
without  the  use  of  a  battery,  but  to  transmit  in  facsimile  the  tones 
of  the  human  voice,  so  that  a  voice  shall  be  as  certainly  recognized 
when  heard  over  a  distance  of  a  few  hundreds  of  miles  as  if  its  owner 
were  speaking  in  the  room  by  our  side,  .*\nd  the  telephone  does 
not  fall  short  of  its  profession.  Scientific  men  have  had  their  wonder 
and  curiosity  aroused  even  more  than  the  unscientific  public,  since  a 
scientific  man  appreciates  the  enormous  difficulties  to  be  overcome  be- 
fore such  an  instrument  can  be  realized.  Had  any  hardy  speculator  a 
few  years  ago  proposed  a  telephone  which  should  act  on  the  principle, 
and  be  constructed  in  the  form,  of  Mr.  BelPs  instnmient,  he  would 
probv^bly  have  been  considered  a  lunatic.  The  effects  are  so  marvel- 
ous J  the  exciting  causes  at  first  sight  so  entirely  inadequate  to  produce 
them.* 

•*  These  last  remarks  arc  utter  nonsense,  except  so  far  as  they 


576  ELLEN   OR   THE 

might  be  aimed  against  erroneous  theories  of  sound,  for  nothing 
could  be  simpler  than  that  sound,  which  is  an  entity  consisting 
of  infinitesimal  particles  of  electrical  matter,  thrown  off  by  the 
sounding  body,  when  placed  where  it  must  enter  a  wire,  should 
be  carried  instantaneously  through  the  wire  to  where  arrange- 
ment was  made  for  it  again  entering  the  air,  and  that 
having  done  this  it  should  appear  precisely  as  it  did  before  it 
entered  the  wire,  except  somewhat  weakened  by  the  trip,  and 
perform  the  same  phenomena.  And  this  is  exactly  what  takes 
place  in  the  telephone.  A  person's  speech  is  transferred,  and 
being  the  same  speech,  that  is,  the  same  particles  of  matter, 
appears  the  same  in  the  atmosphere  to  which  it  is  carried,  as  it 
did  in  that  from  which  it  is  brought,  and  is  as  readily  recognized 
in  one  place  as  in  the  other  as  the  voice  of  the  speaker.  In- 
deed, it  would  be  impossible  that  all  of  this  should  not  be  true. 
'*  As  we  have  seen  under  parallel  circumstances  speech  can- 
not be  kept  from  entering  a  wire,  any  more  than  it  can  from 
cntcrini^  the  air.  The  cause  of  wonder  and  the  only  cause  is  the 
ridiculous  tlicory  of  sound  that  tlie  scientists  have  fastened 
upon  themselves. 

M.ct  us  enriuire  for  a  moment  what  is  the  nature  of  the  apparatus 
which  we  have  been  using  for  the  last  thirty  or  forty  years  for  the  trans- 
mission of  telegraphic  signals.  The  instruments  chiefly  employed  have 
been  the  single-needle  telegraph,  and  the  Morse  instrument.  In  the 
former  a  (^oil  of  wire  surrounds  a  magnetized  needle,  which  is  susi)enderl 
in  a  vertical  position.  When  an  elec  trical  current  j)asses  through  the 
coil,  the  needle  is  deflected,  to  right  or  left,  according  to  the  direction 
of  the  current.  The  sender  l)y  means  of  a  handle  can  pass  either  posi- 
tive or  negative  (nirrents  into  the  circuit.     Tlie  right  and  left  deflections 


WHISPERINGS   OF  AN   OLD    PINE 


577 


of  the  needle  are  combined  in  various  ways  to  form  the  letters  of  the 
alphabet,  and  the  letters  form  words.  Thus  at  the  sending  station  a 
message  is  broken  up  into  little  bits,  each  bit  or  part  of  a  bit  trans- 
mitted separately,  and  the  process  of  building  these  up  again  performed 
at  the  receiving  station.  Some  of  the  letters  of  the  alphabet  are  indi- 
cated by  a  single  movement  of  the  neetlle,  that  is  by  a  single  current ; 
for  others,  as  many  as  four  are  required.  In  the  Morse  instrument  only 
one  current  is  utilised,  which  may  be  either  positive  or  negative,  and 
the  requisite  variety  is  obtained  by  allowing  the  current  to  pass  through 
the  circuit  for  a  longer  or  shorter  inlen^al  The  esi»ential  pari  of  the 
instrument  consists  of  an  electro- magnet  with  an  iron  armature  attached 
to  one  end  of  a  lever.  At  the  end  of  the  lever  is  a  pointer  or  pencil, 
and  a  paper  ribbon  moves  at  a  constant  rate  in  front  of  the  end  of  the 
pointer.  When  the  coils  of  the  electro- magnet  are  traversed  by  a  cur- 
rent, the  iron  armature  is  attracted,  and  the  pointer  comes  in  contact 
with  the  paper  ribl)on,  on  which  it  makes  a  mark,  long  or  short,  accord- 
ing  to  the  duration  of  the  current.  Thus  are  produced  the  dots  and 
dashes.  These  are  combined  in  a  similar  way  to  the  right  and  left 
movement  of  the  needle  in  the  needle  instrument.  In  some  of  the 
most  refined  instruments  letters  are  indicated  and  even  printed  directly 
at  the  receiving  station.  This  is  of  course  a  great  simplification  :  but 
with  such  arrangement  we  cannot  have  more  than  this*  The  page  of 
print  represents  the  limit  of  what  such  instruments  and  methods  can  do 
for  us.  It  is  true  that  a  skilled  operator  with  the  Morse  instniment  can 
interpret  the  signals  as  they  arrive  without  looking  at  the  marks  on  the 
paper,  simply  by  using  his  ears.  Every  time  the  circuit  is  made  or 
broken  a  click  is  heard*  and  long  practice  has  taught  him  to  rely  on 
the  evidence  of  his  ears  with  as  much  confidence  as  one  less  accus- 
tomed to  the  work  would  Irust  his  eyes.  Nevertheless  he  hears  only  a 
succession  of  clicks  which  must  be  interpreted  before  they  become 
intelligible  to  any  one  but  himself. 


^ 


3 


ELLEN    OR  THE 

I  these  forms  of  apparatus,  H  will  be  observed^  the  currents  are 

:iit ;  each  current,  circulating  throuj^h  the  coil,  is  foUowed  by 

Tal  of  rest-    They  begin  and  end  abruptly,  and  all  perform  the 

kind  of  work  ;  that  is,  they  deflect  a  needle,  or  produce  marks  on 

jce  of  paper.' 

'*Thus  far  thi?  scientist,  for  we  recognize  him  as  such,  and  no 

bt  he  stands  high  in  his  profession,  has  confined  himself  to 

s,  but  now,  the  necessity  having  ariseui  he  cuts  loose  from 

I     lese  and  shows  himself  an  expert  in  teaching  things  which  arc 

»t  so;  thus  continuhig; 

H  'Telephonic  currents,  on  the  other  hand,  rise  and  fall,  ebb  and  flow, 
tge  in  intenjjity  within  comparatively  wide  limits^  but  preserve  their 
itmuity  so  long  as  continuous  sounds  are  being  uttered  in  the  neigh- 
borhood of  the  telephone.  They  are  called  undulatory  currents,  to 
distinguish  them  from  the  intermittent  currents  of  the  ordinary  tele- 
graphic  apparatus,  and  their  peculiar  character  is  an  essential  feature 
of  the  telephone.* ''  j^^^^^^ 


"Then  Ellen  doesn't  believe  in  these  telephonic  currents?" 
"It's  pure  romancing,"  she  replied,  ** but  Ellen  doesn't  care 
to  discuss  it  further  here  than  to  point  out  the  folly  of  it.  It 
is  an  attempt  to  explain  what  causes  a  diafram,  or  any  other 
inanimate  thing  not  made  to  do  it  to  repeat  the  sounds  of 
other  bodies.  But  the  assumed  fact  of  its  repeating  sound 
being  impossible,  the  attempted  explanations  of  its  movements 
are  without  significance. 

"Under   the   heading  *  Theory  of  the   Telephone,'   Modem 
Applications  of  Electricity  says : 

'The  theory  of  the  transmitter  presents  no  difficulty,  and  has  been 


WHISPERINGS   OF 


579 


explained  several  times  in  Ihe  preceding  pages;  we  need  not  refer  to 
it  again.  The  discussions  which  arose  on  the  theory  of  the  telephone 
especially  referred  to  the  receiving  apparatus.  How  does  a  receiver — 
Bell's  telephone,  for  instance — transform  an  undulatory  current  into  an 
articulate  sound?  What  are  the  physical  phenomena  which  bring 
about  this  transformation? 

*We  have  admitted  as  a  provisional  theory,  convenient  lor  the  explana- 
tion of  the  apparatus,  that  the  undulatory  current  produced  in  the 
receiver  a  successivfe  strengthening  and  weaking  of  the  magnetic  force 
of  the  magnet^  which  manifested  itself  by  greater  or  lesser  attractions 
of  the  plate,  which  then  vibrated  s>ti chronically  with  the  undulations 
of  the  current  and  the  magnetic  po\i^er  of  the  magnetized  bar. 

*This  plausible  explanation  is  sometimes  verified  in  battery  tele- 
phones with  the  Carlson  transmitters,  but  it  is  inadmissible  with  BelPs 
telephone.  Count  du  Mancel,  who  from  the  outset  rejected  this 
exjilanation,  has  seen  his  ideas  partly  confirmed  by  the  numerous  experi- 
ments which  have  followed  Bell's  invention  ;  nowadays  his  theory  is 
almost  universally  adopted,  an<l  we  are  going  to  put  it  before  our 
readers  in  a  few  words. 

'Numerous  experiments  and  measurements  made  by  Warren  de  la 
Rue,  Brough,  Galileo,  Ferrari,  and  others,  have  proved  that  the  intensity 
of  the  currents  developed  by  Bellas  telephone  does  not  exceed  that  of  a 
Dani ell's  element  after  having  traversed  io,ooo»ooo  kilometres  of  tele- 
graph wire^ — that  is  to  say,  100,000,000  ohms — which  represents  a 
telegraphic  circuit  of  a  length  equal  to  250  times  the  circumference  of 
the  earth. 

*This  makes  it  very  diflficull  to  believe  that  the  difference  of  magnet- 
ism produced  in  the  magnetized  bar  by  currents  of  such  feeble  intensity 
could  manifest  themselves  by  variations  in  the  attraction  of  the  vibrating 
plate  placed  at  a  distance. 

*  Br^guet's  experiments,  nude  with  plates  of  fifteen  centimetres  thick- 


58o  ELLEN   OR   THE 

ness,  and  Ader's,  who  employed  no  plate  at  all,  put   an  explanation 
based  on  magnetic  attractions  alone  out  of  the  question. 

*  Page's  experiments  have  shown  that  an  iron  rod  placed  in  a  bobbin 
vibrates  under  the  influence  of  internipted  currents.  Reis'  musical 
telephone  is,  as  we  have  seen,  a  practical  application  of  this  phenome- 
non. These  vibrations  are  occasioned  in  the  very  core  itself  by  suc- 
cessive changes  of  magnetization  of  the  core. 

'This  second  phenomenon,  however,  is  not  sufficient  to  explain 
Ader's  telephone  without  magnetic  core ;  a  third  influence  must  be 
admitted,  due  to  the  action  of  the  spirals  of  the  helix  upon  each  other. 
In  other  cases  the  helix  and  the  magnetised  bar  act  upon  one  another, 
and  this  contributes  to  the  production  of  sounds. 

*  Sometimes  a  fifth  influence  of  purely  mechanical  origin  is  at  work, 
manifesting  itself  in  the  same  way  as  the  transmission  of  sound  through 
solid  bodies.  Crcpaux's  experiments  are  the  most  curious  and  most 
remarkable  instance  of  this. 

*  These  various  considerations  will  sufficiently  show  that  the  theory  of 
the  telephone  is  very  complicated,  and  that  it  is  very  difficult  exactly 
to  define  the  part  played  by  each  of  the  aiijencies  at  work.  In  any  case 
it  is  (piite  certain  that  molecular  artion,  which  is  as  yet  so  imperfectly 
known,  plays  an  important  part  in  a(  oustic  phenomena,  and  that  the 
telephone,  like  the  phonograph,  will  give  a  new  impetus  to  research  in 
this  direction,  by  oj)ening  u|)  for  that  branch  of  physical  science  a  hori- 
zon as  vast  as  it  is  unknown.' 

"  \Vc  have  here  experiment  after  experiment  showing  that 
previous  exi)lanatic)ns  did  not  explain,  and  a  man  ready  to  give 
a  number  more  of  similar  character ;  but  the  evidence  is  that 
there  is  only  one  way  to  stop  the  sounds  in  a  telephone  and  that 
is  to  stop  the  current.  Vou  may  take  the  diafram  out  of  the 
instruments;    take  the   magnets  out  and  the   helix  or  bobbin  of 


WHISPERINGS   OF   AN   OLD   PINE 


$61 


wire  about  the  magnet  out;  still  the  sounds  will  go  through, 
articulate  speech  or  other  sound.  But  stop  the  current  and 
always  you  will  stop  the  sounds.  Why?  Because  the  cur- 
rent carries  the  sound,  and  when  that  stops  there  is  no  tele- 
phone. 

"That  the  sounds  are  transferred  by  the  current  explains 
fully  and  instantly  every  experiment  that  ever  was  tried,  and 
no  other  theory  will  explain  satisfactorily  a  single  one. 

**  Ellen  will  return  to  the  article  from  the  Westminster  Review : 

'At  the  Newport  torpedo  station,  in  Rhode  Island,  speaking  was 
carried  on  through  a  line,  including  five  miles  of  submerged  cable 
and  an  equal  length  of  land  wire.  Resistance  coils  were  added  two 
thousand  ohms  at  a  time,  until  twelve  thousand  ohms  were  introduced 
into  the  circuiti  without  interfering  with  the  transmission  of  speech. 
The  importance  of  this  test  will  be  understood  when  it  is  remembered 
that  the  resistance  of  the  Atlantic  cable  is  equal  to  seven  thousand 
ohms  only.  The  experiments  at  New-port  were  continued  by  the 
addition  of  a  total  resistance  of  thirty  thousand  ohms,  but  beyond 
twelve  thousand  ohms  the  sound  was  found  lo  diminish  in  intensity. 
Mr.  Dell  stales  that  the  maximum  amount  of  resistance  through  which 
the  undulating  currents  vvHl  pass,  and  yet  retain  sufficient  force  to 
produce  an  audible  sound  at  the  distant  end,  has  yet  to  be  determined. 
In  the  laboratory  he  has  conversed  through  a  resistance  of  sixty  thous- 
and ohms.' 


•*  All  this  talk  of  resistances  to  be  overcome  resolves  itself  into 
whether  or  not  there  is  sufficient  current  to  carry  the  sound, 
and  in  such  case  the  intensity  is  proportional  to  the  sound  car- 
ried through. 

"The  writer  continues: 


r^i^i 


ELLEN  OR  THE 

There  is  a  practical  difficulty  m  transmitting  telephonic    signals 
jgh  a  telegraph  wire  running  parallel  to  a  number  of  other  wires 

£h  are   being   used  for  ordinary  telegraphic  purposes.      Induction 
ts  are  produced  in  the  telephone  wire,  which  greatly   interfere 

|tfte  distinctness  of  the  sounds.    The  diflficulty  is  said  to  be  over- 

f  having  an  extra  return  wire,  instead  of  utilising  the  earth  for 

li  of  the  circuilj  as  is  ordinarily  done.     The  two  wires  arc  put  side 

„ide  in  close  proximity,  and  the  detiimental  effect  of  the  induclive 
currents  is  thus  disposed  oL 

'The  constmction  of  the  telephone  is  remarkably  simple  :    It  consists 

a  steel  cylindrical  magnet,  about  five  inches  long  and  three-etghlhs 

m  inch  in  diameter,  encircled  at  one  extremity  by  a  short  bobbin  of 
>od  or  elwnite,  on  which  is  wound  a  quantity  of  very  fine  insulated 
copper  wire*    The  magnet  and  coil  are  contained  in  a  wooden  cylindri- 
cal case*     The  two  ends  of  the  coil  are  soldered  to  thicker  piei'cs   of 
coppjer  wire,  which  traverse  the  ^*ooden  envelope  from  one  end  to  the 
otherj  and  terminate  in  the  binding  screws  at  its  extremity.    Immediately 
in  front  of  the  magnet  is  a  thin  circular  iron  plate,  which  is  kept  tn  its 
place  by  being  jammed  between  the  main  portion  of  the  wooden  case, 
and  a  wooden  cap  causing  the  mouth  or  ear  trumpet    These  two  parts 
are  screwed  together.    The  latter  is  cut  away  at  the  centre  so  as  to 
expose  a  portion  of  the  iron  plate,  about  half  an  inch  in  diameter.     In 
the  experiments  which  Mr.  Bell  has  carried  out  in  order  to  determine 
the  influence  of  the  various  parts  of  the  telephone  on  the  results  pro- 
duced, and   their  relations  to  each  other  when  the  best   effects  are 
obtained,  he  employed  iron  plates  of  various  areas  and  thicknesses,  fiom 
boiler  plate  three  eighths  of  an  inch  in  thickness  to  the  thinnest  plate 
procurable.     Wonderful  to  relate,  it  appears  that  scarcely  any  plate  is 
too   thin  or  too  thick  for  the  purpose,  but  the  best  thickness  is  that 
of  the  ferrotype   plate  used  by  photographers.    Thin  tin-plate  also 
answers  very  well.    The  iron  plate  is  cut  into  the  form  of  a  disc,  about 


PINE 


583 


two  inches  in  diameter,  and  is  pbced  as  near  as  possible  to  the  extrem* 
ity  of  the  steel  magnet  without  actually  touching  it.  The  dimensions  of 
the  various  parts  of  the  instrument  given  above  are  found  to  be  con- 
venient, but  they  are  by  no  means  essential.  Good  results  have  been 
obtained  by  means  of  a  magnet  only  an  inch  and  a  haU  long,  and  a 
working  instrument  need  not  be  too  large  for  the  waist  coat  pocket. 
There  is  no  difference  between  the  transmitting  and  the  receiving 
telephone;  each  instniment  serves  both  purposes.  Nevertheless  in 
order  to  avoid  the  inconvenierce  of  shifting  the  instniraent  backward 
and  fonvard  between  the  ear  and  the  mouth,  it  is  better  to  have  two 
on  the  circuit  at  each  station.  The  operator  then  holds  one  perma- 
nently to  his  ear,  while  he  talks  with  the  other. 

'It  will  not  be  supposed  that  the  idea  of  this  roarvelously  simple 
piece  of  apparatus  was  evolved  ready  formed  from  the  inventor's  brain; 
very  far  otherwise.  It  is  the  final  outcome  of  a  long  series  of  patient 
researches  carried  out  by  Mr.  Bell  in  the  most  skillful  and  philosophical 
manner,  in  which  one  modification  suggested  another,  accessory  after 
accessory  was  discarded,  and  finally  the  instrument  was  pruned  down 
to  its  present  form  and  dimensions.  Telephones  have  been  long 
known.  A  few  years  ago  a  simple  arrangement  whereby  articulate 
sounds  could  be  transmitted  over  a  distance  of  fifty  or  sixty  yards,  or 
even  farther,  could  be  bought  in  the  street  for  a  penny.  It  consisted 
of  a  pair  of  pill  lioxes,  the  lx)ttoms  of  which  were  connected  by  a  piece 
of  string  stretched  tight,  while  over  the  mouth  of  each  was  pasted  tissue 
paper.  On  speaking  to  one  of  the  pill-boxes  the  tissue  paper  and 
enclosed  air  were  set  in  vibration.  The  vibrations  so  produced  were 
communicated  to  the  thread  and  transmitted  to  the  distant  pill-lx)x, 
which  was  held  close  to  the  ear,  where  they  affected  the  air  in  such  a 
way  as  to  produce  the  original  sounds/ 

**This  last  sentence  is  a  very  good  illustration  of  scientific 
explanation.     'Affected   the  air  in  such  a  way' — what  way? 


584  ELLEN    Ok   THE 

Is  it  the  air  that  produces  the  original  sounds?  Do  these  vibra- 
tions of  the  tissue  paper  repeat  the  sound,  and  if  so,  those  of 
the  thread  and  distant  pill  box?  Certainly  if  the  modern  tele- 
phones repeat  them,  because  repeating  the  vibrations,  there 
must  be  talk  all  along  the  line ;  and  everywhere  else  ;  that  is, 
everything  must  talk  everywhere,  and  talk  equally  well.  Isn't 
it  about  time  that  the  scientists  did  less  talking  and  more  think- 
ing? Certainly  less  talking  unless  they  know  something  about 
the  subject  they  discuss. 

'The  simple  a|)paratus  was  more  effective  than  would  be   a  priori 
imagined.     Mieclric  telephones  were  devised  in  this  country  aboiil  the 
same  time  that  the  telegraph  was    introduced,  but  the  best    of   them 
dillereil  widely  from  the  modern  inslriiment.     They  were   capable  of 
conveying  to  a  distance  sounds  of  various  pitch,  so  that  the  succession 
of  notes   constituting  a  melody  could  be  produced  many  miles  away, 
but  the  sperial  cliaracter  of  the  voice  by  which  the  melody  was  originated 
was  (.Mitircly  lost.      Now  the  great  interest  whi(^h  attaches  to    Mr.  I  Jell's 
telcpiione,  and  the  intense  wonder  :ind  curiosity  it  has  aroused  are  ibie 
to  its  ]>o\ver  of  (  onveyin,::  absolutely  unaltered  every  peculiarity  of  the 
voice  or  musical   instrument.     A  violin  note  reappears  as  a  violin  note  : 
it  cannot  be  mistaken   for  anything  else.     And  in  tlie  case  of  a  human 
voice,  it  is  not  le>s  rasy  to  distinguish  one  sj^eaker  from  another  than  it 
would  be   if  the  speakers  were   in   the  roo:n   close  by  instead  of   being 
miles  or  even   hundreds  of  iniK.'s  :nv  ly.     This  is  the  charm  of   the  new 
telephone;   this   it   is  which   renders   it    innne  i^urahly  superior   to    any- 
thing of  the  kind  whi(  h  j)recedeil  it. 

*  Mr.  r.ell's  researches  in  electric  telejihony  began  with  the  artificial 
production  of  musical  sounds,  sugge^te.i  by  the  work  in  which  he  was 
then  engaged  in  lioston,  vi/.  :  teaching  the  deaf  and  dumb  to  speak. 
Deaf  mutes  are  duml)  merelv  because  thev  are  deif.     There  is  no  local 


WHISPERINGS   OF  AN   OLD    I'INE 


585 


Icfcct  to  prevent  utterance*  Mr,  Bell  has  practically  demonstrated  by 
two  thousand  of  his  own  pupils  that  when  the  deaf  and  dumb  know 
how  to  control  the  action  of  their  vocal  organs,  they  can  articulate  with 
comparative  facility.  Striving  to  perfect  his  system  of  teaching,  it 
occurred  to  Mr*  Bell  that  if,  instead  of  presenting  to  the  eye  of  the 
deaf  mute  a  system  of  symbols,  he  could  make  visible  the  vibrations  of 
the  air,  the  apparatus  might  be  used  as  a  means  of  leat  hing  articulation. 
In  this  part  of  his  investigations  Mr*  Bell  derived  great  assistance  from 
the  phonautograph.  He  succeeded  in  vibrating  by  the  voice  a  style  of 
w.^od,  about  a  foot  in  length,  attached  to  the  membrane  of  the  phonau- 
tograph ;  and  with  this  he  obtained  enlarged  tracings  of  the  vibrations 
of  the  air,  produced  by  th*  vowel  sounds,  ufwn  a  jjlain  surface  of 
smoked  glass.  Mr.  Bell  traced  a  similarity  between  the  manner  in 
which  this  piece  of  wood  was  vibrated  by  the  membrane  of  the  pho- 
nautograph  and  the  mtnner  in  which  theossiculxof  the  human  ear  were 
moved  by  the  tympanic  membrane.  Wishing  to  constrnctan  apparatus 
closely  resembling  the  human  ear,  it  was  suggested  to  him  by  Dr. 
Clarence  J.  Blake,  a  distinguished  aurist  of  Boston,  that  the  human  ear 
itself  would  be  still  better  and  a  specimen  wn^  prepare<l, 

'The  tympanic  membrane  of  the  ear  is  connected  with  the  interna!  ear 
by  a  series  of  little  bones  called  respectively  the  malleus,  the  idcus,  and 
Ihe  stapes,  from  their  peculiar  shapes.  Mr.  Bell  removed  the  stapes 
and  attached  to  the  end  of  the  incus  a  style  of  hay  alK>ut  an  inch  in 
length.  Upon  singing  into  the  external  artificial  ear,  the  style  of  hay 
was  thrown  into  vibration,  and  tracings  were  obtained  upon  a  plain 
surface  of  smoked  glass  passed  rapidly  underneath.  The  curves  so 
obtained  are  of  great  interest,  each  showing  peculiarities  of  its  own, 
dependent  upon  the  vowel  sound  that  is  sung.  Whilst  engageil  in  these 
experiments  Mr.  Bell's  attention  was  arrested  by  observing  the  wonder- 
ful disproportion  which  exists  between  the  size  and  weight  of  the  mem- 
brane— no   thicker   than    tisstie  piper — and  the  weight  of   the  bones 


S86  ELLEN   OR   THE 

vibrated  by  it,  and  he  was  led  to  inquire  whether  a  thicker  membrane 
might  not  be  able  to  vibrate  a  piece  of  iron  in  front  of  an  electro- 
magnet. ITie  experiment  was  at  once  tried.  A  piece  of  steel  spring 
was  attached  to  a  stretched  membrane  of  goldbeater's  skin  and  placed 
in  front  of  the  pole  of  the  magnet.  This  answered  very  well,  but  it  was 
found  that  the  action  of  the  instrument  was  improved  by  increasing  the 
area  of  metal,  and  thus  the  membrane  was  done  away  with  and  an  iron 
plate  substituted  for  it.* 

**  Of  course  the  membrane  no  thicker  than  tissue  paper 
doesn't  vibrate  the  bones.  No  such  absurd  thing  happens  at 
all,  but  it  assists  the  sounds  in  their  course  towards  the  brain, 
and  doubtless  protects  the  interior  passage. 

"The  statement  made  that  the  experiment  was  at  once  tried, 
whether  a  thicker  membrane  might  not  vibrate  a  piece  of  iron, 
etc.,  is  not  true.  The  experiment  tried  being  what  a  steel 
spring  attached  to  a  membrane  might  do. 

*It  was  importanl  at  the  same  time,  to  determine  the  effect  pro- 
duced by  altering  the  strength  of  the  magnet ;  that  is,  of  the  current 
which  passed  round  the  coils.  The  battery  was  gradually  reduced 
from  fifty  rells  to  none  at  all,  and  still  the  etTects  were  observed,  but 
in  a  less  marked  degree.  The  action  was  in  this  latter  case  doubtless 
due  to  residual  miignetism  ;  hence,  in  the  ])resent  form  of  apparatus  a 
])ermancnt  magnet  is  employed.  Lastly  the  effect  of  varying  the 
dimensions  of  the  rnW  was  studied,  when  it  was  found  that  the  sounds 
became  louder  as  its  length  was  diminished;  a  certain  length  was. 
however,  ultimately  reached,  beyond  whic:h  no  improvement  was  effected, 
and  it  was  found  to  ])e  only  nccesssary  to  enclose  one  end  of  the  mag- 
net in  tiie  coil  of  wire. 

'  Before  attempting  any  explanation  of  the  action  of  the  telephone  it 
mav  be  well  to  draw  the  attention  of  our  readers  to  the  special  charac- 


*'  '^' 


teristics  of  the  htimm  voice,  and  ti  those  peculiarities  which  distinguish 
one  musical  note  from  another.  Whatever  the  differences  in  question 
may  depend  upon,  it  is  certain  that  they  are  transmitted  and  repro- 
duced in  the  telephone  with  unerring  fidelity  and  it  is  therefore  import- 
ant that  we  should  understand  their  nature  and  origin.  Take  a  tuning 
fork  and  set  it  in  vibration  by  striking  or  drawing  a  violoncellu  bow 
across  its  prongs.  The  fork  yields  its  own  proper  note,  which  will  be 
loud  or  the  reverse  according  as  the  fork  has  been  struck  energetically 
or  lightly.  So  long  as  we  use  one  fork  only  it  is  obvious  that  the  only 
variation  which  can  be  produce  I  in  the  sound  is  a  variation  of  intensily. 
If  the  extent  of  vibration  be  small,  the  resulting  sound  is  feeble ;  its 
loudness  increases  with  the  excursion  of  the  prongs.  What  is  true  of 
the  timing  fork  is  true  of  any  other  musical  instrument,  and  hence, 
generally  the  loudness  of  a  musical  sound  depends  ufxjn  the  amplitude 
of  vibration  of  thit  which  produced  i^.  Now  take  two  similar  tuning 
forks  of  different  pitch  and  suppose  that  one  is  exactly  an  octave  above 
the  other.  They  raiy  be  excited  in  such  a  way  that  the  notes  emitted 
are  of  equal  loudness  an  1  then  the  only  respect  in  which  they  differ 
from  each  other  is  in  pitch.  The  pitch  of  a  lork  depends  upon  its  rate 
of  vibration.  It  is  conipiratively  cisy  with  suitable  apparatus  to  meas- 
ure the  rate  of  vibration  of  a  tuning  fork  and  were  we  to  test  the  two 
forks  in  question  it  would  be  foun  I  that  that  giving  the  higher  note 
vibrates  exactly  twice  as  !ast  as  the  other.  If  the  one  performs  a 
hundred  oscillations  in  a  second,  the  other  which  is  an  octave  above, 
cQmpletes  two  hundred  in  the  same  interval  of  time.  Thus  the  pitch 
of  a  note  yielded  by  a  tuning  fork  depends  upon  its  rate  of  vibration 
and  on  nothing  else  and  the  same  is  true  of  a  pianoforte  wire,  the  air 
in  an  organ  pipe,  harmonium  reed,  etc.  We  have  now  accounted  for 
two  of  the  characteristics  of  a  musical  note,  its  loudness  and  its  pitch  ; 
but  there  is  a  third,  equally,  if  not  more  important  and  by  no  means 
so  simple  of  explanntion.     We  refer  to  what  is  usually  spoken  of  in 


k^.^..,a^a 


590  ELLEN   OR  THE 

English  books  on  acoustics  as  the  quality  of  the  note ;  the  French  call 
it  timbre,  and  the  Germans  Klangforbe.     It  is  that  which    constitutes 
the  difference  between  a  violin  and  an  organ,  or  between  an  organ  and 
a  pianoforte,  or  between  two  human  voices ;  indeed  between   any  t^-o 
musical  sounds  which  are  of  the  same  pitch  and  loudness,  but  are  still 
distinguishable  from  each  other.     In  order  to  explain  the  physical  cause 
of  quality,  we  will  suppose  we  have  a  thin  metallic  wire  about  a  yard 
long   stretched   between   two   points   over   a  sounding  board.      When 
plucked  at  its  centre  the  wire  vibrates  as  a  whole ;  the  tu'o  ends  are 
points  of  rest,  and  a  loop  is  formed  between  them.    The  note  emitted 
by  the  wire  when  vibrating  in  this  manner  is  called  its  fundamental 
note.     If  the  wire  be  damped  at  the  centre,  by  laying  on  it  with  slight 
pressure  the  feather  of  a  quill  pen  and  ])lucked  at  a  point  half  way  be- 
tween the  centre  and  one  end,  Ix^th  halves  will  vibrate  in  the  same 
manner  and  independently  of  each  other.     That  i^  to  say,  there  will  be 
two  ecpial  vibrating  segments  and  a  point  of  rest  or  note  at  the  centre. 
But  the  rapidity  of  vibration  of  each  segment  will  be  twice  as  great  as 
that  of  the  wire  when  vibrating  as  a  whole  and  conse(]uently  the   note 
emitted  will  l)e  the  <)<'tave  of  the   fundain'Mital.     When  damped    at  a 
j)oint  one  third  of  thj  length  from    either  extremity  and   plucked  half 
way  between  that  [)oint  and  the  nearer  extremity,  the  wire  will  vibrate 
in  three  ecjual  divisions,   just  as  it  vibrates  in  two  divisions  in   the  ]>re- 
vioiis  ea>e.     The  rate  of  vibration  will  be  now   three  times  as  great   as 
at  first  and  the  note  ])r()(lii(ed  will  be  a  twelfth  above  the  fundamental. 
Similarly,  by  damping  and   plucking  at  suitable  points  the  wire  may  \jc 
made  to  vibrate   In  four  i)arts,    five   parts,  six   parts,  etc.,   the  rate  of 
vibration   increasing  to  four,  five,   six  et(\,  times  what  it  was  at    first. 
Let  us  suj^pose  that  when  the  wire  was  swinging  as  a  whole  and  sound- 
ing its   fundamental  note,   the   number  of  oscillations  performed   in  a 
second  was  one  hundred.     Then  we  see  that  by  taking  suitable  precau- 
tions, the  wire  can  be  made  to  break  up  into  two,  three,  four,  five,  six 


WIIISPERIXOS    OF    AN    OLD    PINE 

etc.,  vibrating  segment>,  the  rates  of  vibrating  being  respectively  two 
hundred,  three  hundred,  four  hnndred,  five  hundred,  six  hundred,  etc, 
and  the  series  of  notes  emitted  being  the  octave  above  the  fundamental^ 
the  fifth  above  the  octave^  the  double  octave,  the  third  and  fifth  above 
the  double  octave,  and  so  on,* 

**Thus  far  this  writer  has  distinguished  between  those  things 
which  he  knew  and  those  which  he  did  not.  and  given  some 
very  interesting  information. 

*  We  now  come  to  an  important  point,  which  is  this — that,  the  wire 
being  free,  it  is  practically  impossible  to  strike  or  pluck  it  in  such  a  w*ay 
as  to  make  it  vibrate  according  to  one  of  the  alx)ve  systems  only.  It 
will  vibrate  as  a  whole,  wherever  and  however  it  be  struck,  but  this 
mode  has  ak^ays  associated  with  it  or  superposed  upon  it  some  of  the 
other  modes  of  vibration  to  which  we  have  just  referred.  In  other 
words,  the  fundamental  note  is  never  heard  alone,  but  always  in  com- 
bination wnth  a  certain  number  of  its  overtones,  as  they  are  called. 
Each  form  of  vibration  called  into  existence  sings  as  it  were  its  own 
song,  without  heeding  what  is  being  done  by  its  fellows,  and  the  conse- 
quence is  that  the  sound  which  reaches  the  ears  is  not  simple  but 
highly  composite  in  its  character.  The  word  clang  has  been  suggested 
to  denote  such  a  composite  sound,  the  constituent  simple  sounds,  of 
which  it  is  the  aggregate,  being  called  its  first,  seconrl,  third,  etc*, 
partial  tones.  All  the  possible  partial  tones  are  not  necessarily  present 
in  a  clang,  nor  of  those  which  are  present  are  the  intensities  all  the 
same.  For  instance,  if  the  wire  be  struck  at  the  centre,  that  point 
cannot  be  a  node,  but  mu^t  be  a  point  of  maximum  disturbance ;  hence 
all  the  even  partial  tones  are  excluded  and  only  the  odd  ones,  the  first, 
third,  fifth  and  so  on  are  heard.  That  characteristic  of  a  musical  note 
or  clang  which  is  called  its  quality,  depends  upon  the  number  and 
relative  intensities  of  the  partial  tones  which  go  to  form  it*    The  tone 


592  ELLEN  OR  THE 

of  a  tuning  fork  b  approximately  simple ;  eo  is  that  of  a  8to|^>ed  ^ 
organ  pipe  of  large  aperture  blown  by  only  a  slight  preHure  of  wind. 
Such  tones  sound  sweet  and  mildi  but  also  tame  «nd  ipiritlrM      In  die 
clang  of  the  violin,  on  the  other  hand,  a  large  number  of  partial  tonei 
are  represented;  hence  the  vivacious  and  brilliant  character  of   Om 
instrument.    The  sounds  of  the  human  voice  arc  prodnced  hf  die 
vibrations  of  the  vocal  chords,  aided  by  the  resonance  of  tlie  moatli. 
The  size  and  shape  of  the  cavity  of  the  mouth  may  be  altered  by  open- 
ing and  closing  the  jaws  and  by  tightening  or  loosening  the  lipa.     We 
should  expect  that  these  movements  would  not  be  without  effect  on  the 
resonance  of  the  contained  air,  and  such  proves  on  experiment  to  be 
the  fact    Hence,  when  the  vocal  chords  have  originated  a  clang  con- 
taining numerous  well-developed  partial  tones,  the  mouth  cavity,  fay 
successively  throwing  itself  into  different  postures,  can   fitvpr   fay  in 
resonance  first  one  overtone  and  then  another;  at  cme  moment  riii« 
group  of  partial  tones,  at  another  that.    In  this  manner  endlen  varieties 
of  quality  are  rendered  possible.    Any  one  may  prove  to  himael^  by 
making  the  experiment,  that  when  singing  on  a  given  note  he  can  only 
change  from  one  vowel  sound  to  another  by  altering  the  shape  and  size 
of  his  mouth  cavity.* 

**  Ellen  has  proved  beyond  question,  as  she  will  show  later, 
that  sound  is  produced  in  bodies  by  shock  or  disturbance, 
which  always  takes  place  before  vibration,  and  causes  vibration, 
which  in  turn  helps  decide  the  character  of  the  sound  emitted. 

"  Our  author  although  not  knowing  these  facts  still  keeps  fairly- 
well  within  the  lines  of  experiment  and  truth.  But  in  the  next 
advance  he  is  hopelessly  wrecked  by  a  theory  which  has  wrecked 
nearly  every  one  that  has  touched  it.  Every  statement  made 
in  connection  with  this  theory,  which  refers  to  air  waves,  is  not 
only  untrue  but  impossible.     Every  one  of  them  is  as  incorrect 


WHISPERINGH   OF  AS    OLD    PTNE 


593 


as   that  made   in   the    Encyclopaedia    Britannica   which  Kllen 
exposed*   * 

*  Having  thus  briefly  intlicated  ihe  physical  causes  of  the  various 
differences  in  musical  notes,  and  the  production  of  sounds  by  the  organs 
of  voice,  we  will  devote  a  few  moments  to  consider  how  these  sounds 
are  propagated  through  the  air  and  reach  the  plate  of  the  telephone. 
WTien  a  disturbance  is  produced  at  any  point  in  an  aerial  medium,  the 
particles  of  which  are  initially  at  rest,  sonorous  undulations  spread  out 
from  that  point  in  all  directions.  These  undulations  are  the  effect  oC 
the  rapid  vibratory  motions  of  the  air  particles*  The  analogy  of  water 
waves  will  help  us  to  undersumd  what  is  taking  place  under  these  cir- 
cumstances. If  a  stone  be  dropped  into  the  still  water  of  a  jiond,  a 
series  of  consecutive  circular  waves  is  produced,  each  wave  consisting 
of  a  crest  and  a  hollow*  The  waves  travel  onwards  and  outwards  from 
the  centre  of  distu:bance  along  the  surface  of  the  water,  while  the 
drops  of  water  which  constitute  them  have  an  oscillatory  motion  in  a 
vertical  direction.  That  is  to  say,  following  any  radial  line,  the  water 
particles  vibrate  in  a  direction  at  right  angles  to  that  in  which  the  wave 
is  prof>agAted.  The  distance  between  two  successive  crests  or  two  suc- 
cessive hollows  is  called  the  length  of  the  wave  ;  the  amplitude  of  vibra- 
tion is  the  distince  through  which  an  individual  drop  moves.  In  a 
similar  manner  sonorous  undulations  are  propagated  through  air  by  the 
oscillatory  motion  of  the  air  particles.  But  there  is  this  important 
difference  between  the  two  cases,  that,  in  the  latter  the  vibrating  parti- 
cles move  in  the  sa-iie  direction  in  which  the  sound  is  being  propagated. 
Consequently  such  waves  are  not  distinguished  by  alternate  crests  and 
hollows,  but  by  alternate  condensations  and  rarefactions  of  the  air,  the 
transmission  of  which  constitutes  the  transmission  of  sound.  The 
wave-length  is  the  distance  between  two  consecutive  condensations  or 


*  See  pages  401-405 


594  ^^^^         ELLEN   OR  THE 

rarefactions.     It  depends  upon  the  pitch  of  the   transmittoi   sound* 
being  shorter  as  the  sound  is  more  acute,  while  the  extent  of   vibfatioa 
of  the  air  particles  increases  with  the  loudness.    Such  are  the  peculmii* 
ties  of  the  vibratory  motion  in  air  corre^jponding  to  the  pitch  and  Icmd* 
ness  of  the  traaismitled  sound.     But  what  is  there  in  the  character  oC 
the  motion  to  account  for  difference  in  quality?     A  little  consideralion 
will  show  that  there  is  only  one  thing  left  to  account  for  these,  ajiil 
that  is  the  form  of  the  vibration.     Let  us  mentally  isolate  a   pofticle  of 
air,  and  follow  its  movements  as  the  sound  passes.     If  the  drstiirbaace 
is  a  simple  one,  produced,   say,  by  the  vibration  of  a  tuning  fork,  the 
motion  of  the  air  particle  will  be  simple  also,  that  h^  it  will  vibrate  to 
and  fro  like  the  bob  of  a  pendoJumi  coming  to  rest  at  each  end  of  its 
excursion  and  from  these  points  increasing  in  velocity  until  it  p^^es  ila 
neutral  point     Such,  however,  is  clearly  not  the  only  mode  of  vibration 
possible*     If  the  disturbance  be  produced  by  a  clang  conaprising  a 
number  of  partial  tones  of  various  intensities,  all  excited  simultaneoiislv^ 
it  is  obviotis  that  the  air  particle  must  vibrate  in  obedience  to  every  one 
of  these*     Its  motion  will  be  the  resultant  of  all  the  motions  due  to  the 
separate  partial  tones.     We  may  imagine  it,  starting  from  its  position 
of  rest,  to  move  forward,  then  stop  short  and  turn  back  for  an  instant, 
then  on  again  until  it  reaches  the  end  of  its  excursion.     In  returning  it 
may  perform  the  same  series  of  to-and-fro  motions  in  the  opposite 
direction,  or  it  may  move  in  a  totally  different  way.     Nevertheless, 
however  complex  its  motion  may  be — and,  as,  a  rule  it  will  be  exceed- 
ingly complex — its  periodic   character  will  be  maintained.     All    the 
tremors  and  perturbations  in  one  wave-length  will  recur  in  all  the  others 
*When  sonorous  undulations  impinge  upon  the  iron  plate  of  the  tele- 
phone, the  latter  is  set  in  vibration,     Its  particles  move  to  and  fro  in 
some  way  or  other.     The  complexity  of  their  motion  will  depend  upon 
that  of  the  air  from  which  it  was  derived.     But  for  the  sake  of  sim- 
plicity we  will  assume  that  the  plate  has  a  simple  pendulous  motion* 


WmSf'ERINGS    OF   AN    OLD    PINE 


595 


It  will  be  remembered  ihat  the  iron  plate  is  placed  quite  close  tO;  but 
not  quite  in  contact  with,  the  exlremit)^  of  the  stee!  magnet.  It  be- 
comes, therefore,  itself  a  magnet  by  induction  ;  and  as  it  vibrates,  its 
magnetic  power  is  constantly  changing,  being  strengthened  when  it 
approaches  the  magnetic  core,  enfeebled  as  it  recedes.  Again,  when  a 
magnet  moves  in  the  neighborhood  of  a  coil  of  wire,  the  ends  of  which 
are  connected  together,  an  electrical  current  is  developed  in  the  coil 
whose  strength  depends  upon  the  mpidity  with  which,  and  the  distance 
through  which,  the  magnet  moves.  In  the  telephone  then,  as  the  plate 
moves  towards  the  coil,  a  current  is  induced  in  the  latter  which  traverses 
the  whole  length  of  wire  connecting  it  with  the  distant  instrument ;  the 
plate  returning,  another  current  with  reversed  sign  follows  the  first. 
The  intensity  of  these  currents  depends,  as  we  have  said,  on  the  rapidity 
with  which  these  movements  are  effected,  but  is  largely  influenced  also 
by  the  fact  that  the  plate  does  not  retain  a  constant  magnetic  strength 
throughout  its  excursions.  Under  the  assumption  we  have  made  with 
res|iect  to  the  simplicity  of  the  plate's  motion  it  follows  that  the 
induced  currents,  alternately  positive  and  negative,  follow*  each  other  in 
a  uniform  manner,  and  with  a  rapidity  corresponding  to  the  pitch  of 
the  exciting  note.  These  currents  pass  along  the  circuit  and  circulate 
round  the  coil  of  the  distant  telephone.  There  they  modify  the  mag- 
netic relations  between  the  steel  magnetic  co[e  and  the  iron  plate  in 
such  a  way  that  one  current— -say  the  positive — attracts  the  plate,  w^hile 
the  other— the  negative — repels  it.  And  since  the  arriving  currents 
follow  each  other,  first  positive  and  then  negative,  with  perfect  regular- 
ity, the  plate  will  also  vibrate  in  a  uniform  manner  and  will  perform  the 
same  number  of  vibrations  per  second  as  did  the  plate  of  the  sending 
instrument.  Hence  the  sound  heard  will  be  an  exact  copy,  except  as 
to  loudness,  of  that  produced  at  the  sending  station.  Having  thus 
followed  tlie  sequence  of  phenomena  in  this  simple  case,  we  are  enabled 
to  extend  our  explanation  to  the  case  in  which  composite  sounds  of 


S96  ELLEN   OE  THE 

more  or  kai  complexity — tiovel  looDcis  and  speech — are  tranaanilted- 
We  are  compelled  to  adntit  tJiat  every  detail  tn  Uie  moiloii  cf  an  air 
ptrtkJe,  evcfy  tsrn  and  twisty  most  be  passed  on  izioliefed  to  ti^  iroo 
membfanep  aiKl  that  erer)-  modilkatioii  oC  the  loation  oC  the  tsei&bimiie 
mtuit  bare  iti  count^mit  m  a  modificstioo  ol  the  induced  cmrrente. 
nieie  in  their  turn,  aHecting  the  bon  pkte  of  the  receiTing  telephone 
It  kXhm*  that  the  pbtes  of  the  two  tclefihwies  mtist  be  vibrating  in  an 
thftolaCely  idrotkal  manner/ 

**This  is  perhaps  as  coinplctc  a  statement  of  what  the  writer 
supposes  might  take  place,  assttmtng  the  undulatory  theory  of 
iound  to  be  true,  as  could  well  be  made/* 

*' And  Ellen  docHU't  think  that  any  of  the  different  things  take 
place  here  referred  to?*' 

''Practically  none  of  them/'  she  answered,  **but  instead,  as 
Ellen  has  said,  all  sound  consists  of  infinitesimaL  particles  of 
electrical  matter  thrown  off  by  the  sounding  body ;  and  these 
particlcj*  permeate  the  air,  moving  at  a  fixed  rate  of  speed. 
When  uttered  into  a  telephone  they  enter  the  wire  and  are 
carried  by  the  electric  current  instantaneously  to  the  receiving 
instrument,  where  they  are  conducted  to  the  listener's  ean 
Like  all  ol  nature's  operations  when  understood  this  is  very 
simple,  and  every  part  of  it  Ellen  proves. 

**Thc  many  tilings  mentioned  by  the  voluminous  writer* 
whom  Elljen  quotes,  are  none  of  them  proven,  and  for  the 
most  part,  as  Kllen  has  shown,  or  will,  are  not  only  wholly 
incorrect  but  very  ridiculous. 

"Their  culmination  is  that  the  plates  of  the  two  tele* 
phono**  vibrate  in  an  absolutely  identical  manner;    and  if  this 


^ 


WHISPERINGS    OF   A^    OLD    PINE 


597 


has  any  significance  it  means  that  the  diafram  of  the  recerv- 
ing  instrument,  thus  vibrating,  repeats  the  sound — -that  is 
talks, 

**  This  is  the  same  explanation  of  the  action  of  sound  at  a 
telephone »  that  we  have  had  before,  and  the  only  one  possible 
if  the  undulatory  theory  of  sound  is  retained.  Of  course  if 
one  diafram  by  thus  vibrating  repeats  the  sound  the  other  must 

'*This  idea  that  the  movement  of  a  diafram,  mis-called  vibra- 
tion, if  existing,  might  under  any  circumstances  make  the 
diafram  emit  the  same  sound  as  some  other  body,  or  that  any 
movement  could  n^ake  any  body  do  this,  except  in  the  rare 
cases  when  there  is  sympathetic  vibration,  has  become  one  of 
the  fundamental  errors  of  science.  As  Ellen  has  shown  it  is 
entirely  without  foundation,  and  is  absurd  and  impossible. 

••This  writer  concludes  as  follows: 

*  We  can  thus  follow  in  a  general  manner  the  course  of  the  phenomena 
and  explain  how  air  vibrations  are  connected  with  the  vibrations  of  a 
magnetic  plate — how  these  latter  give  rise  to  electrical  currents,  which, 
passing  over  a  circuit  of  hundreds  of  miles,  cause  another  magnetic 
plate  to  vibrate,  every  tremor  in  the  first  being  reprrKluced  in  facsimile 
in  the  second,  and  thus  excite  sonorous  undulations  which  pass  on  to 
the  ear.  We  can  understand  all  this  in  a  general  way,  but  we  are  not 
the  less  lost  in  wonder  that  the  sequence  of  events  should  be  what  it  is. 
That  a  succession  of  currents  could  be  transmitted  along  a  telegraph 
wire  without  the  aid  of  a  battery,  that,  by  simply  talking  to  a  magnetic 
membrane  in  front  of  a  coil  of  wire,  the  relations  of  the  magnetic  field 
between  the  two  could  be  so  far  modified  as  to  produce  in  the  coil  a 
succession  of  electrical  currents  of  sufficient  power  to  traverse  a  long 
circuit  and  to  reproduce  a  series  of  phenomena  identical  with  those  by 


m^M 


598  ELLEN  pR  THB_ 

which  the  currents  were  brought  into  exiatem^  would  have  been  a  tern 
years  ago  pronounced  an  impossibility.  A  man  would  hanre  been 
derided  who  proposed  an  instrument  constructed  on  sach  piincdples. 
Nevertheless,  here  it  is  realized  in  our  hands.  We  can  no  loiq^ 
doubt,  we  can  only  wonder,  and  admire  the  sagacity  and  patience  with 
which  Mr.  Bell  has  worked  out  his  problem  to  a  socceaafiil 


'-^-'^r..  LiLSOX  AND 


WHISPERINGS   OF   AN   OLD    I'LNE 


601 


XLl. 


^^T^HIS  is  a  very  excellent  early  account  of  the  telephone. 
^     But  probably  never  in  the  history  of  the  world  has  the 
power  of  authorit}  to  hold  thought  in  check  been  more  remark- 
ably  illustrated,     Ellen  will  repeat  several  sentences: 

*Had  any  hardy  speculator  a  few  years  ago  proposed  a  telephone 
which  should  act  on  the  principle,  and  be  constructed  in  the  form  of 
Mr.  Bell's  instrument,  he  would  probably  have  been  considered  a 
lunatic.  The  effects  are  so  marvelous ;  the  exciting  causes  at  first  sight 
so  entirely  inadequate  to  produce  them.' 

"This  is  evident  enough,  but  why  didn't  thought  break  away 
from  a  position  so  hideously  absurd,  and  find  the  truthi  at  least 
seek  it*  For  a  single  gleam  of  common  sense  explains  the 
whole.  And  it  would  have  been  understood  almost  instantan- 
eously by  nearly  every  beholder,  only  for  those  who  believed 
in  the  air  wave  theory  of  sound,  and  prevented  by  their  imme- 
diate suggestions, — ^hypotheses  stated  as  facts,  they  being  the 
ones  to  whom  naturally  the  world  at  large  looked  for  knowl- 
edge,— an  intelligible  and  truthful  explanation. 

"There  was  only  one,  is  only  one  possible  explanation,  that 
the  talk  of  each  individual,  or  the  sound  of  every  instrument,  is 
carried  through  tlie  wire  by  the  electric  current.     Instantly  this 


■te«^.,«faA 


602  ELLEN   OR  THE 

remarkable  phenomenon  becomes  entirely  simple.  Why 
shouldn't  sound  be  thus  carried?  In  the  nature  of  things  it 
would  be  impossible  for  it  not  to  be.  For  we  know,  because 
of  the  universality  of  natural  law ;  and  equally  well  because  of 
the  action  of  the  thing  itself,  as  illustrated  by  the  form  of  the 
ear,  the  natural  aid  in  the  phenomena  of  sound,  or  the  artificial 
aids  of  an  ear  trumpet,  a  megaphone  or  a  diafram,  how  sound 
is  made ;  it  couldn't  within  the  scope  of  reason  possibly  be  any- 
thing else  than  infinitesimal  particles  of  matter,  and  doubtless 
as  Oersted  discovered  electrical  matter.  And  it  couldn't  possi- 
bly help,  under  the  conditions,  going  into  the  wire,  when  it 
would  be  caught  instantly  by  the  current,  and  would  as  certainly 
get  out  at  any  opportunity,  for  it  moves  naturally  in  all  direc- 
tions. 

**  This  writer  further  says : 

'The  words  are  repeated  by  the  instrument  at  the  other  end  of  the 
circuit  with  the  same  pitch,  the  same  cadences,  and  the  same  relative 
loudness.  But  what  strikes  one  the  most  is  that  the  character  of  the 
speaker's  voice  is  faithfully  preserved  and  reproduced.  Thus  one  voice 
is  readily  distinguished  from  another.  No  i)eculiarity  of  inflection  is 
lost.  ♦  *  *  I  happened  to  know  some  of  the  parties  in  PVance 
[this  was  in  England]  and  was  able  to  recognize  their  voices.  They 
also  recognized  mine,  and  told  immediately,  a  lady  spoke,  that  it  was  a 
female  voice.' 

**  And  all  of  this  was  said  to  be  accomplished  by  a  piece  of 
iron ;  or  if  not  by  that,  by  some  other  thing,  as  the  core  of  a 
magnet,  or  a  helix,  or  a  box,  all  made  for  other  purposes.  As 
well  suppose  a  wagon,  or  a  bushel  basket,  would  perform  the 
functions  of  a  piano. 


WHISPERINGS   OF  AN   OLD    PINE 


603 


'* There  is  nothing  strange  that  an  instrument  might  be 
created  which  would  repeat  sounds.  Hand  organs  have  long 
done  it,  and  many  instruments  might  be  made  to  do  it*  But  in 
all  such  cases  an  instrument  is  made  in  accordance  with  the 
laws  by  which  all  sound-producing  instruments  are  made. 
Here  nothing  of  the  kind  takes  place  or  possibly  can,  and  the 
scientific  explanation  is  that  an  effect  takes  place  without  any 
adequate  cause.     It  is  not  true. 

**  Always  a  cause  exists  for  an  effect.  Always  that  cause  is 
appropriate.  Always  it  is  the  same, — other  things  being 
equal, — so  exact  and  perfect  is  the  method  of  law  and  order  by 
which  the  Universe  is  made.  Easily  intelligence  can  correctly 
interpret  these  relations.  Certainly  no  intelligence  which  can- 
not, is  of  any  use  in  writing  text-books,  or  endeavoring  to 
explain  natural  phenomena." 

*'The  old  Pine  sees  that  Ellen  is  entirely  right  in  regard  to 
the  action  of  sound  in  a  telephone^  and  he  hopes  to  see  her 
make  equally  clear  the  laws  of  sound  through  which  a  grapho- 
phone  record  is  made  and  reproduced/' 

'*  Ellen  has  already  referred  to  these  laws/'  she  answered, 
**but  she  and  the  old  Pine  will  now  attempt  to  examine  them 
more  fully. 

**  Ellen  has  shown  how  intimately  connected^ — indeed  how 
absolutely  essential  in  the  production  of  sound,  at  least  so  far 
as  our  existence  upon  this  earth  extends,— are  both  Intelligence 
and  matter.  There  can  be  no  sound  here  without  the  reciprocal 
action  of  these  apparently  distinct  essences;  a  condition  evi- 
dently that  is  as  broad  as  this  phase  of  existence,  whatever 
other  existences  there    may  be.     That  is,   it   is  only  by  the 


6o'4  ELLEN   OR  THE 

combination  of    the  material  with  the  spiritual  that  any  per- 
ceptible or  intelligent  existence  can  take  place  on  earth." 

"  But  the  day  is  fine,"  I  said,  **  the  waters  of  the  rivers  sweet, 
and  every  cloud  is  beautiful." 

**  Ellen  recognizes  all  of  that,"  she  replied,  "that  the  material 
universe  as  it  appears  to  us, — and  Ellen  means  by  us  the  divine 
instinct  which  can  use  all  material  things  for  its  own  pleasure 
and  progress, — is  most  beautiful.  Indeed  it  is  in  this  that 
beauty,  as  we  usually  speak  of  it,  is  outlined.  It  all  enters,  too, 
into,  and  makes,  the  sensation  of  sight,  and  indirectly  those  of 
taste,  and  touch.  It  is  the  material  upon  which  spirit  feeds 
and  exists  in  present  conditions.  But  what  especially  we  are 
considering  now,  are  the  laws  governing  sound. 

"As  Ellen  has  repeatedly  said  all  material  things  are  made 
by  a  mixture  of  matter  in  its  different  conditions  and  propor- 
tions. Then  certainly  it  cannot  make  any  difference  who  mixes 
them.  At  least  it  would  not  if  each  party  was  equally 
skilled.  And  therefore  sound,  infinitesimal  particles  of  clectri> 
cal  matter,  might  be  mixed  b\'  different  forces?  To  illustrate 
this  principle  from  odors  I^llen  will  cjuote  again  from  the 
noted  French  writer,  Ferdinand  Papillon  :    * 

*  Sueh  is  the  chemical  nature  of  most  of  the  odorous  principles  of 
vegetable  origin.  But  chemistry  has  not  sto|)i)ed  short  with  ascertain- 
ing the  inmost  composition  of  these  substances ;  it  has  succeeded  in 
rej^roducing  quite  a  number  of  them  artificially,  and  the  compounds 
thus  manufactured,  wholly  from  elements,  in  laboratories,  are  absolutely 
identical  with  the  products  extracted  from  ])lants.' 


*     Sec  pages  14-2J 


WHISPERINGS   OF  AN   OLD   PINE 


60s 


**  If  all  of  this  is  true  as  to  odors ;  and  if  sounds  like  odors 
are  made  from  the  mixture  of  different  conditions  of  matter  in 
different  proportions,  it  should  be  equally  true  that  sounds 
might  be  mixed  or  made  by  different  forces. 

'*Yet  while  Ellen  admits  nature's  ability  to  reproduce  by 
other  methods  than  those  she  generally  uses,  she  is  morally 
certain  that  nature  will  not  do  this,  in  the  same  conditions, 
because  the  methods  she  uses  are  the  best  possible  for  these 
conditions.  Of  course  they  are,  for  why  should  nature  use  them 
if  they  w^ere  not;  but  whilst  the  mechanical  contrivances,  as  a 
whole,  which  man  enjoys  for  the  purposes  of  articulate  speech, 
do  not  occur  elsewhere,  so  far  as  we  know,  and  could  not  in 
any  graphophone  record,  because  there  is  no  space  for  them,  it 
is  evident  that  the  necessary  machinery  for  making  different 
sounds  could. 

'*  And  it  would  appear  that  the  indentation  made  by  sound 
is  so  shaped  that  when  re-entered  by  a  proper  instrument  the 
original  sound  which  made  it  will  be  reproduced.  And  this 
means  that  similar  particles  of  matter  will  be  made  as  those 
w^hich  made  the  indentations.  But  if  so»  it  is  done  in  accord- 
ance with  the  laws  of  sound  and  not  in  opposition  to  them. 
Every  law  of  sound  which  operated  before  the  graphophone 
was  invented  operates  yet  New  laws  may  be  discovered,  but 
they  will  not  overthrow  old  ones.  The  truth  is  eternal  that  you 
cannot  gather  grapes  of  thorns  or  figs  of  thistles;  eternal  as 
the  laws  of  righteousness  upon  wliich  every  part  of  creation 
IS  based. 

'*  And  when  any  man  in  his  astonishment  at  new  discoveries 
supposes  that  a  diafram  or  any  tiling  else  that  was  not  made  to 


606  ELLEN   OR  THE 

do  it,  talks,  or  repeats  sounds  under  any  possible  circumstances, 
he  is  mistaken. 

**0r,  if  he  thinks  that  any  law  of  motion, — as  that  where 
multiple  motions  act  upon  a  body  at  the  same  time,  the  move- 
ment accomplished  is  not  that  of  either  one  but  a  resultant  of 
the  whole, — is  superceded — again  he  is  mistaken.  The  trouble 
isn't  with  nature's  laws,  but  in  man's  ignorance.  The  old  laws 
stand.  Once  more,  if  he  thinks  that  any  body  can  be  made  to 
vibrate  with  any  other  except  the  one  with  which  it  has  the 
same  normal  vibration ;  he  is  still  again  mistaken.  As  Ellen 
says,  no  newly  discovered  law  will  overthrow  any  old  one  but 
instead  must  act  in  harmony  with  it.  And  if  some  theory 
stands  in  its  way,  the  theory  must  be  abandoned. 

"  Take  articulate  speech ;  for  it  is  that  which  we  are  especially- 
considering.  We  know, — that  is,  any  one  with  good  sense 
does, — that  like  odor,  or  light,  articulate  speech  consists  of  very 
small  particles  of  matter,  which  are  manufactured  by  the  organs 
of  speech,  all  of  these  being  necessary  for  the  complete  result. 
Thus  a  number  of  letters  it  is  impossible  to  make  with- 
out closing  the  lips;  M  for  example.  Some  use  the  tongue 
more  than  others,  all  require  the  mouth,  and  are  uttered  from 
it;    so  that  with  all  the  mouth  must  be  open. 

"We  can  sec  the  remarkable  character  of  the  machinery 
by  which  articulate  speech  takes  place,  and  the  apparent 
impossibility  of  its  taking  place  without  such  machinery 
when  connected  with  a  human  body,  and  thus  at  man's  com- 
mand to  use.  Rut  as  has  been  found  out  that  telegraphy 
can  be  accomplished  without  wires ;  that  is,  by  an  invisible 
wire,  so   it  is  entirely  possible  that  sound  can  be  made  by  in- 


WHISPERINGS   OF  AN   OLD   PINE 


607 


visible  machiaery,  as  for  instance  in  the  brafn,  as  Ellen  has 
suggested^  for  the  purposes  of  memory. 

**  The  electricity  of  the  air  may  be  used  in  telegraphy  as  well 
as  that  in  a  wire,  and  Ellen  supposes  similar  currents  can  be 
used  for  floating  sound.  For  she  knows  as  she  has  repeatedly 
told  the  old  Pine  that  particles  of  sound  in  infinite  number  will 
ascend  the  point  of  the  finest  needle.  This  anyone  may  find 
out  by  experiment ;  and  that  means  they  are  small  enough  to 
go  in  invisible  wires»  or  be  carried  by  invisible  forces. 

**  Again,  nothing  happens  throughout  this  wonderfully  per- 
fect universe  not  in  harmony  with  all  its  conditions.  That  is, 
no  log  will  float  in  any  stream  unless  the  stream  is  big  enough 
to  float  it.  Neither  will  any  particle  of  sound.  And  it  is  just 
as  true  that  neither  log  or  sound  can  exist  without  proper 
conditions  for  producing  them.  So  far  as  we  know  the  logs  are 
grown  in  soil,  and  there  is  no  other  way  that  they  can  be  pro- 
duced ;  and  sounds  are  made  by  different  instruments,  and 
there  is  no  other  way  that  they  can  be  made. 

*'But»  as  there  is  a  marked  difference  in  size  between  the  logs 
and  sound  so  there  might  be  between  the  machiner>'  fashion- 
ing them.  The  machinery  which  makes  an>'thing  must  be 
strong  enough  and  large  enough  to  make  it.  For  instance, 
that  which  shapes  lumber, — a  sawmill, — must  be  big  enough  to 
do  it,  and  therefore  it  would  be  impossible  that  machinery 
capable  of  dressing  lumber  could  be  included  in  a  grapho- 
phone  record.  But  it  might  be  very  different  with  machinery 
to  make  sounds,  any  sounds.  For  we  have  seen  that  these 
particles  of  sound  are  according  to  our  standards  infinitely 
small     Then  the  machinery  necessary  to  make  them  according 


6o8 


ELLEN   OR  THE 


to  our  standard,  migTit  be  infinitely  small,  and  therefore  te  in- 
cluded in  a  graphophone  recordt  if  there  was  anything  to  rnake 
this  machinery  and  place  it  there. 

'*  Very  possibly  those  instruments  which  we  recognize  as 
sound-producing  instruments  are  fashioned  large  so  that  we 
can  use  them ;  that  is,  so  that  they  will  harmonize  unth  other 
things  which  we  use  and  generally  be  conveoient  for  our  use; 
and  not  at  aU  because  such  size  is  necessary  to  produce  the 
sounds  which  they  make.  In  this  view  it  would  be  possible 
that  every  sound  might  produce,  in  miniature,  the  instrument 
which  could  make  it,  and  that  this  was  included  in  the  grapho- 
phone record ;  although  as  Ellen  thinks,  with  these  infinitesimal 
sound  instruments,  diaframs  and  megaphones  are  necessary  for 
satisfactory  results. 

"But  this  is  certain  all  sounds  do  produce  miniature  instru- 
ments which  will  repeat  the  sounds  producing  them,  so   that 
Ellen  is  obliged    to  accept  the   fact,  and  account   for  it  the 
best  she  can.     And  naturally  she  accounts  for  it  in  part  because 
the  sounds  themselves  are  of  such  infinitesimal  character.      It 
is  of  course  inconceivable  that  it  should  connect  with  any  sup- 
posed system  of  air  waves.     But  it  teaches  Ellen  that  in  that 
region  impervious  to    our  vision  conditions  of    matter   exist, 
governed  by  laws  similar  to  those  which  we  see  operate;   and 
from  this  region  are    drawn  forces  and  things  without  which 
there  could  be  no  universe;   and  these  include  sound,  light, 
and  heat,  and  doubtless  a  million  other  things  whether  more 
or  less  important  she  does  not  know, — for  she  believes  all  to 
be  important, — than  the  stone   that  she  sees,  or  the  bird,  or 
the   tree.     And    these   infinitesimals,  she   can   well   imagine. 


•V 


WHiSrERlNGS   OF  AN    OLD    FINE 


609 


indeed  with  her  mind's  eye  perceive,  make  up  in  quantity 
what  they  may  want  in  size;  for  where  there  is  one  stone,  or 
one  bird,  or  one  tree,  there  may  be  hundreds  of  millions  of 
these,  to  us  infmitesimals,  permeating  infinite  space. 

**  But  beyond  question  they  differ,  as  do  those  things  which 
we  see,  and  from  similar  causes;  that  is,  they  differ  chemi- 
cally. Thus  we  have  waters,  milks,  saps,  liquors,  all  fluids,  but 
with  differences  between  them;  and  thus  we  have  electricity,  a 
fluid  of  a  very  different  quality,  but  unquestionably  belonging 
to  a  class,  and  all  a  part  of  that  element  which  we  call  matter, 
and  which  though  in  its  different  phases  governed  by  very 
different  laws,  so  that  some  things  fall  and  others  rise,  yet  as 
a  whole  is  subservient  to  certain  universal  laws  controlling  its 
manner  of  formation,  and  the  character  of  those  forms. 

'*In  the  long  article  from  the  Westminster  Review  is  a  very 
excellent  description  of  the  action  of  the  telegraph,  for  no 
false  theory  fortified  with  thousands  of  years  of  talk  and  study, 
and  numerous  text-books,  interfered  to  mislead  ;  but,  on  account 
of  these,  everything  connected  w^ith  the  telephone  is  far-fetched 
and  mythical,  and  much  of  it  absurd  and  impossible. 

** These  two  great  systems  of  communication,  like  all  things 
in  nature,  are  both  exceedingly  plain  and  simple.  The  tele- 
graph depends  upon  the  laws  governing  electricity  and  magne- 
tism. And  the  telephone  upon  those  governing  electricity 
and  sound.  Indirectly  sound  enters  into  the  telegraph,  but  in 
a  very  different  way  from  what  it  docs  into  the  telephone, 
being  practically  a  side  issue.  The  telephone  deals  more 
directly  with  sound,  transferring  it. 

**  One  simple  law  that  sound   may  be  instantaneously  trans- 


6lO  ELLEN  OR  THE 

ferred  by  an  electric  current,  answers  eveiy  purpose.  The 
vibration  of  the  diafram,  the  different  ways  it  is  made  to 
vibrate,  its  repeating  speech  or  other  sounds,  or  its  making 
the  graphophone  records — all  belong  to  the  category  of  things 
that  the  scientists  treasure  up,  which  are  not  so. 


XLII 


^^]^LLEN  will- now  quote  to  the  old  Pine  various  experi- 
ments and  facts  given  by  Count  Du  Monccl,  Membre  de 
L'Institut,  in  his  book  'The  Telephone,  The  Microphone  and 
The  Phonograph,*  translated  and  published  by  Harper  Bro- 
thers, 1879.  These  amount  to  a  flood  of  demons^trations 
that  none  of  the  explanations  hitherto  given  in  science  of  the 
operation  of  the  telephone  explain,  and  also  that  Ellen's 
explanation,  that  sound  is  an  entity  carried  by  the  electric 
current  through  the  wire,  does  explain  ever}'  experiment  and 
all  known  conditions: 


THE   HISTORY  OF  THE   TKLEPHOXE. 

*  Strictly  Speaking,  ihe  telephone  is  merely  an  instrument  adapted  for 
the  transmission  of  sound  to  a  distance,  and  this  idea  of  transmitting 
sound  is  a^old  as  the  world  itself.  The  Creeks  made  use  of  means 
which  might  affect  it,  and  there  is  no  doubt  that  these  means  were 
sometimes  iLsed  for  the  pagan  oracles.  But  such  transmission  of  sound 
was  within  somewhat  narrow  limits,  and  certainly  did  not  exceed  those 
of  a  speaking-tube.  Mr.  Freeze  considers  that  the  earliest  document  in 
which  this  transmission  of  sound  to  a  distance  is  distinctly  formulated 
dates  from  1667  :  he  refers  to  a  paper  by  one  Robert  Hooke,  who 
writes  to  this  effect :     *'  It  is  not  impossible  to  hear  a  whisper  at  a 


rii^M&i 


6t4 


ELLEN   OR   THE 


furlong's  distance,  it  having  been  already  done;  and  perhaps  the 
nature  of  the  thing  would  not  make  it  more  hupossible,  though  that 
furlong  should  be  ten  times  multiply'd.  Antl  though  some  famotis 
authors  have  affirmed  it  impossible  to  hear  through  the  thinnest  pbte 
of  mascovy  glass,  yet  1  know  a  way  by  which  'lis  msy  enough  to  hear 
one  speak  through  a  wall  a  yard  thick*  It  has  Tiot  yet  l:>een  thoroughly 
examined  how  far  olacousticons  may  be  iniiiroved,  nor  what  other 
ways  there  may  be  of  quickening  our  hearing,  or  conveying  sound 
through  other  bodies  than  the  air ;  for  that  is  not  the  only  medium,  I 
can  assure  the  reader  that  I  have,  by  the  help  6f  a  distended  wire 
propagated  the  sound  to  a  very  considerable  distance  in  an  instant,  or"" 
with  aa  seemingly  quick  a  motion  as  that  of  light,  at  least  incoaipa^bly 
quicker  than  that  which  at  the  same  time  was  propagated  through  the 
air :  and  this  not  only  in  a  straight  line  or  direct,  but  in  one  bended  in 
many  angles/' 

'  This  plan  for  the  transmission  of  sound  is  the  principle  of  the 
string  telephones  which  have  attracted  attention  for  some  years,  and  it 
remained  in  the  stage  of  simple  experiment  until  1819,  when  Sir 
Charles  VVheatstone  applied  it  to  the  magic  lyre.  In  this  instrument 
sounds  were  transmitted  through  a  long  strip  of  deal,  with  one  end  in 
connection  with  a  sounding  board :  one  step  more  led  to  the  use  of 
the  membrane  employed  in  string  telephones.  It  would  be  difficult  to 
say  with  whom  this  idea  originated,  since  it  is  claimed,  as  if  beyond 
dispute,  by  several  telephone-makers.  If  we  may  believe  some  trav- 
ellers, it  has  long  been  used  in  Spain  for  the  correspondence  of  lovers. 
However  this  may  be,  it  was  not  to  be  found  among  the  scientific 
appliances  of  some  years  ago,  and  it  was  even  supposed  by  many 
persons  that  the  cord  consisted  of  an  acoustic  tube  of  slender  diameter. 
Although  the  instrument  has  become  a  child's  toy,  it  has  great  scien- 
tific importance,  for  it  proves  that  vibrations  capable  of  reproducing 
speech  may  be  extremely  minute,  since  they  can  be  mechanically 
transmitted  more  than  a  hundred  yards. 


WHISPERINGS   OF  AN   OLD    PINE 


615 


■  From  the  telegraphic  point  of  view,  howex  er,  the  problem  of 
transmitting  sounds  to  a  distance  was  far  from  being  solved  in 
this  way,  and  the  idea  of  applying  electricity  to  this  mode  of  trans- 
mission naturally  arose  as  soon  as  the  wonderful  effects  of  electric 
telegraphy  were  observed,  that  is,  in  the  years  subsequent  to  1839.  A 
surprising  discovery  made  in  America  by  Mr*  Page,  in  1837,  and  after* 
ward  investigated  by  MM*  Wertheim,  de  la  Rive,  and  others,  must  also 
have  led  up  to  it,  for  it  was  observed  that  a  magnetic  bar  could  emit 
sounds  when  rapidly  magnetized  and  demagnetised  ;  and  these  sounds 
corresponded  with  the  number  of  currents  which  produce  them/    •     * 

'*In  speaking  of  the  box  and  string-wire  telephone,  which  has 
neither  electric  current  or  magnetism,  this  book  says: 

*  Messrs.  Heaviside  and  Nixon,  in  their  experiments  at  Newcastle- 
on-Tyne,  have  ascertained  that  the  most  effective  wire  was  No.  4  of 
the  English  gauge.  They  employed  wootlen  disks  an  eight  of  an  inch 
in  thickness,  and  these  may  be  placed  in  any  part  of  the  length  of  the 
wire.  When  the  wire  was  well  stretched  and  motionless,  it  was  possi- 
ble to  hear  what  was  said  at  a  distance  of  690  feet,  and  it  seems 
that  Mr.  Huntley,  by  using  very  thin  iron  diaframs,  and  by  insulating 
the  line  on  glass  supports,  was  able  to  transmit  speech  for  2450  feet, 
in  spite  of  the  ziz-zags  made  by  the  line  on  its  supports/ 

**In  other  words  sound  went  through  the  wire  and  was  heard 
over  three  times  as  far  when  the  wire  was  insulated,  which  sus- 
tains in  the  strongest  possible  manner  Oersted  and  Kitter's 
statements  that  sound  was  electrical. 

•  #•••»• 

•  Mr.  Treece  wrote  on  the  subject  in  a  paper  entitled  **  On  some 
Physical  Points  cotmected  with  the  Telephone,"  which  was  published 
in  Aprils  1878,  He  observes  that  all  the  attempts  to  improve  the  tele- 
phone have  ended  in  disappointment   and  failure.     One  of  the  first 


ELLEN    OR   THE 


fipts  of  the  kind  was  made  by  Mr,  AMlmol,  who  expected  to  obtain 
krable  results  by  augmenting  the  number  of  diaframs,  helices  and 
fnets,  connecting  the  helices  in  2.  series^  und  causing  them  to  act 
lultaneously,  so  as  to  increase  the  energy  of  the  currents  developed  by 
lence  of  the  voice ;  but  experience  showed  thai  when  the  instni- 
nient  acted  directly,  the  vibratory  effect  of  each  of  the  diaframs 
reased  in  proportion  to  their  number,  and  the  general  effect 
lined  the  same  as  with  a  single  diafram.  Mr,  Wilmot's  instnimeiit 
made  in  the  beginning  of  October,  1877,  and  that  of  M.  Trouve 
was  only  an  imitation  of  it.     *     *     *     * 

'  Thus,  for  example,  it  appears  that  the  vibrations  of  air  caused  in  the 
mouth-piece  ought  to  be  immediately  directed  on  the  surface  of  the 
diaframs  by  means  of  distinct  channels  ;  It  is  necessary  that  the  empty 
space  around  each  diafram  should  be  sufficiently  limited  to  prevent 
echoes  and  intermptions,  unless  the  case  is  so  large  that  there  is  no 
danger  of  such  effects^  Above  all,  it  is  necessary  that  the  organs  shottid 
be  fixed  in  some  material  unsusceptible  of  reverberation,  and  for  this 
reason  a  prefereTiLC  is  piven  to  iron  or  ebonite.  It  h  certain  fhal^ 
when  the  instrument  is  properly  made,  its  effects  are  superior  to  those 
of  the  Bell  telephones;  and  it  is  asserted  in  the  Telegraphic  Journal 
that  experiments  were  made  with  one  of  these  instruments  before  the 
Royal  Society,  in  London,  May  ist,  1878,  and  that  the  intensity  of 
sound  was  in  proportion  to  the  number  of  diaframs.  This  instrument 
was  designed  by  Mr.  Cox  Walker,  of  York,  and  possessed  eight 
diaframs.  He  considers  that  this  is  the  arrangement  which  gives  the 
best  results.     *     *     *     * 

Experiments  on  the  Part  taken  by  the  Different  Telephonic  Organs 
in  the  Transmission  of  Speech, 

*  In  order  to  introduce  all  the  improvements  of  which  a  telephone  is 
capable,  it  is  important  to  be  quite  decided  as  to  the  effects  produced 
in  the  several  parts  of  which  it  is  composed,  and  as  to  the  part  taken 


WHlSPERi:Nu>    uF 


PTNE 


617 


by  the  several  organs  which  arc  at  work.  To  attain  this  object  several 
men  of  science  and  engineers  have  undertaken  a  series  of  experiments 
which  have  produced  ver>'  interesting  results, 

*One  of  the  points  on  which  it  was  most  important  to  throw  light 
was  that  of  ascertaining  whether  the  vibrating  plate,  used  in  their  tele- 
phone receivers  by  Messrs.  Bell  and  (Jray,  is  the  only  cause  of  the  com- 
plex vibrations  which  reproduce  speech,  or  if  the  different  parts  of  the 
electro-magnetic  system  of  the  instrument  all  conduce  to  this  effect* 
The  experiments  made  by  Mr.  Page  in  1837  on  the  sounds  produced 
by  the  resonant  electro-magnetic  rods,  and  the  researches  pursued  in 
1846  by  Messrs,  de  la  Rive,  Wertheim,  Matteucci,  etc.,  on  this  curious 
phenomena,  allow  us  to  state  the  question,  which  is  certainly  more 
complex  than  it  first  appears, 

•  In  order  to  start  from  a  fixed  point,  it  must  first  be  ascertained 
whether  a  telephone  can  transmit  speech  without  a  vibrating  plate. 
Experiments  made  by  Mr.  Edison  in  November,  1877,  with  telephones 
with  copper  diaframs,  which  produced  sounds,  make  the  hyp'^thesis 
credible ;  and  it  receives  greater  weight  from  the  experimenis  made  by 
Mr,  Preece  and  Mr.  Blylh.  The  fact  was  placed  bevond  a  doubt  by 
Mr.  Spottiswoode  (see  the  TdegraphU  Journal  of  March  ist,  1878), 
who  assures  us  thai  the  vibrating  plate  of  the  telephone  may  be  entirely 
suppressed  without  preventing  the  transmission  of  speech,  pro\nded  that 
the  j>ol3r  extremity  of  the  magnet  be  |>lared  quite  close  to  the  ear ; 
and  it  was  after  this  that  I  presented  to  the  Acadt5mie  ties  .St.iences  my 
paper  on  the  theory  of  the  telephone,  which  led  to  an  interesting  dis- 
cussion which  I  shall  speak  of  presently.  At  first  the  authenticity  of 
these  results  was  denied,  and  then  an  attempt  was  made  to  explain  the 
sounds  heard  by  Mr.  Sptittiswoo^le  as  a  mechanical  transmission  of  the 
vibrations,  eflfected  aflcr  the  manner  of  string  telephones;  but  the 
numerous  experiments  which  have  subsequently  been  made  by  Messrs. 
Warwick,  Rossetti,  Hughes,  Millar,  Moyd.  Buchin,  CanestrcUi,  Wisen- 


^IliMil^ 


iitfaki 


'^"^  —^ 


6l8  ELLEN  OR  THE 

danger,  Varley,  and  many  others,  show  that  this  is  not  the  case,  and 
that  a  telephone  without  a  diafram  can  transmit  speech  electrically. 

'  Colonel  Navez  himself,  who  had  first  denied  the  fact,  now  admits 
that  a  telephone  without  a  diafram  can  emit  sounds,  and  even,  under 
certain  exceptional  conditions,  can  reproduce  the  human  voice ;  but  he 
still  believes  that  it  is  impossible  to  distinguish  articulate  words. 

'This  uncertainty  as  to  the  results  obtained  by  the  different  physicists 
who  have  studied  the  matter  shows  that  at  any  rate  the  sounds  thus 
reproduced  are  not  clearly  defined,  and  that  in  physical  phenomena, 
only  appreciable  to  our  senses,  the  appreciation  of  an  effect  so  unde- 
fined must  depend  on  the  perfection  of  our  organs.  We  shall  pres- 
ently see  that  this  very  slight  effect  can  be  largely  increased  by  the 
arrangement  adopted  by  Messrs.  Bell  and  Gray,  and  we  shall  also  see 
that,  by  a  certain  mode  of  magnifying  the  vibrations,  it  has  been 
decisively  proved  that  a  telephone  without  a  diafram  can  readily  repro- 
duce speech.  I  proceed  to  give  the  description  of  such  a  telephone 
which  was  shown  by  Mr.  Millar  at  the  meeting  of  the  British  Association 
at  Dublin  in  August,  1878. 

*  This  instrument  consists  of  a  small  bar  magnet,  three  inches  in 
length  and  five-sixteenths  of  an  inch  in  width  and  thickness,  and  a 
copper  helix  (No.  30)  of  al)oiit  six  metres  in  length  is  wound  round 
the  bar.  It  is  fixed  in  a  box  of  rather  thick  pasteboard,  fitted  above 
and  below  with  two  zinc  plates,  which  render  it  very  portable.  With 
a  telephonic  battery  sender  and  single  Leclanche  cell,  speech  can  be 
perfectly  transmitted ;  the  whistling  of  an  air,  a  song,  and  even  the 
act  of  respiration  becomes  audible.  It  seems  also  that  the  instrument 
can  act  without  a  magnet,  merely  witii  a  piece  of  iron  surrounded  hv 
the  helix ;  but  the  sounds  are  then  much  fainter. 

*  Signer  Ignace  Canestrelli  obtained  the  same  results  by  making  one 
of  the  carbon  telephonic  seiulers  react  on  a  telephone  without  a  dia- 
fram, by  means  of  an  induction  coil  influenced  by  two  Bunsen  cells. 
He  writes  as  follows  on  the  subject : 


5PERINGS   OF   AN 


PINE 


*"\Vith  this  arrangement  I  was  able  to  hear  the  sound  of  any  musi- 
cal instrument  on  a  telephone  without  a  diafram  ;  singing,  sneaking, 
and  whistling  were  perfectly  andible.  Whistling  could  be  heard  even 
when  the  telephone  without  a  dialram  was  placed  at  some  distance 
from  the  ear.  In  some  cases  depending  on  the  pitch  of  the  voice,  on 
the  distance  of  the  sending  station,  and  on  the  joint  pressure  exerted 
by  the  carlx>ns,  I  could  even  distinguish  words. 

*  **  I  finally  discharged  the  currents  of  the  transmitter  into  the  coils 
of  insulated  copper  wire  with  which  the  two  poles  of  a  magnet  were 
pro%^ided.  This  magnet  was  placed  on  a  musical  box,  made  of  very 
thin  slips  of  wood,  and  on  placing  the  ear  at  the  opening  of  the  box  I 
obtained  the  same  results  as  with  the  ordinary  telephones  without  a 
diafram." 

*  I  repeat  finally  the  account  of  some  experiments  made  by  Mr. 
Hughes  and  M.  Taul  Roy  which  are  interesting  from  our  present  point 
of  view, 

*  I  If  an  armature  of  soft  iron  is  applied  to  the  poles  of  an  electro- 
magnet, with  its  two  branches  firmly  fixed  on  a  board,  and  if  pieces  of 
paper  are  inserted  between  this  armature  and  the  magnetic  poles,  so  as 
to  obviate  the  effects  of  condensed  magnetism  ;  if,  finally,  this  electro- 
magnet is  connected  with  a  speaking  microphone  [see  Figure  21,  page 
399],  it  is  pos.sible  to  hear  the  words  spoken  in  the  microphone  on  the 
board  which  supports  the  electro- magnet. 

'  2.  If  two  electro- magnets  are  placed  in  communication  with  a 
microphone,  with  their  poles  of  contrary  signs  opposite  to  each  other, 
and  if  their  poles  are  separated  by  pieces  of  paper,  speech  will  be  dis- 
tinctly reproduced,  without  employing  armature  or  diafram.  These 
experiments  are,  however,  delicate,  and  demand  a  practised  ear. 

*  3.  If,  instead  of  causing  the  current  produced  by  a  microphone  to 
pass  through  the  helbt  of  a  receiving  telephone,  it  is  sent  directly  into 
the  bar  magnet  of  this  telephone  in  the  direction  of  its  axis — that  is, 
from  one  pule  to  another — the  words  pronounced  in  the  microphone 


—  .■^. — 1:^-     -    L  j^n^^  "Ajw  -wi'm' 


:      :     .:.  ..dtt^TT.      "^irtn     ~:e-:i:*   n" 


.-■y  .a;.  :r.^  j.  nr.jer  on 


'■•;/-'  ..:■•'.  .  ,  ..yvever,  snow  th-it  v::»rv 
•■  'i  .fr.rji  rr  v.-  rL-«.ci%-ing  telephone:  they 
i.iMit,   :,rit  .Mr.   li'.ake    asserts   that    they    are 


WHtSPERINGS   OF   AN   OLD    liNE 


621 


enough  to  cause  a  very  light  index,  resting  on  the  diafram,  to  make 
slight  inflections  on  a  line  which  it  describes  on  a  register.  Vet  this 
small  vibration  of  the  diafram  does  not  show  that  it  is  due  to  the  effect 
of  attraction,  for  it  may  result  from  the  act  of  magnetization  itself  in  the 
center  of  the  diafram.  An  interesting  experiment  by  Mr»  Hughes, 
rei>eated  under  different  conditions  by  Mr.  Millar,  confirms  the  opinion.' 


•'These  accurate  experiments  in  regard  to  the  so-called  vibra- 
tions  of  diaframs  practically  show,  as  Ellen  has  said,  that  they 
do  not  vibrate  at  all.     The  whole  thing  is  a  humbug. 

'  If  the  magnet  of  a  receiving  telephone  consists  of  two  magnetized 
bars,  perfectly  equal,  separated  from  each  other  by  a  magnetic  insu- 
lator, and  they  are  so  placed  in  the  coil  as  to  bring  alternately  the  i>oles 
of  the  same  and  of  contrary  signs  opposite  to  the  diafram,  it  is  known 
that  the  telephone  will  reproduce  speech  better  in  the  latter  case  than 
in  the  former.  Now,  if  the  effects  were  due  to  attraction,  this  would 
not  be  the  case  ;  for  the  actions  are  in  disagreement  when  the  poles  of 
contrary  signs  are  subjected  to  the  same  electric  influences,  while  ihey 
are  in  agreement  when  these  jioles  are  of  like  signs. 

'  On  the  other  hand,  it  is  known  that  if  several  iron  plates  are  put 
together  in  onkr  to  form  the  diafram  of  the  receiver,  the  transmission 
of  soun<ls  is  much  stronger  than  with  a  simple  diafram  ;  and  yet  the 
attraction,  if  it  has  anything  to  do  with  it,  could  only  be  exerted  on 
one  of  the  diaframs. 

*  It  further  appears  that  it  is  not  merely  the  magnetic  core  which 
emits  sounds,  but  that  they  are  also  produced  with  some  distinct- 
ness by  the  helices.  Signor  Rossetti  had  already  ascertained  this  fact, 
and  had  even  remarked  that  they  could  be  animated  by  a  slight  oscil- 
latory movement  along  the  bar  magnet,  when  they  were  not  fixed  upon 
it     Several  observers,  among  others,  M-  Paul  Roy,  Herr  Wiesendanger, 


622  ELLEN   OR  THE 

and  Signor  Canestrelli,  have  since  mentioned  nmilar  fuits,  which  arc 

really  interesting. 

'"If,"  writes  M.  Paul  Roy,  "a  coil  of  fine  wire,  which  is  at  the 
extremity  of  the  bar  magnet  of  a  Bell  telephone,  receives  the  pulsatory 
currents  transmitted  by  a  carbon  telephone,  it  is  only  necessary  to 
bring  the  coil  close  to  the  ear  in  order  to  hear  the  sounds. 

'  "  The  sounds  received  in  this  way  are  very  faint,  but  become  mach 
stronger  if  a  piece  of  iron  is  introduced  into  the  circuit  coil.  A  mag- 
net acts  with  still  greater  force,  even  when  it  consists  of  a  simple  Mag- 
netized needle.  Finally,  the  sound  assumes  its  maximum  intensity 
when  an  iron  disk  is  inserted  between  the  ear  and  the  coiL 

'  "  By  placing  the  end  of  the  coil  to  the  ear,  and  sending  a  current 
through  it  from  the  bar  magnet,  it  is  ascertained  that  the  sound  is  at 
its  minimum  when  the  neutral  line  of  the  magnet  is  enclosed  by  the 
coil,  and  that  it  increases  until  attaining  its  maximum,  when  the  magnet 
is  moved  until  one  of  its  poles  corresponds  to  the  coil. 

' "  lliis  fact  of  the  reproduction  of  sounds  by  a  helix  is  universal. 
Every  induction  coil  and  every  electro-magnet  are  capable  of  reproduc- 
ing s^nind  wiicn  the  rurrents  of  the  senler  are  of  sufficient  intensity." 

*  Signr)r  Canestrelli  writes  as  follows:  "With  the  combination  of  a 
carbon  teiej>hone  an<l  one  without  diafram  or  magnet — that  is,  with 
only  a  simple  coil — I  was  able  to  hear  whistling  through  the  coil, 
placed  close  to  the  ear.  This  coil  was  of  very  fine  copper  wire,  and 
the  currents  were  pro  luced  through  an  induction  coil  by  two  Bunsen 
elements.  The  contacts  of  the  telephone  were  in  carbon,  and  it  was 
inserted  in  the  jjrimary  circuit. 

'  **  I  fastened  the  coil  to  the  middle  of  a  tightly-stretched  membrane 
which  served  as  the  base  of  a  short  metal  cylintler.  When  a  magnet 
was  j)laced  near  this  part  of  the  coil,  the  sounds  were  intensified,  and 
when  I  fixed  the  magnet  in  this  ])osition,  I  could  hear  what  was  said. 

*"I  afterward  substituted  for  the  magnet  a  second  coil,  fastened  to  a 


WnrsPERlNGS   0¥   AN    (JLD    PINE 


623 


wooden  bar,  and  on  causing  the  indnceil  currents  to  pass  into  both 
coils  at  once  I  was  able  to  hear  articulate  speech,  although  not  without 
difficulty* 

*  *'  Under  these  latter  conditions  I  found  it  possible  to  construct  a 
telephone  without  a  magnet^  but  it  required  a  strong  current,  and  it 
was  necessary  to  speak  into  the  sender  in  a  special  manner,  so  as  to 
produce  strong  and  concentrated  sounds/* 

'Another  very  interesting  experiment  by  M.  A,  Brc^guet  shows  that 
all  the  constituent  parts  of  the  telephone — the  handle,  the  copper 
rims,  and  the  case,  as  well  as  the  diafram  and  the  electro- magnet — can 
transmit  sounds.  RL  Br^guet  ascertained  this  fact  by  the  use  of  string 
telephones,  which  he  attached  to  different  parts  of  the  telephone  on 
which  the  experiment  was  made.  In  this  way  he  was  not  only  able  to 
establish  a  correspondence  between  the  person  who  worked  the  electric 
telephone  and  the  one  who  was  listening  through  the  string  telephone, 
but  he  also  made  several  string  telephones  act,  which  were  attached  to 
different  parts  of  the  electric  telephone.* 

**The  only  possible  explanation  of  this  experiment  is  that 
sound  is  an  entity,  carried  first  by  the  ekctriQ  current,  and  then 
making  its  way  through  the  string  telephone  by  its  power  of 
movement,  as  it  always  does  and  will  so  long  as  it  keeps  its 
life. 

'Tiiese  two  series  of  experiments  show  that  sounds  may  be  obtained 
from  different  parts  of  the  telephone  without  any  very  appreciable 
vibratory  move  men  ts»  But  Stgnor  Luvini  wished  for  a  further  assur- 
ance of  the  fact,  by  ascertaining  whether  the  magnetization  of  any  mag- 
netic substance,  followed  by  its  demagnetization,  would  involve  a  vari- 
ation in  the  form  and  dimensions  of  this  substance*  He  consequently 
caused  a  large  tubular  electro- magnet  to  be  made^  which  he  filled  with 


.jm^ 


,;'■  -  i.'.i       "..  r.n  '.W'.ra.. —    '.r   l:it   IiTiLlW^  1=rT    IT  tilt   -StrL"^^- 

'/'     ",    vi.'"     '      ■:'    -...•*     I.  -i'.i-.^  ■     .''    ^:.J    ir-LiiKTiiia::   itt    i^nii 
-  *-  .  .'.V:.-    *     ......^  •-*    ;-. --.rr:-*    —    -  •-.■  -**^--t  ■r'.?.rTH--^T— «7^T>j.  x^.; 

*    ','*.>  "Ai"  '.".    *"".'.■''*  "1  »''^T'^  " -ii "  ~  ''  '^'t  --nil  sirs-  rc-s  ^.-li  ?-.  • 


jrOfj   '..    K    .ili'l    \>.:'  ':■ 


:'.  ■:  ''.  •'  :  -.■..'';■  ;  .-  •:'.  '.z^t.  to  the  ear.  the 
-■■-  ■;  '.  ■■■  '  ■  •  -'  '.  -"-*  r.-r:ire:.  Aliho'-ij^h  iron 
'.:.  '  '•■■:  -.*:.*.  '  :.  '.  =!<s  are  not  absolutely 
■.:...::.-•.  -.  <-:.  '--  ^.-^o  :xt  penectly.  I 
:.-.  .V-.  V.  :■  '  ^  ::.•  !  >tan'  e,  ani  conkl  not  heai 
,  ;  '  -,:.*:.:.  :-:  r.  -  '  ■.'.•  ':.x:'.jy.ri.  I  took  away  the 
.':'  .-';-.-,  ih--    iintri.-iiciit  a  wiile  iron   bar  an   inch 


WHISPERINGS   OF  AN   OLD   PINE 


thick.  On  applying  my  ear  to  it,  I  could  hear  every  sound  distinctly, 
but  somewhat  more  faintly.  A  piece  of  copper,  tliree  inches  square, 
was  substituted  for  it ;  although  the  sound  waii  still  distinct,  it  was 
fainter  than  before.  Thick  pieces  of  lead,  zinc  and  steel  were  alter- 
nately tried.  The  steel  acted  in  almost  the  same  way  as  the  iron,  and, 
as  in  the  other  cases,  each  word  was  heard  faintly  but  distinctly* 
Some  of  these  metak  are  diamagnetic,  and  yet  the  action  took  place. 
Some  non-metallic  substances  were  next  tried  :  first,  a  piece  of  window 
glass,  which  acted  very  well*  The  action  was  faint  with  a  piece  of  wooden 
match-box  ;  but  on  using  nieces  of  gradually  increasing  thickness  the 
sound  was  sensibly  increased,  and  with  a  piece  of  solid  wood,  one  inch 
and  a  half  in  thickness,  the  sound  was  perfectly  distinct.  I  next 
replaced  it  by  an  empty  wooden  box,  which  acted  very  well,  A  piece 
of  cork,  half  an  inch  thick,  acted,  but  somewhat  faintly.  A  block  of 
razor-stone,  two  Inches  thick,  was  placed  upon  the  instrument,  and,  on 
applying  the  ear  to  it,  it  was  quite  easy  to  follow  the  speaker.  I  then 
tried  to  hear  without  the  insertion  of  any  substance,  and,  on  applying 
my  ear  close  to  the  coil  and  magnet,  I  heard  a  faint  sound,  and  on 
listening  attentively  I  understoo<i  all  that  was  said.  In  all  these 
experiments  the  sounds  were  perceived,  but  the  sounds  transmitte<i  or 
attempted  did  not  act  precisely  alike.  The  soimd  of  a  tuning  fork, 
placed  on  the  iron  disk  itself  or  on  the  case  of  the  instrument,  was 
clearly  heard  ;  thin  iron  disks  were  more  ef!ective  for  articulate  speech. 
With  other  substances,  stone,  solid  wood,  glass,  zinc,  etc.,  the  sound 
of  the  tuning  fork  was  heard,  whether  it  rested  upon  them,  or  the 
^^m  vibrating  fork  was  held  above  them.  These  substances  were  not 
^^^  adapted  for  transmitting  the  soimd  of  the  voice.  These  wxre  all  laid 
^^^  aside,  and  the  sounding  instniment  was  held  directly  above  the  pole  of 
^^P  the  magnet ;  the  sound  was  clearly  heard,  although  there  was  nothing 
■  but  air  between  the  end  of  the  magnet  and  the  tuning-fork.    The  sound 

^^L        was  perhaps  less  intense  when  the  tuning-fork  was  held  directly  above 


626  ELLEN   O^.  THE 

the  pole  than  when  it  was  at  the  end  of  the  magnet.  I  next  tried  if 
my  voice  could  be  heard  with  this  arrangement.  The  result  was  rather 
doubtful,  but  I  think  that  some  action  must  have  taken  place,  for  the 
tuning-fork  was  heard  when  it  was  simj)ly  vibrated  near  the  pole.  The 
effect  of  the  voice  can  only  have  differed  in  the  degree  of  intensity  :  it 
was  too  faint  to  be  heard  at  the  otiier  extremity.  I  repeated  these 
effects;  I  assured  myself  of  them,  and  I  succeeded  in  transmitting 
distinctly  on  the  \to\e  without  a  disk,  and,  on  the  other  hand,  by  apply- 
ing my  ear  to  the  instrument,  I  was  able  to  hear  distinctly  all  that  was 
said,  although  there  was  no  disk."     *     *     *     ♦ 

*  Mr.  Preece  sought  for  the  cause  in  the  induced  currents  developed 
in  any  conducting  body  when  a  magnet  is  moved  before  it,  which  give 
rise  to  the  phenomenon  discovered  by  Arago,  and  known  by  the  name 
of  magnetism  by  rotation.  Vet  these  facts  do  not  appear  to  us  to  be 
sufficiently  well  established  to  make  the  theory  worthy  of  serious  con- 
sideration, and  it  is  possible  that  the  effects  observed  resulted  from 
simple  mechanical  transmissions. 

*To  conclude  the  account  of  these  experiments,  we  will  add  that  Mr. 
\V.  F.  r>arrett  thinks  it  somewhat  dit'ticult  to  dol'ine  the  mode  of  vibra- 
tion of  the  (liafram,  >in(0,  while  a  certain  amount  of  compression  exerted 
on  the  iron  destroys  the  sounds  resulting  from  the  peculiar  efTects  of 
ma^^neti/ation  a  still  st^n^^er  compression  causes  them  to  reappear.  It 
is  ceitain  that  the  «|uestion  is  full  of  obscurity,  and  demands  great 
researc'n  :  it  is  enough  to  have  ^hown  that  the  theory  hitherto  held  is 
insufficient. 

'  lux/'trifnrnfs  on  the  rift'cts  i^'hich  result  from  ^f^^hafncai  shock 
CommuJiicatcJ  to  i/ifj'erent  piirts  of  ti  Tel'phonc, — 

*lf  a  piece  of  iron  is  aj)i)lie(l  to  the  screw  whi(h  holds  the  magnet  of 
an  ordinary  telephone,  it  is  observed  that  the  transmitted  sounds  are 
more  distinct,  owing  to  the  fon^e  supj)lied  to  the  active  pole  of  the 
magnet ;  but  at  the  moment  when  the  i)icce  of  iron  is  applied  to  the 


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WHISPERINGS   OF    AN   OLD    PIN! 


screw  a  distinct  noise  is  heard,  which  seems  to  be  due  lo  the  mechani- 
cal vibrations  caused  in  the  magnet  at  the  moment  of  the  shock.  M. 
des  Fortes,  a  lieutenant  in  the  French  navy,  has  lately  made  some  in- 
teresting experiments  on  this  class  of  phenomena.  He  has  observed 
that  if,  in  a  telephonic  circuit  of  ninety  yards  completed  by  the  earth, 
the  sending  telephone  is  reduced  to  a  simple  magnet,  provided  with 
the  coil  which  constituted  its  electro-magnetic  organ,  and  if  this  mag- 
net Is  suspended  vertically  by  a  silken  thread,  with  the  coil  above  it, 
a  blow  struck  upon  the  magnet,  either  by  a  copper  rod  or  a  piece  of 
wood,  will  cause  distinct  sounds  to  be  produced  in  the  receiving  tele- 
phone— sounds  which  will  increase  in  intensity  when  the  blow  is  struck 
close  to  the  coil,  and  which  will  become  still  stronger,  but  less  clear,  if 
a  vibrating  plate  of  soft  iron  is  placed  in  t  on  tact  with  the  upper  jxile 
of  the  magnet, 

'When  the  striking  instrument  is  made  of  iron,  the  sounds  in  ques* 
tion  are  more  strongly  marked  than  if  it  is  made  of  wood ;  and  when 
the  magnet  has  a  vibrating  disk  applied  to  its  active  pole,  a  vibration 
of  the  disk  takes  place  at  the  moment  when  the  shock  is  heard. 

'If  the  striking  body  is  a  magnet,  the  sounds  produced  resemble 
those  obtained  when  it  is  of  iron,  if  the  effect  is  produced  between 
poles  of  the  same  nature ;  but  if  the  poles  are  of  contrary  natures,  a 
second  noise  is  heard  after  each  blow,  which  is  produced  by  drawing 
away  the  magnet,  and  which  appears  to  be  a  blow  struck  with  much 
less  force.  The  sound  is  of  course  increased  if  the  magnet  is  provided 
with  its  vibrating  disk. 

'  If  words  are  uttered  on  the  vibrating  disk  of  the  sending  telephone, 
when  it  is  applied  to  the  pole  of  the  magnet,  various  sounds  are  he^ird 
on  the  receiving  telephone,  somewhat  similar  to  those  produced  by 
vibrating  one  of  the  strings  of  a  violin,  and  the  sound  made  in  with- 
drawing the  disk  from  contact  with  the  magnet  is  distinctly  heard  in 
the  receiver. 


630  ELLEN    OR   THE 

'  The  person  wlio  applies  his  ear  to  the  vibrating  disk  of  the  sender 
when  it  is  arranged  as  above,  may  hear  the  voice  of  any  one  who  speaks 
into  the  receiver.     •     *     * 

*  A  coil  is  not  necessary  in  order  to  perceive  the  IjIows  stmck  upon 
the  magnet  with  a  rod  of  soft  iron.  It  is  enough  to  wind  three  turns 
of  naked  conducting  wire,  which  jicts  as  a  line  wire,  round  one  end  of 
the  magnet,  and  the  sounds  perceived  cease,  as  in  other  experiments, 
when  the  circuit  is  broken,  plainly  showing  that  they  are  not  due  to 
mechanical  transmission*  It  is  a  still  more  curious  fact  that  if  the  mag- 
net is  placed  in  the  circuit,  so  as  to  form  an  integral  part  of  it,  and  if 
the  two  etids  of  the  conducting  wire  are  wound  round  the  ends  of  the 
magnetj  the  blows  struck  upon  the  latter  with  the  soft  iron  rod  are  per- 
ceived in  the  telephone  as  soon  as  one  pole  of  the  magnet  la  provided 
with  a  disk, 

'I  have  myself  repeated  M.  des  Fortes'  experiments  by  simply  striking 
on  the  screw  which,  in  ordinary  telephones,  fastens  the  magnet  to  the 
instrument,  and  I  have  ascertained  that,  w^henever  the  circuit  was  com* 
pletCj  the  blows  struck  with  an  ivory  knife  w^ere  repeated  by  the  tele- 
phone :  they  were,  it  is  true,  very  faint  when  the  vibrating  disk  was 
removed,  but  very  marked  when  the  disk  was  in  its  place.  On  the 
other  hand,  no  sound  was  perceived  when  the  circuit  was  broken. 
These  sounds  were  louder  when  the  blows  were  struck  upon  the  screw 
than  when  they  were  struck  on  the  pole  of  the  magnet  itself  above  the 
coil. 

'  Mr.  Thompson,  of  Bristol,  has  observed  that  if  a  piece  of  iron  and  a 
tin  rod  placed  perpendicularly  on  the  iron  are  introduced  into  the  cir- 
cuit of  an  ordinary  telephone,  it  is  enough  to  strike  the  tin  rod  in  order 
to  produce  a  loud  sound  in  the  telephone.  He  has  also  shown  that  if 
the  two  ends  of  the  bar  magnet  are  enclosed  by  two  induction  coils 
which  are  placed  in  connection  with  the  circuit  of  a  telephone,  and  if 
the  flame  of  a  spirit  lamp  is  moved  below  the  magnet  in  the  space 
dividing  the  two  coils,  a  distinct  sound  is  heard  as  soon  as  the  flame 


d 


WHISPERINGS    OF  AN    OLD    I'lNE 


0» 


exerts  its  influence  on  the  bar  magnet.  This  effect  is  undoubiedly  due 
to  the  weakening  of  the  magnetic  force  of  the  bar  which  is  produced  by 
the  action  of  the  heat.  I  have  my^eU  observed  that  a  scratching  sound 
on  one  of  the  wires  which  connect  the  telephones  is  heard  in  both  of 
them,  at  whatever  point  in  the  circuit  the  scratch  is  made.  The  sounds 
produre<l  are  indeed  very  faint,  but  they  can  be  distinctly  heard,  and 
they  become  more  intense  when  the  scratch  is  made  on  the  binding- 
screws  of  the  telephone  wires.  These  sounds  cannot  result  from  the 
mechanical  transmission  of  vibrations,  since  they  are  imperceplible 
when  the  circuit  is  broken.  From  these  experiments  it  appears  that 
some  sounds  which  have  been  obsened  in  telephones  tried  on  telegraph 
stations  may  arise  from  the  friction  of  the  wires  on  their  supports — a 
friction  which  produces  those  very  intense  soimds  which  are  sometimes 
heard  on  telegraphic  wires.     *     «     ♦     * 

*  Theory  of  the  Tekphone. — It  appears  from  the  several  experiments 
of  which  we  have  spoken  that  the  explanation  generally  given  of  the 
effects  produced  in  the  telephone  is  very  imperfect,  and  that  the  trans- 
mission of  speech,  instead  of  resulting  from  the  repetition  by  the  mem- 
brane of  the  receiving  telephone  (influenced  by  electro-magnetism),  of 
vibrations  caused  by  the  voice  on  the  membrane  of  the  transmitting 
telephone,  is  due  to  molecular  vibrations  produced  in  the  whole  elec- 
tro-magnetic system,  and  especially  on  the  magnetic  core  contained  in 
the  helix.  These  vibrations  must  be  of  the  same  nature  as  those  which 
have  been  observed  in  resonant  electro- magnetic  rods  by  MM.  Page, 
de  la  Rive,  Wertheim,  Matteucci,  etc.,  and  these  have  been  em- 
ployed in  telefihones  by  Reiss,  by  Cecil  and  Leonard  ^Vray,  anil  by 
Vanderweyde*     ♦     ♦     ♦     • 

*  What  is  the  nature  of  the  vibrations  sent  into  the  receiving  tele- 
phone? This  question  is  still  obscure,  and  those  who  have  studied  it 
are  far  from  being  in  agreement :  as  early  as  1846  it  was  the  subject  of 
an  interesting  discussion  betw^een  M.  M,  Wertheim  and  de  la  Rive,  and 


632 


ELLEN   OR  THE 


the  new  discoveries  render  it  still  more  complex,  M.  Wertheim  con- 
siders that  these  vibrations  are  at  once  longitudinal  and  transverse,  and 
arise  from  attractions  exchanged  between  the  spirals  of  the  magnetising 
helix  and  the  magnetic  particles  of  the  core*  M*  dc  la  Rive  holds  that 
in  the  case  we  are  considering  the  vibrations  are  simply  longitudinal, 
and  result  from  molecular  contractions  and  expansions  produced  by  the 
different  combinations  assumed  by  the  magnetic  molecules  under  the 
influence  of  magnetization  and  demagnetifation.     »     •     * 

'  The  difficulty  of  explaining  the  production  of  sounds  in  an  electro- 
magnetic organ  destitute  of  armature  cansetl  the  authenticity  of  the 
experiments  we  have  described  to  be  at  first  denied,  and  Colonel 
Navez  started  a  controversy  with  us  which  Is  not  likely  to  be  soon 
terminated,  yet  one  result  of  this  controversy  is  that  Colonel  Navez  was 
obliged  to  admit  that  the  s&und  of  the  human  v&ice  may  be  reproduced 
ty  a  teiepk&nic  receiver  without  a  disk.     #     *     •     » 

'  In  order  to  show  that  the  action  of  the  diafram  is  less  indispensable 
than  Colonel  Nave^  seems  to  imaginep  and  that  its  vibTations  are  not 
due  to  electro- magnetic  attractions,  it  will  be  enough  to  refer  to  Mr, 
Hughes*  experiments  we  have  mentioned  above.  It  is  certain  that  if 
this  was  the  effect  produced,  we  should  hear  better  when  the  two  bar 
magnets  present  their  poles  of  the  same  nature  before  the  diafram, 
than  when  they  present  the  poles  of  contrary  natures,  since  the  whole 
action  would  then  converge  in  the  same  direction.  Again,  the  more 
marked  effects  obtained  with  multiple  diaframs  in  juxtaposition  com- 
pletely exclude  this  hypothesis. 

«*  ♦  ♦  \Vg  are  not  now  concerned  with  the  discussion  of  mag- 
netic effects;  there  has  been  an  advance  in  science  since  Colonel 
Navez  started  the  controversy,  and  we  must  ask  how  his  theory  of  the 
movements  of  the  telephone  diafram  by  attraction  will  explain  the 
reproduction  of  speech  by  a  receiving  microphone  destitute  of  any 
electro-magnetic  organ,  and  I  can   assert  that  my  experiments  show 


WHISPERINGS   OF   AN   OLD    PINE 


^33 


that  there  can  he  no  mechanical  transmission  of  vibrations,  sirce  no 
sound  is  heard  when  the  circuit  is  broken  or  deprived  of  its  battery. 
Colonel  Navez  must,  therefore,  accept  the  molecular  vibralions.  This 
certainly  gives  us  a  new  field  for  study ;  but  it  is  because  European 
men  of  science  persist  in  remaining  bound  by  incomplete  theories  that 
we  have  allowed  the  Americans  who  despise  them  to  reap  the  glory  of 
the  great  discoveries  by  which  we  have  lately  been  astonished. 

'  The  experiments  quoted  above  show  that  sounds  may  be  reproduced 
not  only  by  simple  helices  without  an  electro- magnetic  organ,  but  also 
by  the  plates  of  a  condenser,  in  spite  of  the  pressure  exerted  upon 
them. 

*  In  conclusion,  the  theory  of  the  telephone  and  microphone  con- 
sidered as  reproductive  organs  of  speech,  is  still  far  from  being  per- 
fectly clear,  and  it  would  be  imprudent  to  be  too  positive  on  questions 
of  such  recent  origin. 

'The  theory  of  the  electric  transmission  of  sounds  in  electro-mag- 
netic telephones  is  somewhat  complex.  It  has  been  seen  that  they 
can  be  obtained  from  diaframs  of  non- magnetic  substance,  and  even 
from  simple  mechanical  vibrations  produced  by  shocks.  The  matter  is 
still  very  obscure.     •     •     ♦    • 

'  Af,  IViesendanger's  Thermaphone, — M.  Wiesendanger,  in  an  article 
inserted  in  the  English  Mer/ianic  ami  IFor/d  of  SdentCy  September 
13th,  1878,  ascribes  the  reproduction  of  speech  in  certain  telephones 
to  vibratory  movements  resulting  from  molecular  expansions  and  con- 
tractions produced  by  variations  of  temperature,  and  these  variations 
would  follow  from  the  currents  of  varying  intensity  which  are  trans- 
mitted through  the  telephonic  circuits.  He  was  conscious  of  one 
objectioD  to  this  theory,  namely,  that  the  movements  of  expansion  and 
contraction  due  to  heat  are  slowly  produced,  and  consequently  are  not 
capable  of  substantial  action,  rapid  enough  to  produce  vibrations ;  but 
he  considers  that   molecular  effects    need  not    take  place  under  the 


634  ELLEN  OR  THE 

same  conditions  as  those  which  are  displayed  in  the  case  of  material 
sutetances. 

'M.  Wiesendanger  believes  that  tiiis  hypothecs  wiD  explain  ttte 
reproduction  of  speech  in  the  receiving  microphones  of  Mr.  Hn^ei^ 
and  that  it  may  even  be  applied  to  the  theory  of  the  electro  mimetic 
telephone  if  we  consider  that  a  magnetizing  hdix,  as  well  as  a  mag- 
netic core,  round  which  an  electric  current  circulates,  is  more  or  less 
heated,  according  to  the  intensity  of  the  current  whidi  traverses  it, 
especially  when  the  wire  of  the  helix  and  the  core  are  bad  conductors 
of  electricity  and  of  magnetism.  Pursuing  this  idea,  M.  Wiesendanger 
has  sought  to  construct  telephones  in  which  calorific  effects  are  more 
fully  developed,  and  with  this  object  he  used  very  fine  wire  of  German 
silver  and  platinum  to  make  the  coils.  He  ascertained  tbaX  these  coils 
could  produce  sounds  themselves,  and,  to  increase  their  intensity,  he 
put  them  between  disks  of  iron,  or  on  tin  tubes,  placed  on  rescmant 
surfaces  close  to  the  disks.  In  this  way  he  says  that  he  was  able  to 
make  a  good  receiving  telephone  without  employing  magnets.  He 
afterward  arranged  the  instrument  in  different  ways,  of  which  the 
following  two  are  the  most  noteworthy : 

'  In  the  first,  the  electro -magna  tic  system  was  simply  formed  by  a 
magnetic  disk  with  a  helix  wound  round  it,  of  which  the  wire  was 
in  connection  with  the  circuit  of  a  microphone  and  which  was  fastened 
to  the  parchment  membrane  of  an  ordinary  string  telephone ;  the  disk 
consisted  of  two  plates  separated  by  a  carbon  disk  of  smaller  diameter, 
and  the  whole  was  so  compressed  as  to  form  a  solid  mass. 

*  In  the  second,  the  helix  was  wound  on  a  tin  tube,  six  inches  long 
and  five-eighths  of  an  inch  in  diameter,  which  was  soldered  by  merely  a 
point  to  the  center  of  the  diafram  of  an  ordinary  telephone. 

*  The  inventor  asserts  that  the  tube  and  diafram  only  act  as  reson- 
ators, and  that  the  sounds  produced  by  this  instrument  are  nearly  the 
same  as  those  obtained  from  the  ordinary  string  telephone :  the  tunes 


WHISPERINGS   OF  AN   t)l,D    PINE 


635 


of  a  musical  box  were  heard,  and  the  reproduction  of  speech  Wiis 
perfect,  both  in  intensity  and  in  distinctness  of  sound ;  it  even  appeared 
that  telephonic  sounds  were  audible  with  the  tin  tube  alone,  surroimded 
by  the  helk.  M.  Wiesendanger  says  that  these  *' different  receiving 
telephones  show  clearly  that  the  diafram  and  magnet  are  not  essential, 
but  merely  accessory  parts  of  a  telephone."     •     •     • 

*  It  is  true  that  the  telephone  can  only  reveal  the  variations  of  an 
electric  current,  however  faint  they  may  be,  but  I  have  been  able,  by 
the  use  of  a  very  simple  expedient,  to  reveal  by  its  means  the  presence 
of  a  continuous  current,  also  of  extreme  faintness.  I  send  the  current 
in  question  into  the  telephone,  and  to  obtain  its  variations,  I  break 
this  current  mechanically  with  a  tuning-fork.  If  na  current  n  trav- 
frsing  the  trkphone,  it  remains  silent.  If,  on  the  other  hand,  the 
faintest  current  exists,  the  telephone  vibrates  in  unison  with  the  tuning- 
fork.     •     •     • 

'Mr.  Warren  de  la  Rue,  as  we  have  seen,  used  Thomson's  galvano- 
meter, and  compared  the  deviation  produced  on  the  scale  of  this 
galvanometer  with  that  caused  by  a  Baniell  cell  traversing  a  circle 
completed  by  a  rheostat :  he  ascertained  that  the  currents  discharged 
by  an  ordinary  Bell  telephone  are  equivalent  to  those  of  a  Daniell  cell 
traversing  loo  megohms  of  resistance — that  is,  6,200,000  miles  of  tele- 
graphic wire.  Mr.  Brough,  the  Director  of  Indian  telegraphs,  considers 
that  the  strongest  current  which  at  any  given  moment  causes  a  Bell 
telephone  to  work  does  not  exceed,  ^oAoaa  *^^  ^^^  ""^^  ^^  current,  that 
is,  one  Weber,  aijd  the  current  transmitted  to  the  stations  on  the  Indian 
telegraphic  line  is  400,000  times  as  strong.  Finally  Professor  Peirce, 
of  Boston,  compares  the  effects  of  the  telephonic  current  with  those 
which  would  be  produced  by  an  electric  source  of  which  the  electro- 
moiive  force  should  be  ^^(nT^  P*^^^  ^^  ^  ^^^^*  ^^  ^^^  Daniell  cell  Mr. 
Peirce  justly  remarks  that  it  is  difficult  to  estimate  the  real  value  of 
these  kinds  of  currents  at  any  precise  sum,  but  it  may  be  affirmed  that 


■'■'■^ 


636  ELLEN  OR  THE 

it  is  less  than  the  looiffoo  P^^  ^^  ^^^  cprrent  usually  employed  fo  w(»k 
the  instrument  on  telegraphic  lines.    ♦    •    •    • 

*  Experiments  by  M.  Zetsche. — There  are  always  a  few  perverse  minds 
impelled  by  a  spirit  of  contradiction,  to  deny  evidence,  and  tiiiis 
they  attempt  to  depreciate  a  discovery  of  which  the  glory  irritatses 
them.  The  telephone  and  the  phonograph  have  been  the  objects  of 
such  unworthy  criticism.  It  has  been  said  that  electric  action  had 
nothing  to  do  with  the  effects  produced  in  the  telephone,  and  that  it 
only  acted  imder  the  influence  of  mechanical  vibrations  transmitted  by 
the  conducting  wire,  just  as  in  a  string  telephcme.  It  was  in  vain 
to  demonstrate  to  these  obstinate  minds  that  no  sound  is  produced 
when  the  circuit  is  broken,  and  in  order  to  convince  them  M.  Zetsche 
has  made  some  experiments  to  show,  from  the  mode  in  which  sound  is 
propagated,  that  it  is  absurd  to  ascribe  the  sound  produced  in  a  tele- 
phone to  mechanical  vibration.  He  wrote  tp  this  effect  in  an  article 
inserted  in  the  Journal  T^Ugraphique,  Berne,  January  35th,  1878 : 

*"The  correspondence  by  telephone  between  Leipzig  and  Dresden 
affords  another  proof  that  the  sounds  which  reproduce  words  at  the  re- 
ceiving station  are  due  to  electric  currents,  and  not  to  mechanical 
vibrations.  The  velocity  with  which  sound  is  transmitted  by  vibrations 
on  the  wire,  in  the  case  of  longitudinal  undulations,  may  be  estimated 
at  three  miles  one  furlong  a  second,  so  that  the  sound  ought  to  traverse 
the  distance  from  Leipzig  to  Dresden  in  twenty-five  seconds.  The 
same  time  ought  to  elapse  before  receiving  the  answer :  consequently 
there  should  be  an  interval  of  more  than  three-quarters  of  a  minute 
allowed  for  each  exchange  of  communication,  whicli  is  by  no  means 
the  case."     *     *     * 

^Experiments  which  may  be  made  by  any  one, — We  will  conclude 
this  chapter  devoted  to  the  account  of  the  different  experiments  made 
with  the  telephone,  by  the  mention  of  a  singular  experiment  which, 
although  easily  performed,  has  only  been  suggested  a  few  months  ago 


WHISPERINGS   OF 


PINE 


by  a  Pennsylvania  newspaper.  It  consists  in  the  transmission  of 
speech  by  a  telephone  simply  laid  on  some  part  of  the  human  body 
adjacent  lo  the  chest.  It  has  been  asserted  that  any  part  of  the  body 
will  produce  this  effect,  but  according  to  my  experience,  I  could  only 
succeed  when  the  telephone  was  firnaly  applied  to  my  chest  Under 
such  conditions,  and  even  through  my  clothes,  1  could  make  myself 
heard  when  speaking  in  a  very  loud  voice, 

*Mr.  Preece  also  made  experiments  on  the  subterranean  telegraplis 
between  Manchester  and  Liverpool,  a  distance  of  thirty  miles,  and 
found  no  difficulty  in  exchanging  correspondence  ;  and  it  was  the  same 
with  the  cable  from  Dublin  to  Holyhead,  a  distance  of  sixty-seven 
miles.  This  cable  had  seven  conducting  wires,  and  when  the  telephone 
was  connected  with  one  of  them,  the  sound  was  repeated  through  all 
the  others,  but  in  a  fainter  degree.  Wlien  the  currents  of  the  tele- 
graphic instruments  passed  through  the  wires,  the  induction  was  appar- 
ent, but  not  so  great  as  to  prevent  telephonic  communication,     •     • 

•Since  copper  is  relatively  harder  than  lead,  the  copper  plate  on 
which  the  vibrations  are  traced  will  afford  an  unlimited  number  of 
reproductions.  To  obtain  this  result,  a  lead  wire  must  be  applied  to 
the  plate*  and  due  pressure  must  be  exerted  on  it.  The  wire  is  flattened 
and  takes  the  impr^sion  of  all  the  traces,  which  then  appear  in  relief. 
If  the  edge  of  a  card  is  passed  through  this  impressed  tracing,  the  same 
sounds  are  produced  as  those  which  are  obtained  from  the  copper 
plates.     •     •     ♦ 

'As  I  said  in  the  last  chapter,  there  is  a  great  difference  between  the 
production  and  the  reproduction  of  a  sound,  and  a  machine  like  the 
phonograph,  adapted  for  the  reproduction  of  sound,  may  differ  essen- 
tially from  a  machine  which  really  speaks.  In  fact,  the  reproduction 
even  of  articulate  sounds  may  be  very  simple ;  but  in  order  to  produce 
them,  it  is  necessary  to  set  in  motion  a  number  of  special  organs, 
fulfilling  more  or  less  exactly  the  functions  of  the  lar)'nx,  the  mouth. 


638  ELLEN  OR  THE 

the  tongue,  the  lips,  and  even  the  nose.  For  tfiis  Teaaoo,  a  1 
machine  is  necessarily  very  complicated^  and  this  is  preckdy  the  cue 
with  the  machine  we  are  now  considering.  Such  a  machine  is  not  now 
made  for  the  first  time,  and  the  Academy  has  lately  been  reminded 
of  a  speaking-head  which  was  in  the  possesnon  of  the  phikMopher 
Albertus  Magnus  in  the  Thirteenth  century,  and  which  was  destroyed 
by  St.  Thomas  Aquinas  as  a  diabolical  invention.     •     •     • 

*  Further  Remarks  on  the  Theory  of  ihe  Teie^ane. — FoUowing  tiie 
example  of  a  certain  skeptic  in  the  Acad^mie  des  Sciences,  Colonel 
Navez  continues  to  maintain  the  theory  first  formed  as  to  the  nEX>de  in 
which  the  telephone  acts,  in  spite  of  the  clearest  proofs  of  its  insuf- 
ficiency ;  but  most  scientific  men  who  consider  the  question  have  come 
round  to  our  opinion,  and  admit  the  concurrence  of  several  causes 
in  the  reproduction  of  speech  by  this  remarkable  instrument.  Mr. 
Fleeming  Jenkin  writes  to  this  effect  in  the  new  edition  of  a  treatise  on 
electricity  and  magnetism. 

*  Note  on  some  fresh  Experiments  with  Telephones  wiihout  am 
Diaframs. 

'  In  a  paper  published  March  4th,  1878,  I  made  some  suggestions  on 
the  theory  of  the  sounds  produced  in  the  telephone,  and  on  the  contra- 
dictory assertions  of  physicists  as  to  the  transmission  of  speech  by 
ordinary  telephones  when  devoid  of  diafram.  These  remarks  induced 
M.  Ader  to  undertake  several  experiments  which  not  only  demonstrate 
the  truth  of  my  oi)inion,  but  bring  to  light  some  fresh  facts  which  may 
be  of  great  importance  to  acoustic  science. 

*  M.  Ader  has  in  fact  not  only  succeeded  in  making  a  telephone 
without  a  diafram  speak,  but  he  has  made  it  speak  more  loudly,  and 
with  less  alteration  of  the  voice  than  we  find  to  be  the  case  with  a 
small  model  of  the  ordinary  telephone.  No  one,  therefore,  can  now 
mamtain  that  the  sounds  produced  by  the  magnetic  cores  are  so  faint 
that  they  cannot  be  taken  into  account  among  the  effects  produced 


WHISPERINGS   OF   AN   OLD    TINE 


639 


and  that  it  is  at  any  rate  impossible  for  them  to  reproduce  articulate 
sounds. 

*  To  obtain  this  result,  M.  Ader  reduced  the  size  of  the  magnetic 
core  to  that  of  a  simple  iron  wire,  one  millimetre  in  diameter,  and  he 
fastened  it  by  one  of  its  ends  to  a  small  wooden  board.  Under  these 
conditions^  it  was  enough  to  fasten  a  small  helix  of  fine  wire  on  this 
iron  wire,  and  to  apply  the  board  to  the  ear  in  order  to  hear  speech 
distinctly,  with  the  aid  of  a  microphonic  speaker  actuated  by  a  voltaic 
current.  But  the  range  of  sotind  was  considerably  increased  if  a  mass 
of  metal  was  applied  to  the  free  end  of  the  iron  wire :  in  this  case  it 
was  possible  to  hear  when  the  wooden  board  was  removed  to  a  distance 
of  ten  or  fifteen  centimetres  from  the  ear. 

*  If  the  wire  is  in  contact  with  masses  of  melal  at  each  end,  the 
effect  is  further  increased  j  but  the  two  masses  must  not  be  in  metallic 
communication  with  each  other,  and  must  be  to  some  extent  insulated 
by  a  more  or  less  clastic  medium.  H  the  metalic  masses  arc  soldered 
to  the  wire,  the  effects  are  still  greater. 

*  M.  Ader  was  able  to  reproduce  speech  by  using  a  simple  coil  with- 
out a  magnetic  core,  but  in  this  case  the  spirals  must  be  open,  and  not 
pressed  together.  If  they  are  steeped  in  gum,  no  sound  is  heard,  but 
speech  will  become  instantly  audible  if  a  wire  or  a  magnetize*!  needle 
is  inserted  in  the  coil,  ur  even  if  a  second  metallic  helix  is  placed  in  the 
circuit :  always  provided  that  one  of  the  ends  of  these  magnetic  organs 
rests  upon,  or  is  fastened  to,  the  board  on  which  the  coil  is  fixed. 

*  M.  Ader  has  likewise  obtained  a  very  distinct  reproduction  of 
speech  at  a  distance  of  two  or  three  yards  from  the  instrument  by  in- 
serting betk^'een  the  two  stretched  membranes  of  two  tamlxnirines  a 
bent  wire  which  acts  as  a  spring  and  passes  through  an  electro  magnetic 
coiL 

*  M.  Ader  has  often  had  occasion  to  make  one  curious  remark, 
namely,  that  the  timbre  of  the  voice  and  its  high  or  low  key  varies  with 


640  ELLEN  OR  THE 

the  degree  of  tenskm  given  to  the  wire;  tmtif  the  luidaiaciitB]  note 
of  the  wire  is  deadened  Iqr  {veamig  it  between  the  fiiigen»  tte 
iqwoduced  then  becomes  dnil  and  monoloDOos.    They  aie  alsD  i 
what  fainter. 

'Mr.. Edison  has  abo  now  made  a  pfactical  af^ilicatidi  of  the  chemi- 
cal tdei^ione  we  have  mentioned  before.  The  trials  made  witfi  it  hsve 
been  very  satisfoctory,  showing  diat  soonds  transmitted  in  thfe  way  can 
be  heard  in  a  large  room.' 

''The  experiments  quoted  from  this  book  fully  demonstratie 
that  the  scientific  explanations  of  the  action  of  sound  at  a  tele- 
phone are  entirely  fallacious,  but  all  sustain  the  theory  that 
sound,  consisting  of  infinitedmal  particles  of  electrical  matter, 
is  carried  through  the  wire  of  a  telephone  by  Ae  electric 
current" 


■ 

THE  J!KW  TORK 
PUBLIC  LIBRART 

WHISPERINGS   OF  AN  OLD    PINE 


643 


XUIL 


^^  pLLEN  has  been  very  thorough  in  her  discourse  on  the 
'^^  telephone,"  I  said,  '*  and  it  is  very  satisfactory,  and  she 
has  also  thrown  light  upon  the  graphophone,  but  the  o!d  Pine 
wishes  that  Ellen  would  still  further  illustrate  the  operation 
of  the  graphophone,  and  the  principles  which  govern  its 
action." 

"Very  well,'*  she  said,  '*when  Ellen  makes  her  visits  to  the 
old  Pine  she  is  always  ready  to  tell  him  what  she  can,  for  she 
knows  that  he  is  one  of  her  best  friends,  and  she  thinks,  too, 
that  he  questions  Ellen  more  to  instruct  her,  than  to  be  taught 
himself. 

**The  graphophone  when  it  first  made  its  advent  was 
one  of  the  most  mysterious  innovations.  Ellen  called  it  the 
spook,  and  it  seemed  to  be  defiant  of  all  law ;  but  of  course 
the  laws  under  which  it  operates  are  as  fixed  and  beneficent 
as  any.  And  now  Ellen  can  see  that  instead  of  being  outside 
of  law,  it  is  wholly  a  creation  of  law,  as  it  extends  into  the,  to 
us,  unexplored  realm  of  infinitesimals,  those  things  which  we 
cannot  see,  but  which  are  none  the  less  a  fact,  and  a  most  im- 
portant part  of  the  universe. 

•*In  considering  these  the  scientists  have  made  some  very 
uncalled  for  blunderSi  and  such  as  they  could  not  have  made 
with  a  correct  theory  of  sound. 


644  ELLEN  OR  THE 

"The  explanation  they  have  given  of  both  telephone  and 
graphophone  is  an  assumption,  by  those  high  in  authority » of  a 
universe  without  law  or  order ;  for  a  diafram  and  a  thousand 
other  things,  more  or  less,  not  made  to  talk,  or  repeat  speech, 
are  announced  as  doing  it;  the  necessities  of  the  undulatory 
theory  of  sound  compelling  such  belief,  or  announcement. 
But  the  corpuscular  theoiy  of  sound  accepted,  aU  difficulties 
vanish. 

"  Sound,  consisting  of  infinitesimal  particles  of  electrical  mat- 
ter, can  be  manufactured  in  the  miniature  indentations  of  a 
graphophone;  always  these  indentations  manufacturing  the 
same  sounds  which  made  them. 

"For  these  indentations,   because  shaped  by  the  peculiar 
form  and  motion  of  sound,  or  sounds,  re-create  when  struck 
the  particular  particles  of  electrical  matter  which  represent, 
these  sounds. 

"The  machinery  acting  in  or  through  these  indentations 
is  a  small  bead,  or,  in  a  disk  record,  a  needle,  and  it  is 
important  that  this  bead  or  needle  should  fully  enter  the 
indentations. 

**  These  particles,  too,  as  Ellen  demonstrated  in  the  experi- 
ments of  the  sounding^  board  and  needle  are  infinitesimals  of 
a  pronounced  type,  just  the  tiniest  little  bits  of  things,  so  small 
that  it  is  almost  impossible  for  Ellen  to  imagine  them,  but  they 
are  made  in  vast  quantities,  and  would  appear  to  be  of  infinite 
numbers,  so  that  after  thrown  off  by  the  sounding  body  they 
fill  the  atmosphere  in  all  directions.  Smoke  to  a  certain 
extent,  as  the  smoke  of  an  engine,  acts  similarly,  as  also  do 
clouds." 


WHISPERINGS   OF   AN   OLD    PINE 


645 


**And  does  Ellen  think  that  such  infinitesimal  particles  could 
be  the  cause  of  any  sensation?*' 

**  There  is  no  question  about  the  power  of  infinitesimals,"  she 
replied,  *' certainly  when  massed.  The  lightning  is  an  illustra- 
tion of  that  power. 

*God  moves  in  a  mysterious  way 

His  wonders  to  perform, 
He  plants  his  footsteps  on  the  sea, 
And  rides  ujx>n  the  storm/ 

**That  the  particles  of  sound  manufactured  in  these  records 
enter  the  ears  of  all  within  reach,  and  coming  in  contact  with 
man,  and  by  man  Ellen  means  the  souK  produce  in  him  the 
sensation  of  hearing,  is  beyond  any  possible  question.  As  Ellen 
has  said  before,  they  do  this  as  naturally  as  a  peach,  or 
plum,  or  any  other  article  of  food  creates  the  sensation  of 
taste.  And  it  is  only  a  question  of  good  sense  that  all  sensa- 
tions are  similarly  created,  that  is,  by  the  action  of  matter  upon 
spirit.  Ellen  thinks  that  we  can  all  agree  upon  this,  or  will 
before  long.*' 

**Thc  old  Pine  thinks  that  Ellen  makes  everything  very  plain 
after  the  particles  of  sound  are  created,  but  he  would  like  to 
understand  better  exactly  how  these  particles  are  made.  And 
first,  whether  the  sound  of  a  graphophone  record  might  not 
be  the  same  sound  that  was  uttered  into  it,  preserved  by 
some  process  in  the  indentations, — as  fruit  and  vegetables 
may  be  preserved  if  kept  from  the  air, — and  aftcnvards  released 
by  the  reproducer?" 

**  Ellen  thought  of  that,'*  she  said,  "and  looked  into  it  quite 


646  ELLEN  OR  THE 

carefully,  and  found  that  the  disks  upon  which  the  records  of 
graphophones  are  now  largely  made  are  from  a  mold,  taken 
from  a  wax  like  disk  upon  which  the  original  record  is  made  by 
the  sounds,  as  follows : 

"The  wax  like  disk  is  coated  with  a  suitable  substance,  such 
as  plumbago  and  copper  plated  by  electricity.  This  copper 
plate  is  then  removed  from  the  wax  and  backed  up  by  some 
aluminum  or  zinc  alloy  to  make  it  strong.  Into  this  negative 
the  blank  material,  out  of  which  the  commercial  records  are 
composed,  is  pressed,  while  the  material  is  hot  The  pressure 
used  is  said  to  be  about  ten  tons. 

''From  this  it  is  certain  that  the  sounds  of  the  graphophone, 
whether  music,  articulate  speech,  or  other  sounds,  are  made 
in  the  indentures  caused  by  sound,  or  in  precisely  similar 
indentures  made  from  them  by  ah  electrotyping  process? 

"To  a  certain  extent,  then,  it  is  a  matter  of  form  bf  these  in- 
dentures. For  as  would  appear  to  be  certain,  and  as  Ellen  has 
found  by  experiment,  the  same  sound  will  always  make  a  similar 
indenture.'* 

"In  what  way?"  I  asked. 

*•  Ellen  will  have  to  answer  she  does  not  know  yet,  but  she 
thinks,  or  at  least  hopes,  that  the  old  Pine  and  she  will  be  able 
to  find  out  by  reasoning  or  experiment,  or  both. 

"As  Ellen  has  said  everything  made  by  nature  is  the  best 
possible  for  its  purpose,  in  the  conditions  in  which  it  exists. 
But  if  the  conditions  are  different,  there  might  be  something 
infinitely  better  to  perform  the  same  purpose.  And  indeed,  a 
thing  which  in  certain  conditions  might  be  the  best  possible  for 
certain  purposes,  in  other  conditions  could  not  be  used  at  all. 


WHISPERINGS   OF  AS   OLD    PINE 


647 


This  must  constantly  happen*  The  lock  which  would  answer 
for  a  church  door»  wouldn't  do  at  all  for  a  delicate  box  in  which 
a  lady  kept  her  jewelry.  Always  the  sizes  of  things  should, 
and,  to  a  certain  extent,  will  have  to  correspond.  And  from 
this  cause  alone  the  machinery  necessary  to  accomplish  certain 
things,  and  capable  of  doing  it  in  perfection,  might  have  to  be 
entirely  reconstructed  to  perform  the  same  purpose  in  other 
conditions. 

**  Take  articulate  speech,  The  machinery  of  the  vocal  organs, 
with  the  assistance  of  the  mouth  and  its  appurtenances,  and 
the  lungs  for  an  acting  force,  is  unquestionably  the  best 
arrangement  possible  to  enable  man  to  talk.  It  is  inconceiv- 
able that  he  could  talk  without  the  necessary  machinery  to  do 
it,  but  it  is  no  less  inconceivable  that  a  diafram,  or  any  other 
tiling  in  the  universe,  could,  unless  supplied  with  such  machin- 
ery ;  which  we  know  that  no  diafram,  or  any  other  such  thing 
is.  But  it  appears  that  a  graphophone  record  has  a  certain 
amount  of  such  machinery;  not  indeed  one  complicated 
machine  capable  of  making  all  articulate  speech,  but  an  assort- 
ment, more  or  less,  of  different  machines,  each  one  capable  of 
making  a  particular  letter  or  word.  And  therefore  it  is  evident 
that  the  conditions  required  for  the  production  of  articulate 
speech  in  man,  and  in  a  graphophone,  are  altogether  different. 

*'And  from  all  this  Ellen  sees,  first,  that  the  graphophone 
record  has  the  machinery  necessary  to  make  certain  sounds, 
and  that  these  may  include  parts  of  articulate  speech,  words 
and  letters.  Second,  that  the  direct  cause  of  this  record  is 
sound.  And  Ellen  can  perceive,  or  at  least  she  thinks  she 
can,  that  the  principle  of  reproduction  of  each  thing  after  its 


i^i. 


648 


ELLEN    OR   THE 


kind,  entors  fnto  this  discussion.  For  when  sound  re-crcato 
sound,  there  takes  place  the  reproduction  of  a  thing  after  ite 
kind,  and  under  such  conditions  as  are  suggestive  of  a  fixed  and 
eternal  law, 

**  Third,  the  graphophone  record  is  nbundantly  large  to  in- 
clude the  necessary  machinery'  (or  making   individual    sounds 

which,  as  we  have  seen,  r- "  •-—  'nfinitesimal    according  to 

our  standards  of  size. 

•'Fourths  as  all  sound  consists  of  infinitesimal    particles  of 
matter,  in  part  at  least  electrical. — which  must  mean  that  it 
composed  entirely  of  a  certain  quality  of  matter   in   a  certain 
amount,  or,  far  more  probable,  of  different  qualities  combined j 
in  certain  amounts, — very  simple  machinery,  under  certain  con- 
ditions, would  suffice  to  produce  it»  each  sound  being  produced 
by  its  appropriate  machinery.     And,  as  all  sounds   are    infinr- 
tesimal,   it  would    be  possible,  so   far  as  we  know,  that  the 
machinery,    necessary    for    producing   all    sound,   might    be 
included  in  a  graphophone  record." 

"But  what  may  be  the  exact  character  of  such  machinery?" 
I  asked. 

**This  consists  first,"  she  answered,  "'of  indentures,  which  are 
records  of  sound ;  that  is,  represent  its  form.  And  second, 
a  small  instrument  of  glass  or  metal  which  must  enter  these 
indentures.  Unquestionably  the  machinery  consists  of  both 
of  these.  If  either  was  absent  we  would  get  no  sound,  except, 
possibly,  a  similar  but  somewhat  different  instrument  might 
answer  as  a  reproducer." 

"And  in  what  manner  do  these  reproduce  the  sound?"  I 
asked. 


WHISPERING*;   OF  AN   OLD    P!NE 


649 


"The  indenture  must  act  as  an  instrument/'  she  replied, 
•*to  produce  certain  sounds  by  separating  or  combining  certain 
particles  of  matter  necessary  to  accomplish  this. 

'*That  only  sounds  uttered  into  a  graphophone  will  come 
from  it  would  demonstrate,  if  we  did  not  know  by  other  means> 
that  they  are  the  seed  of  the  sounds  which  it  repeats. 
But  each  sound  records  itself,  that  is,  makes  an  indenture 
corresponding  to  its  size  and  action*  completely  if  entering 
alone,  and  as  complete  as  possible*  if  entering  with  other  sounds. 

*'The  instrument  is  made,  and  sound  has  made  it  with  abso- 
lute accuracy.  In  another  sense  it  was  made  by  man  by  whose 
intelligence  the  different  things  necessary  to  make  it  were 
brought  together.  But  beyond  all  this  the  principle  was  made 
by  the  highest  Intelligence  in  the  furnishment  of  the  universe, 
as  Ellen  thinks,  to  provide  the  soul  with  a  record  of  sounds  for 
the  purpose  of  memory.  Nor  as  Ellen  thinks,  was  it  especially 
intended,  otherwise,  for  the  use  of  man.  but  discovered  by 
him  it  becomes  a  thing  of  much  interest  and  some  use.*' 

"And  Ellen  thinks  the  principle  may  be  used  to  assist 
memory?*' 

"Yes,"  she  answered,  ''and  therefore  is  it  an  important  part 
of  creation.  And  an  essential  part  in  the  creation  of  sound, 
because  a  law  of  that  creation.  That  is.  every  body  which 
vibrates  at  all,  has  a  vibration  of  its  own,  and  all  bodies 
having  the  same  vibration  emit  the  same  sound,  nor  is  it  possi- 
ble for  any  body  to  emit  this  sound,  which  does  not  have  this 
same  vibration. 

**  And  this  vibration  is  made  by  sound,  which  itself  is  caused 
by  shock.     And  therefore  takes  place  what  is  called  sympathetic 


6sO  ELLEN  OR  THB 

vibration.  That  is,  sound  from  a  tunings  fork  of  a  certnn 
vibration  will  enter  another  fork,  in  the  same  room,  having  the 
same  vibration,  and  cause  it  to  vibrate,  when   it  will  emit  the 

same  sound."     (See  page  i86). 

"  In  this  case  sound  makes  more  sound,  does  it  not  EIIe&T^ 
I  asked. 

"  In  this  case,  as  Ellen  thinks,"  she  answered,  "  sound  is  hdd 
up  or  accumulated,  the  same  that  water  in  rivers  may  be  in 
ponds  along  their  paths,  and  this  becomes  a  source  of  supply 
being  thrown  off  slowly  in  the  usual  manner  by  vibration. 

"The  sounds,  then,  emitted  by  the  different  indentures  of 
the  graphophone  are  conducted  by  the  reproducer  into 
the  diafram,  and  by  that  reflected  into  the  megaphone  and 
room,  but  the  diafram  has  nothing  else  to  do  in  the  matter 
than  its  double  action,  first,  in  conducting  particles  of  sound  to 
make  the  record  in  the  wax,  and  second  conducting  similar 
particles  made  by  that  record  into  a  megaphone  and  room. 

•*That  sound  makes  vibration  explains  sympathetic  vibration. 
And  it  explains  more  than  anything  else  ever  has  the  funda- 
mental connection  between  vibration  and  sound.  The  cause 
of  vibration  is  sound.  But  the  vibrating  body  decides,  in 
part  at  least,  the  character  of  sound ;  fits  it  for  the  market, 
and  delivers  it  for  distribution. 

**That  sound  is  an  entity,  created  like  all  other  entities  by  the 
combination  of  matter  in  its  different  conditions  and  propor- 
tions, Ellen  has  abundantly  shown. 

**It  is  noticeable  that  scientists  confine  their  discussion  of 
waves  to  those  supposed  to  be  acting  in  the  air,  although  sound 
travels  in  wood   and  metals  much  faster,  and  in  water  about 


WHISPERINGS   OF   ,\N    OLD    TINE  65 1 

five,  and  fron  sixteen  times  faster  than  in  air,  It  would  be 
amusing  to  hear  one  of  them  describe  the  actions  of  waves  in 
solid  bodies,  supposed  to  be  acting  Hke  those  upon  the  surface 
of  a  pond. 

"But  Ellen  understands  that  there  are  many  who  arc  still 
teaching  undulatory  theories.  The  attention  of  these  she 
will  again  call  to  the  fact  that,  it  being  impossible  for  the 
diafrani  or  anything  else  to  make  any  sound  except  the  one 
it  was  made  to  make,  there  is  no  possible  explanation  of  the 
action  of  sound  at  the  telephone,  except  that  it  is  carried 
instantaneously  through  the  wire  to  the  place  of  its  delivery  by 
the  electric  current, 

'*The  blow  by  the  reproducer  upon  any  indenture  made  by 
sound,  creates  the  sound  normal  to  that  instrument,  or  any 
instrument  of  the  same  form,  whether  larger  or  smaller. 

'*  And  as  the  different  bodies  or  things  of  the  world  make  all 
its  sounds,  and  every  body,  always,  though  struck  repeatedly, 
repeats  the  same  particular  sound,  it  must  be  true  that  some 
bodies  make  the  sounds  of  the  different  letters  and  words,  that 
is,  make  the  sounds  of  articulate  speech,  and  every  possible 
such  body  when  struck  will  emit  its  particular  part  of  articulate 
speech, 

**  But  the  graphophone  record  demonstrates  that  the  record 
of  any  sound  is  the  particular  form  which  being  struck  emits 
the  sound,  which  made  it/' 

**  And  Ellen  thinks,*'  I  said,  **that  sound  is  made  by  shock?" 

*' Yes,**  she  answered,  "with  a  broad  meaning  for  shock — 
blow  or  disturbance,  Ganot  uses  the  words,  shock  or  friction* 
This  always  precedes  the  vibration." 


6S2  ELLEN  OR  THE 

''And  that  the  same  body  always  emits  the  same  sound?** 

"Beyond  question.  Take  a  book  and  a  stick.  Strike  the 
book  on  the  side,  no  matter  how  many  times,  you  will  get  each 
time  subtantially  the  same  sound.  For  each  one  is  imdded  by 
the  same  conditions.  Strike  the  book  on  its  edges,  there  will  be 
a  different  sound,  for  conditions  are  different,  atnd  unquestion-^ 
ably  vibrd.tions  different,  but  struck  constantly  on  same  edge 
the  sounds  will  again  be  alike. 

"The  better  class  of  graphophone  records  certainly  suggest 
that  if  the  work  is  perfectly  done,  the  same  mold  will  emit  in 
every  respect  the  same  sound. 

"Well,  the  lesson  teaches  us  that  sounds  are  manufactured 
in  molds,  that  is,  in  bodies  of  certain  form,  each  sound  by  a 
body  of  particular  form.  It  shows  us,  too,  that  sound,  all 
sound,  is  as  much  a  material  thing  as  candy  or  snowflakes^ 
and  that  no  matter  where  it  is  made  whether  in  the  vocal 
organs,  or  a  graphophone  record,  if  of  the  same  brand,  it  will 
produce  the  same  sensation  in  every  person. 

**  Common  sense  will  tell  any  one,  who  has  it,  that  the  five 
sensations,  sight,  hearing,  smell,  taste,  and  touch,  are' all  caused 
similarly  by  the  effect  of  matter  upon  spirit. 

"And  without  the  possibility  of  anything  emitting  iden- 
tical sounds  with  any  other  thing,  unless  it  was  made  to, 
that  is,  made  with  the  same  normal  vibration,  and  then  that 
it,  or  any  possible  one  thing,  can  only  emit  one  sound ; — the 
fact  that  sound  consists  of  infinitesimal  particles  of  matter 
is  demonstrated  beyond  any  possible,  question  by  the  tele- 
phone. 

"  Another  principle  is  most  fully  demonstrated  by  the  g^apho- 


WHISr'ERINGS   OF   AN    OLD    PINE 


653 


phone  and  that  is,  that  the  laws  governing  infinitesimals  are  as 
exact  and  rigorous  as  those  operating  with  larger  bodies. 

**Sounds^  then,  Ellen  thinks  the  old  Pine  will  see.  maybe 
sorted  like  apples,  and  any  brand  can  be  had  if  only  the  sources 
can  be  found  %vhrch  yield  it'* 

'*  And  Ellen  thinks  the  reproducer  is  the  instrument  that  plays 
upon  this  sound-producing  instrument,  bringing  out  its  music, 
as  the  bow  will  that  of  a  violin,  or  the  fingers  that  of  a  harpi*" 

**Yes/*  she  said,  "and  the  indentures  are  separate,  and  it 
plays  upon  each  one,  its  weight  resting  upon  the  cylinder,  and 
that  turning  rapidly,  so  that  it  gives  the  usual  blow  or  shock 
which  in  each  case  produces  the  normal  vibration.  And  this 
normal  vibration  is  that  which  is  appropriate  to  the  particular 
sound  which  made  the  indenture.  And  so  each  indenture 
pours  out  a  beautiful  lot  of  the  sounds  it  was  made  to  make.'* 

**  Ellen  has  discovered  the  secret/'  I  said, 

"Yes,"  she  answered,  "Ellen  and  the  old  Pine." 

"But  the  old  Pine  didn't  help  any,"  I  replied. 

** Oh  yes  he  did,"  she  answered;  "he  was  so  tall,  and  then  he' 
was  Ellen's  friend/' 

** Thank  God,"  she  continued,  ** Ellen  thought  the  old  Pine 
and  she  would  think  it  out     And  He  has  enabled  them  to  do  it 

** There  is  only  the  square  where  the  four  sides  are  alike; 
and  to  every  sound  there  is  only  one  record,  that  can  repeat  it, 
which  it  writes  itself  with  the  beautiful  hand  of  TkUTit 
'  How  anient  I  seixed  it  with  hands  that  were  glowing 

And  quick  to  the  white  pebbled  bottom  it  fell ; 
Then  soon  with  the  emblem  of  Truth  overflowing 
And  dripping  wiih  coolness,  it  rose  from  the  well.' 


6S4 


ELLEN    OR   THE 


"And  Ellen  wants  to  say  a  word  for  Mr,  Edison,  who  practP 
cally  worked  out  the  problem,  in  the  long  days,  and  in  the  long 
nights. 

*'  The  old  Pine  will  see,  that  everywhere  throughout  the 
universe,  always,  law  and  order  rule*  Nowhere  is  there  any 
variableness  or  shadow  of  turning.  The  chimneys  don't  talk» 
the  curbstones  don't  talk,  the  nails  don't  talk;  nothing  talks 
except  what  was  made  to  talk.  Nothing  ever  repeats  a  word 
or  a  sound,  that  wasn't  made  to  repeat  it,  that  is,  which  doesn't 
include  the  machinery  to  repeat  it.  No  diafram  ever  talked 
or  ever  repeated  a  word,  for  it  was  not  made  to,  and  couldn*! 
do  it  any  more  than  it  could  make  a  dictiona^>^  or  build  a 
stone  bridge.  Everything,  animate  or  inanimate,  always  obeys 
the  laws  of  its  being.  Included  in  this  is  the  graphophone 
record.  And  also  all  laws  of  sound  are  obeyed  by  sound, 
wherever  it  is  made. 

**  Echoes  repeat  sounds,  but  this  would  appear  to  come  from 
particles  of  sound  rebounding.  The  only  sound-producing  in- 
strument to  make  the  record  of  a  graphophone  is  the  person, 
or  thing,  which  utters  the  sound  into  it.  A  graphophone 
record,  however  short  or  long  it  may  be,  is,  as  Ellen  has  said, 
an  instrument  for  producing  sound,  like  a  piano,  or  violin,  or 
drum,  and  like  them,  or  all  other  sound  producing-instruments, 
it  will  produce  the  sounds  it  was  made  to  produce.  And  as  the 
different  keys  of  the  piano,  or  different  strings  of  a  violin,  or 
notes  of  a  flute,  will  give  forth  every  time  the  same  note,  and, 
if  in  tune,  would  continue  to  when  struck,  forever,  so  will  each 
key  or  indenture  of  a  graphophone;  for  these  indentures  act  as 
keys,  or  notes»  made  so  as  to  produce  certain  sounds,  and  no 


^Ma 


^^ 


658  ELLEN  OR  THE 

"That  sound  is  made  entirely  and  absolutely  by  the  shape  of 
the  instrument  which  makes  it ;  though,  so  far  as  Ellen  knows* 
it  may  be  of  any  shape,  but  the  same  shaped  thing  will  ghre  the 
same  sound ;  and  this  because  of  the  character  of  its  vibratioiL 
For  the  vibration  of  any  instrument  is  made  by  the  passage 
of  sound  to  and  fro  in  that  instrumenti  and  the  form, — and  to 
that  extent  the  character,  of  the  sound  itself^ — ^is,  at  least  may 
be,  molded  by  the  nature  of  the  interstices  of  the  body  in  which 
it  is  created,  and  through  which  it  circulates.  It  would  be 
impossible  in  the  nature  of  things  for  this  not  to  be  so.  For 
the  machinery  of  nature  always  works  precisely  as  that  of  man 
would  under  the  same  circumstances.  That  is,  whatever  man, 
or  any  other  lesser  intelligence,  accomplishes,  is  done  in  accord- 
ance with  the  great  laws  of  nature,  which  govern  all  mechanical 
forces.     It's  dreadfully  simple." 

"Yes,"  I  said,  "to  Ellen." 

"  It  is  also  evident,"  she  continued : 

"That  this  instrument  is  always  a  material  thing,  whether 
situated  within  the  body  of  man,  as  are  the  vocal  organs,  or 
without. 

"That  for  a  certain  part  of  articulate  speech,  what  part  she 
doesn't  know,  there  must  be  a  mill,  and  for  all  articulate  speech 
many  mills.  For  articulate  speech  is  composed  of  many  parts 
like  a  house,  and  the  different  parts  are  manufactured  by  differ- 
ent mills,  and  then  put  together.  But  it  makes  no  difference 
whatever  where  they  are  situated,  only  that  it  is  where  the 
proper  material  to  make  sound  may  be  had,  for  sound  like 
everything  else  in  this  material  universe  is  made  front  certain 
kinds  of  matter.     There  is  no  exception  to  this  principle,  and 


WHISPERINGS   OF   AN  OLD    PINE 


657 


others.  Thus  take  the  indenture  made  by  the  letter  A,  and 
therefore  of  the  form  to  produce  the  letter  A,  it  will  turn  A's 
out  in  any  quantity,  whilst  used  to  do  it,  until  it  is  worn  out 
And  so  each  indenture,  the  letter,  word,  or  sound,  which  made 
it  For  all  are  molds,  as  much  fitted  to  make  certain  sounds, 
in  whatever  way  they  may  do  it,  as  those  of  a  furnace  to  make 
certain  forms ;  nor  will  the  one  instrument  fail  to  respond  more 
than  the  other. 

*'But  it  w^ould  appear  to  be  also  evident  that  the  same  sound 
will  have  an  indenture  of  different  size  according  to  its  intensit>% 
and  this  indenture  in  repeating  will  repeat  the  sound  ahvays 
with  the  same  intensity  that  the  sound  had  wiien  it  made  it. 
The  intensity  then  comes  from  the  size  of  the  indenture,  and 
that  comes  from  the  size  and,  as  Ellen  thinks,  motion,  of 
the  sound  which  made  it  And  so  Ellen  notices  that  the 
enlarged  photographs  of  the  indentures  representing  the  same 
letters  or  words,  whilst  of  different  sizes,  are  always  of  similar 
proportions.  And  this  sound  may  be  any  sound,  but  the  point 
that  Ellen  wished  to  emphasize  was  that  it  may  be  any  part 
of  articulate  speech.  And  in  such  mills  as  these  every  part  of 
articulate  speech  can  be  manufactured,  though  Ellen  hasn't 
had  the  time  to  find  out  whether  each  letter  or  each  word,  or 
parts  of  letters,  or  parts  of  words,  make  an  indenture,  and  that 
means  the  forms  wiiich  make  any  part  of  articulate  speech,  or 
in  which,  as  a  whole  articulate  speech  is  made.  But  this  cer- 
tainly can  be  discovered.  The  scientists  have  made  such  bad 
work  of  this  whole  theor>'  of  sound  that  Ellen  doesn't  dare  to 
tie  to  anything  which  they  have  said,  but  has  to  study  it  all  out 
herself.     But  it  is  evident  from  these  conditions; 


658  ELLEN  OR  THB 

"  That  sound  is  made  entirely  and  absolutely  by  tiie  shape  of 
the  instrument  which  makes  it;  though,  so  far  as  Ellen  knows!, 
it  may  be  of  any  shape,  but  the  same  shaped  thing  will  give  the 
same  sound ;  and  this  because  of  the  character  of  its  vibration. 
For  the  vibration  of  any  instrument  is  made  by  the  passage 
of  sound  to  and  fro  in  that  instrument,  and  the  form, — and  to 
that  extent  the  character,  of  the  sound  itself, — is,  at  least  may 
be,  molded  by  the  nature  of  the  interstices  of  the  body  in  which 
it  is  created,  and  through  which  it  circulates.  It  would  be 
impossible  in  the  nature  of  things  for  this  not  to  be  so.  For 
the  machinery  of  nature  always  works  precisely  as  that  of  man 
would  under  the  same  circumstances.  That  is,  whatever  man» 
or  any  other  lesser  intelligence,  accomplishes,  is  done  in  accord- 
ance with  the  great  laws  of  nature,  which  govern  all  mechanical 
forces.     It's  dreadfully  simple." 

"Yes,"  I  said,  "to  Ellen." 

**It  is  also  evident,"  she  continued: 

"That  this  instrument  is  always  a  material  thing,  whether 
situated  within  the  body  of  man,  as  are  the  vocal  organs,  or 
without. 

"That  for  a  certain  part  of  articulate  speech,  what  part  she 
doesn't  know,  there  must  be  a  mill,  and  for  all  articulate  speech 
many  mills.  For  articulate  speech  is  composed  of  many  parts 
like  a  house,  and  the  different  parts  are  manufactured  by  differ- 
ent mills,  and  then  put  together.  But  it  makes  no  difference 
whatever  where  they  are  situated,  only  that  it  is  where  the 
proper  material  to  make  sound  may  be  had,  for  sound  like 
everything  else  in  this  material  universe  is  made  from  certain 
kinds  of  matter.     There  is  no  exception  to  this  principle,  and 


WHISPERINGS   OF   AN   OLD    PINE 


659 


*no  man  competent  to  treat  of  such  subjects  would  think 
to  make  any.  But  this  matter  in  a  so-called  vacuum,  and  prob- 
ably in  some  other  places,  as  cotton,  or  wool,  isn't  to  be  had.  Or 
this  may  mean  simply  that  in  the  so-called  vacuum  sounds  can- 
not be  made,  which,  in  our  present  conditions,  we  can  hear. 
And  this  is.  as  Ellen  thinks,  for  she  believes  that  the  music 
of  the  spheres  which  plough  their  way  with  such  wonderful 
rapidity  throupjh  the  ether,  never  missing  a  trip,  is  a  beau t if  11 1 
realit>%  heard  by  beings  of  a  higher  order  than  we,  such  as  the 
Scripture  calls  angels.  And  these  spheres  move  in  a  space 
which  perhaps  we  might  call  a  vacuum,  though »  as  Ellen 
thinks,  there  is  no  such  thing  as  a  vacuum. 

**  Againi  perhaps,  when  a  bell  is  rung  in  a  so-called  vacuum 
no  sound  is  heard,  because  there  is  no  proper  medium  to  con- 
vey it. 

** Outside  of  the  vacuum,  or  where  the  material  to  make 
sound  would  appear  to  be  wanting,  the  mills  which  make  these 
different  sounds  might  as  well  be  in  the  space  of,  and  so  com- 
pose, a  graphophone  record,  as  an>^vhere  else.  They  can  be 
anywhere,  where  there's  room  for  them,  and  they  need  but  an 
awful  little  bit  of  room.  But  it  would  be  very  foolish  to  put 
them  anywhere  where  there  wasn't  material  to  make  sound. 
Like  putting  saw-mills,  where  there  was  no  lumber. 

•*  It  follows  from  all  this  that  nearly  eveiything  in  nature,  at 
least  many  things,  will  emit  sound  when  struck.  As  EHen 
has  said,  undoubtedly  every  sound  in  the  world  is  thus  made 
by  a  particular  instniment  or  thing;  and  that  thing  will  always 
make  the  same  soumli  or  sounds,  and  can  make  no  other, 

**It   is   in  this  way   that  the   world's  supply   of   sounds   is 


660  ELU^N  OR  THE 

obtained,  everyone  of  them  being  made  in  a  separlUe  mold. 
And  the  supply  of  sounds,  like  that  of  the  sweet  flowers  which 
deck  our  fields  and  woods,  and  gardens ;  or  the  trees  which 
beautify  the  whole  landscape;  or  the  clouds  that  always 
changing,  and  always  lovely,  adorn  the  heavens;  and  indeed 
all  things  which  furnish  the  Universe;  is  of  infinite  variety,  no 
two  alike,  and  n6  two  made  by  the  same  instrument,  or  part  of 
instrument.  Nor  is  it  possible  that  they  should  be,  so  perfect  is 
the  order  and  system  which  pervades  the  universe.  Thus  a 
diafram,  if  struck,  can  make  a  very  plain  sound  and  can  mate 
no  other.  Under  no  possible  conditions  can  it  make  any  other. 
"Mr.  Tyndall  (On  Sound,  page  no)  says: 

'When  a  body  capable  of  emitting  a  musical  sound — a  tuning-fork, 
for  example — ^vibrates,  it  molds  the  surrounding  air  into  sonorous  wavei^ 
each  of  which  consists  of  a  condensation  and  a  rarefaction.' 

"These  hypothetical  sonorous  waves  are  supposed  to  be 
sound.  Ellen  has  denied  that  there  are  any  such  waves.  The 
fork  doesn't  do  any  such  molding,  and  instead  of  the  vibration 
making  such  sonorous  waves,  Ellen  will  prove  that  sound  makes 
vibration,  not  vibration  sound. 

"The  experiments  of  Prof.  J.  Henry  at  Washington,  * 
proved  that  the  vibration  of  a  tuning-fork,  when  struck, 
might  vary  from  lO  to  252  seconds.  The  foot  of  the  tuning- 
fork  being  placed  successively  on  a  marble  slab,  a  solid  brick 
wall,  and  on  a  wall  of  lath  and  plaster,  its  vibrations  lasted 
respectively  115,  88,  and  18  seconds;  when  suspended  in  the 
air  by  a   fine   cambric  thread   the   fork  vibrated  during  252 

♦  See  page  555. 


WHISPERINGS   OF   AN   OLD    PINE 


66 1 


seconds.  Placed  on  a  large,  thin  pme  board  its  vibrations  lasted 
about  lO  seconds.  Professor  Mayer  saysi  *In  this  the  short- 
ness of  duration  was  compensated  for  by  the  greater  intensity 
of  the  effects  produced.' 

**  And  now  Ellen  wants  anyone  who  would  follow  her  argu- 
ment, to  take  in  one  hand  a  small  spruce  or  pine  stick,  about 
one  inch  by  one-half  inch  in  thickness,  or  of  any  convenient 
size,  placing  one  end  in  the  mouth,  and  with  the  other  hand 
make  a  tuning  fork  vibrate,  and  touch  the  further  end  of  the 
stick  from  the  mouth  with  the  bottom  of  the  fork;  the  sound 
will  run  up  the  stick  into  the  mouth  and  into  the  head.  If  now 
the  same  fork  is  struck  again  and  held  to  the  ear,  or,  if  moved 
quickly  enough,  without  being  struck  again,  the  same  sound, 
that  is,  a  precisely  similar  sound,  will  go  direct  from  it  into  the 
ear,  but  more  slowly. 

*  The  text-books  teach  that  the  vibrations  of  the  fork  make 
this  sound,  which  they  call  sonorous  waves,  in  the  air,  each 
consisting  of  a  condensation  and  a  rarefaction.  This  is  not  only 
entirely  false,  but  also  monstrously  stupid.  The  sound  waa 
in  the  fork  before  it  was  in  the  air,  as  is  demonstrated  by 
its  passage  from  the  fork  through  the  stick  to  the  head,  or  into 
the  sounding  board  and  thence  into  the  air  and  into  the  ear, 
or  from  any  other  outlet  which  may  be  given  to  it.  There 
doesn't  live  any  person  with  ordinary  intelligence  who  cannot 
satisfy  himself  of  the  truth  of  this  by  the  method  proposed. 
With  the  discovery,  the  undulatory  theory  of  sound  goes  out  of 
existence. 

•'Always  the  first  thing  necessary  for  the  production  of  sound 
is  shock,     Ellen  uses  this  word  in  the  broad  sense,  either  a 


662  ELLEN  OR  THE 

blow  or  disturbance,  and  claims  distinctly  diat  what  Mlows 
this  shock  is  sound  and  vibration.  If  we  say  that  vibrattcm 
follows,  the,  question  then  is  what  makes  the  vibiatkm.  Sooie^ 
thing  must  make  it,  and  something  more  than  tiie  shock  or 
blow.  For  this  vibration  must  be  caused  by  something  active 
and  powerful,  that  circulates  back  and  forth,  or  to  and  £ro»  m 
the  fork;  and  this  something  must  have  been  made  by  the 
shock.  Ellen  supposes  the  scientists  will  suggest  ela^c  force. 
Well  neither  they  nor  Ellen  know  what  elastic  force  is.  It 
may  be  sound.  At  any  rate  the  most  noticeable  thing,  and 
the  only  known  additional  thing,  that  occurs  after  the  blow, 
which  might  make  the  vibration,  is  sound.  And  Ellen  will  prove 
that  it  does  make  it  Thus  if  the  sound  was  the  acting  force 
causing  the  vibration  of  the  fork,  that^  vibration  should  stop 
proportionally  as  the  sound  which  made  it  flowed  away. 

**  But  if  the  sound  was  not  the  cause  of  the  vibration,  directly 
or  indirectly,  its  flowing  away  would  not  affect  the  vibration. 

**  As  a  matter  of  fact  the  vibration  does  stop  proportionally 
to  the  sound's  flowing  away. 

**  Again,  something  operating  in  the  fork  made  the  vibration, 
and  there  is  not  evidence  or  suggestion  that  anything  else  has 
operated  but  sound.  This  is  practically  a  demonstration  that 
the  sound  made  the  vibration. 

"But  Ellen  will  now  clinch  the  demonstration.  Ellen  will 
take  two  tuning-forks  which  sound  the  same  note,  that  is,  which 
have  the  same  normal  vibration.     Mr.  Tyndall  says: 

*Two  forks  mounted  on  their  resonant  supports  are  placed  upon  the 
table.     I  draw  the  bow  vigorously  across  one  of  them,  permitting  the 


WHISPERINGS   OF   AN   OLD    PINE 


663 


Other  fork  to  remain  untouched.  On  stopping  the  agitated  fork,  the 
sound  is  enfeebled,  but  by  no  means  quenched.  Through  the  air  and 
through  the  wood  the  vibrations  have  been  conveyed  from  fork  to  fork, 
and  the  untouched  fork  is  the  one  you  now  hear.  When,  by  means  of 
a  morsel  of  wax,  a  small  coin  is  attached  to  one  of  the  forks,  its  power 
of  influencing  the  other  ceases;  the  change  in  the  rate  of  vibration,  if 
not  very  small,  so  destroys  the  sympathy  between  the  two  forks  as  to 
render  a  response  impossible.  On  removing  the  coin  the  untouched 
fork  responds  as  before/ 

**  Sound,  whatever  that  is,  from  the  first  fork  has  gone  into 
the  second,  making  it  vibrate,  because  the  second  fork  is  of  the 
same  tone,  and  has  the  same  vibration  as  the  first  fork.  It  fol- 
lows that  before  it  left^  it  must  have  made  its  own  fork  vibrate. 

"This  demonstrates  that  sound  makes  vibration,  and  also 
that  it  is  an  entity,  for  that  which  makes  vibration  must  be  an 
entity.  But  if  sound  makes  vibration,  as  it  does  in  every  phase 
of  the  phenomena,  there  are  no  undulatory  theories.  For  the 
undulatory  theory  of  sound  is  that  the  vibrating  fork  makes 
sound, — *  molds  the  surrounding  air  into  sonorous  waves,' — that 
is,  that  vibration  makes  sound. 

•*  And  the  above  hypothetical  sonorous  waves  are  the  sound 
thrown  off  by  the  fork,  which  caused  its  vibration,  and  is  still 
continuing  to  make  it  vibrate. 

'  What  fools  we  mortals  l>e  ! ' 

*' Ellen  will  repeat:  These  so-called  sonorous  waves,  are 
thrown  off  by  the  fork  directly  into  the  air,  and  are  the  same 
sound  that  we  can  trace  running  from  the  fork  into  the  sound- 
ing board,  and  thence  into  the  air;  or  running  into  a  stick  held 


664  ELLEN  OR  THE 

by  the  teeth,  and  thence  to  the  head  or  brain;  or  if  the  stkk  is 
placed  on  the  frontal  bones,  directly  to  the  head ;  as  is  easHy 
and  unquestionably  traced  by  the  sensation  of  hearing.  For  this 
sensation  is  as  accurate  as  sight  in  its  tracings,  so  that  a  man 
may  know  as  certainly  the  course  of  a  sound  as  that  ai  any 
visible  thing.  As  is  well  known  blind  pedple  get  their  Imowl- 
edge  largely  or  mainly  from  the  sensation  of  hearing,  and  do  it 
as  certainly  as  they  might  from  that  of  sight  And  therefore 
does  Ellen  say  that  any  statement  that  sonorous  waves  are 
formed  by  the  vibrations  of  the  fork,  is  false,  because  she 
knows,  and  any  one  may  know,  that  these  ^sonorous  vibra- 
tions' ate  particles  of  sound  caused  by  shock,  which  make 
tiie  fork  vibrate,  when  they  are  thrown  off  into  the  air,  or,  if 
given  opportunity,  pass  far  more  rapidly  into  a  sounding 
board,  and  thence  into  the  air,  in  either  case  to  be  gathered 
by  any  listening  ear,  and  by  this,  the  main  line,  conducted  to 
the  soul ;  or,  as  we  have  seen,  they  may  be  conducted  from 
the  fork  to  the  teeth,  or  frontal  bones  and  thence  to  the  soul, 
where  by  pre-arrangement,  made  possible  by  sound,  and  very 
similar  to  that  which  takes  place  with  the  telegraph,  informa- 
tion of  all  kinds  is  delivered.  Ellen  thinks  its  an  awfully  nice 
arrangement  by  which  people  are  able  to  talk  with  one  another, 
and  thus  add  very  greatly  to  their  knowledge,  besides  making 
life  very  much  more  agreeable.  Any  one  may  see,  that,  which- 
ever route  these  sounds  follow  from  the  sounding  body  to  the 
perceiving  intelligence  they  are  the  same, — that  is,  precisely 
similar  sounds, — ^whose  origin  is  with  the  sounding  body. 

"And  therefore  does  she  say  again  the  statement  that  sound 
is  molded  or  made  by  the  vibrations  of  a  tuning  fork,  or  any- 


WHISPERINGS   OF  AN   OLD    PINE  66$ 

thing  else,  is  not  only  false  but  shown  to  be  impossible,  and  the 
undulatory  theories  are  ended." 

"Ellen  has  got  through?"  I  said. 

**Yes,"  she  said.  "The  case  is  taken  out  of  court,  and  all 
that  is  left  for  Ellen  to  do  is  to  gather  up  the  fragments  of  her 
discourse,  so  that  it  will  make  a  harmonious  whole,  and  let  the 
old  Pine  publish  it  to  the  world  with  his  whispering  leaves." 


606  ELLEN   OR  THE 


XLIV. 

^^  T^LLEN  has  described  all  of  this  very  well/*  I  said,  "and 
^  shown  conclusively  that  sound  made  vibration  in  the 
instance  cited,  and  if  there  the  old  Pine  cannot  see  why  it  docs 
not  everywhere.  That  is,  why  always  when  there  is  shock,  and 
sound  follows,  the  instrument  or  thing  in  which  vibration  takes 
place  is  not  thrown  into  vibration  by  the  sound,  which  must  be 
particles  of  matter,  aroused  into  action  by  the  shock." 

*'That  is  what  happens,'*  she  said,  **and  then  these  particles* 
an  infinite  number  of  them,  composed  about  equally  of  matter 
and  motion,  circulate  back  and  forth  within  the  body  in  which 
they  are  formed,  thus  causing  it  to  vibrate,  and  by  the  courses 
which  they  pass  through  being  themselves,  as  Ellen  thinks, 
partly  fashioned.  Somewhat  similarly  bullets  get  their  form 
by  falling  through  the  air  from  a  high  tower. 

*'  Hy  such  vibrations  the  sounds  are  fitted  for  the  markets  of 
the  world,  and  these  are  thrown  off  into  the  air,  where  they 
circulate  for  whatever  time  their  existence  lasts. 

"This  is  sound;  and  if,  in  a  tuning-fork,  a  channel  is  opened 
for  it  by  contact  of  the  handle  with  some  other  body,  as  KUcn 
has  shown,  it  rushes  into  this  body,  and,  if  this  is  of  right  char- 
acter, is  thrown  off  far  more  rapidly  into  the  air,  and  thus 
quickly  the  shower  of  sound  is  drained  from  the  vibrating  body, 
which  again  becomes  quiet. 

**That  the  sounds  are  fashioned  in  the  vibrating  bodies  Kllen 


WHISPERINGS   OF   AN   OLD    FINE 


669 


makes  no  question.  By  the  shock  the  material  for  making 
them  is  formed*  or  loosened  in  the  rough,  and  as  the  mills  of 
man  manufacture  different  goods,  a  saw  mill  different  kinds  of 
lumber  made  from  logs,  a  woolen  mill  woolen  goods,  made 
from  wool,  a  cotton  mill  cotton  goods,  made  from  cotton*  or 
a  silk,  silk  goods,  made  from  silk,  so  these  vibrating  bodies, 
acting  as  mills,  form  the  different  sounds  made  from  sound,  and 
fitted  for  the  markets  of  the  world,  perhaps  of  the  universe.  For 
thus  always  the  laws  governing  the  production  of  natural  and 
artificial  things  are  the  same.  This  is  the  principle  of  the 
universal it>'  of  natural  law  that  Ellen  has  often  referred  to. 
And  it  will  be  seen  that  with  this  principle,  which,  as  Ellen  has 
shown,  all  science  proclaims,  the  corpuscular  theory  of  sound 
fully  accords. 

'*  Ellen  has  spoken  of  this  before,  but  she  cannot  refer  to  it 
too  often,  as  this  alone  would  be  decisive  as  to  the  nature  of 
sound. 

** There  is  no  question  in  regard  to  the  general  accuracy 
of  this  explanation,  based  upon  the  discovery  of  Oersted  that 
sound  was  electrical,  and  in  its  main  features  fully  and  repeated- 
ly demonstrated.  It  is  based^  too^  upon  the  common  sense  of 
every  intelligent  person,  that  sound  being  electrical  might  pene- 
trate the  walls  of  houses  and  other  impediments,  but  that  air 
waves,  particles  of  air,  couldn't  possibly  do  this ;  neither  could 
they  possibly  give  impetus  to  any  other  particles  of  matter  so 
that  they  could  do  it,  and  then  reappear  again — on  tlie  other  side 
of  the  wall  The  whole  conception  is  intensely  ridiculous.  It 
may  do  to  teach,  if  the  principal  object  of  teaching  is  the  pay. 
Or  it  mav  do  for  those  interested  in  the  million  of  dollars  of 


670  ELLEN  OR  THE 

text-books,  already  printed  with  this  stuff  in,  but  them's  no 
further  use  for  it  And,  too,  the  forces  perpetuating  this  error, 
being  organized,  it  may  be  able  to  continue  its  pourse  a  feir 
months  more,  but  Ellen  does  not  believe  it  will  long,  for  tfie 
people  are  fast  learning  to  understand  the  fraud.  And  as  \soon 
as  any  schools  or  colleges  break  away  from  it,  they  will  be  the 
ones  to  be  patronized. 

"Mr.  Newton  in  his  Principia  states,  that  although  the 
Ptolemaic  system  of  Astronomy, — and  this  undulatofy  theory 
of  sound  is  said  to  have  come  from  the  same  source, — had  been 
universally  taught  for  some  1800  years,  through  the  whole  time 
the  abler  minds  protested  against  it,  saying  it  was  erroneous. 

'^The  same  is  true  now  of  these  undulatory  theories.  Prof. 
Thompson  of  Oxford  University,  England,  one  of  the  leading 
ph)r5icists  of  the  world,  in  an  article  in  Harper's  Magazine, 
suggests  that  science  will  be  obliged  to  return  to  the  corpuscu- 
lar theory  of  light,  accepted  by  Newton,  and  taught  in  all  the 
schools  for  over  a  hundred  years.  But  at  the  same  time  this 
was  taught,  the  undulatory  or  wave  theory  of  sound,  as  handed 
down  ffom  the  Greeks,  was  also  taught.  Further  discoveries 
showed  that  the  same  laws  which  governed  light  governed 
sound,  and  in  getting  them  together,  Newton  being  dead,  and 
there  being  no  other  such  really  great  and  safe  leader  living, 
guided  by  Dr.  Young,  a  fine  scholar,  but  not  at  all  a  safe  guide, 
or  especially  able  man,  the  mistake  was  made  of  shifting  the 
one  that  was  right,  and  so  making  them  both  wrong. 

"And  thus  the  absurd  and  impossible,  handed  down  from 
the  ignorance  of  2000  years  ago,  has  been  adopted  by  modern 
science.      And   this,   too,   although   in   direct  antagonism   to 


WHISPERINGS    OF  AN   OLD    PINE 


671 


Newton,  generally  recognized  as  the  greatest  of  English  phi- 
losophers. 

*'Well,  it  wasn't  Mr.  Newton's  fault,  but  illustrated  the  old 
adage  that  a  live  dog  is  better  than  a  dead  lion.  There  is  noth- 
ing left  now  lor  the  physicists  of  the  world  but  to  go  back  to 
Newton's  corpuscular  theory  of  light,  and  accepting  the  demon- 
strated fact  that  the  laws  governing  sound  are  the  same  as  those 
governing  light,  accept  the  corpuscular  theory  of  sound, 

"As  the  old  Pine  said,  Ellen  has  proved  that  sound  makes 
vibration.  She  has  shown  also  that  sound  is  a  compound  of 
matter  and  motion;  that  is,  it  contains  within  itself  a  power  of 
movement,  and  is  an  entity.  Certain  fire  works  do  the  same^ 
and  will  move  while  they  last.  So  will  sound;  and  for  the  dis- 
tance it  can  be  heard  it  is  supposed  to  move  at  the  uniform 
rate,  in  air  of  a  certain  temperature,  about  1 140  feet  a  second. 
This  movement,  as  we  can  tell  by  feeling  when  sound  passes 
through  a  stick,  is  of  an  irregular  character,  something  like 
that  of  water  flowing  on  a  decline  over  a  pebbled  bottom. 
The  text-books  speak  of  this  as  vibration,  but  in  no  accurate 
sense  is  it  vibration.  The  sound  makes  vibration,  the  vibration 
of  the  fork,  but  that  is  a  very  different  thing  from  the  sound 
that  makes  it.  Vibration  is  a  movement  to  and  fro.  Sound 
has  a  constant  onward  movement,  besides  permeating  the  air 
like  a  cloud," 

"And  will  not  vibration  produce  sound?"  I  asked.  *'Make 
It,  not  fashion  it?" 

"Not  any  more  than  a  saw  mill  will  make  lumber,**  she  re- 
plied; "or  a  woolen  factory  wool,  or  a  cotton  factory  cotton, 
or  any  factory  the  substance  of  which  it  makes  its  goods," 


672 

"And  how  docs  Ellen  think  that  the  graphophoae  record  is 
made?" 

"By  sound/'  she  added.     *'With  Mr,  Edison  at  the  head  to 
arrange  and  manage  the  necessary  machinery. 

"And  does  the  recorder  make  the  record?" 
-  "Ellen  docs  not  think  it  does." 

"Then  what  can?  ' 

"Sound/*  she  answered,  *Hhc  particles  of  sound.      And  iii- 
deed  when  it  is  claimed  that  the  diafram  mains  it,  tfarotigh  tlie 
recorder,  that  is,  using  the  recorder  a»  a  tool,   it  is  under- 
stood that  the  action  of  the  diafram  depeiids  entirely  itp6n  the 
sound  itself,  the  whole  explanation  being  that  sound  moves  the 
diafram,  and  the  diafram  acting  as  agent,  makes  the  recoid,  or 
in  scientific  language,  the  sound  makes  the  diafram  vibrate  and 
thus,  by  the  stylus  fastened  to  it,  record  the  sound  in  the  paraffin 
and  wax.     The  old  Pine  will  notice  that  the  scientists  here 
claim  that  sound  makes  vibration. 

"This  theory  is  naturally  the  first  one  that  suggrests  itself, 
but  there  are  several  quite  serious  objections  to  it:  First, 
the  question  arises  why  it  wouldn't  be  more  feasible  for  the 
particles  of  sound  to  make  the  impressions  themselves,  than  to 
cause  something  else  to  make  them. 

"  Second,  it  is  impossible  for  a  diafram  to  vibrate  to  the  sound 
of  any  instrument  except  one  in  sympathy  with,  that  is,  having 
the  same  vibration  as,  itself.  *  This  as  Ellen  has  shown  is  a 
fundamental  principle  of  physics.  But  there  could  only  be 
one  kind,  of  the  possible  millions  of  instruments  or  sounds 
which  might  make  the  graphophone  record,  that  could  do  this, 

•  Sec  page  721,  Appendix. 


WHISPERINGS   OF  AN   OLD    PINE 


673 


**Thirdt  Ellen  cannot  see  how,  when  there  are  two  or  more 
sounds  taking  place  at  the  same  time,  as  when  an  orchestra 
is  playingi  or  a  quartette  or  chorus  singing,  or  both  orchestra 
and  chorus,  a  diafram,  supposed  to  be  affected  by  the  motions 
of  all  the  sounds,  can  act  so  as  to  make  independent  records 
of  each.  In  such  conditions  by  the  laws  of  mechanics  a 
record  made  by  the  diafram  would  be  that  of  a  resultant 
motion,  which  could  not  possibly  be  a  separate  record  of  all 
the  sounds  which  made  the  resultant.  Yet  when  such  record 
is  reproduced  the  different  sounds  are  distinctly  heard»  in  the 
same  manner  as  they  would  be  when  performing,  each  sound 
made  by  a  different  sound- producing  instrument,  and  there- 
fore by  numerous  different  motions  instead  of, — as  they  would 
have  to  be  if  made  by  a  resultant, — all  made  by  one. 

"Ellen  knows  that  the  scientists  get  along  with  a  little  diffi- 
culty of  this  kind  b}'  jumping  or  ignoring  it,  thereby  fooling 
the  millions  who  look  to  them  for  knowledge  of  such  matters, 
and  adding  to  their  large  fund  of  knowledge  of  things  which 
are  not  so. 

**And  fourth,  it  is  impossible  to  detect  that  such  diaframs 
vibrate  at  all,  the  best  evidence  showing  that  the}  do  not,  (See 
pages  405,  407). 

•*It  follows  that  the  diaframs  have  nothing  whatever  to  do 
with  making  the  indentures  of  the  graph  op  hone,  excepting  as 
they  may  help  to  collect  and  reflect  the  sounds  which  make 
them  ;  but  that  these  are  made  by  the  sounds  themselves,  con- 
ducted first  into  the  diafram.  and  then  by  the  metal  recorder 
into  the  paraffin  and  wax  prepared  for  such  purposes  by  the 
stylus, 


674 

"In  this  case  the  sounds  are  sown  very  much  as  seed  would 
be,  and  through  the  proper  forms  or  molds  which  they  in»* 
press  upon  the  paraffin  and  wax,  provide  itistrumcnts  lor  that 
own  renewal.  Thus  made  the  Vecord  when  reproduced  woaU 
respond  precisely  as  It  does/* 

"But  I  said,"  **  would  it  be  possible  for  sound  to  make  tlie 
impression  necessary  for  a  record?'' 

"Ellen  thinks  it  would,"  le  answered.  "For  as  Ellen  has 
shown  sound  is  electrical,  that  is,  it  is  compounded  in  part  of 
electricity,  and  certainly  tlie  power  that  can  rend  a  tree  should 
be  able  to  make  a  record," 

"But  why  haven*t  the  scientists  supposed  it  to  have  been 
made  this  way?"  I  asked. 

"Because  with  their  theor>'  of  sound  it  would  be  impossible 
that  it  should  be.  All  the  phenomena  of  sound  can  be  accom- 
plished, and  arc,  by  the  entity  sounds  in  which  is  contained  for 
motion  the  beautiful  and  wonderful  electrical  power,  so  that 
every  sound  starts  off  in  confidence  on  its  path,  whether  that 
be  a  humble  one  or  one  of  glory  and  fame.  The  folly  of  man 
or  the  exigencies  of  teachers,  and  thrift  of  book  makers,  would 
destroy  the  whole  business,  but  luckily  all  they  can  do  is  to 
deceive  those  who  trust  in  them,  and  possibly  themselves  •  but 
the  sounds  of  the  world,  and  of  the  universe,  for  Ellen  thinks 
that  in  some  form  they  are  a  part  of  universal  existence  rise 
above  all  this  and  independently  with  power,  skill  and  beauty 
perform  their  parts." 


WHISPERINGS    OF  AN   OLD   PINE 


^77 


XLV. 


^^PLLEN  has  referred  several  times/*  I  said,  ''to  nature's 
^  great  system  of  Sensations,  by  which  men,  and  other 
animals  as  well,  living  upon  this  earth,  derive  the  knowledge 
which  they  have,  and  the  old  Pine  wishes  that  she  would 
describe  more  fully  this  system,  and  its  method  of  operation/' 
"It  is  a  system  of  Universal  Telegraphy,"  she  replied,  "for 
the  delivery  of  universal  information  to  all  sentient  beings, 
which  live  in  material  conditions.  These  conditions  the  soul  of 
man  enters  completely  ignorant  of  them/* 

"But  where  does  this  soul  come  from?'*  I  asked, 
** Ellen  cannot  say/*  she  answered,  "nor  why  it  comes,  nor 
how.  It  would  appear  to  be  beginning  a  new  life,  when 
all  the  past  has  been  erased.  Certainly  it  comes  without 
possessions,  and  immediately  its  education  begins,  which  is 
accomplished  entirely  by  sensations/' 

"And  how  many  of  these  sensations  are  there?*"  I  asked. 
"Five,'*  she  replied;  "touch,  taste^  smelling,  hearing, 'and 
sight,  and  the  conditions  are  these:  matter  surrounds  us,  and 
in  it  live  myriads  of  animals  and  plants.  How  many  scnsa* 
tions  trees  have,  the  old  Pine  will  have  to  explain,  but  man 
and  other  animals  have  the  ones  Ellen  has  named,  of  which, 
perhaps,  the  most  useful  are  sight  and  hearing/* 


68o 


ELLEN   OR  THE 


of  the  body.  The  thing  to  be  studied,  that  is,  the  cause  ol 
any  particular  sensation,  is  usually  entirely  independent  of  the 
person  learning.  The  method  of  operation,  as  Klicn  has  said 
is  a  system  of  universal  telegraphy.  And  it  is  the  system  pro 
vided  by  the  Power  that  created  this  universe,  for  the  educa 
tion  of  the  intelligent  beings  inhabiting  it. 

**  There  is  a  thinking  substance  capable  of  knowledge.  Thi 
thinking  substance,  or  principle  of  intelligence,  is  providec 
with  a  body,  which  makes  for  it,  while  the  body  lasts,  i 
habitation,  and,  as  Ellen  has  said,  furnishes  it  with  th< 
necessary  means  of  using  its  faculties,  and  accumulating  infor- 
mation. 

**  And  this  soul  has  a  faculty  of  learning.  And  it  has  a  facult> 
of  feeling  which  perhaps  answers  to  that  called  instinct,  stronger 
than  that  of  learning,  and  from  which,  too,  the  superstructure 
of  knowledge  ijiay  be  built.  That  is,  the  intuitive  feeling  may 
be  used  for  the  beginning  of  thought. 

•'Thus  the  ^irl  Helen  Keller,  who  was  both  deaf  and  bh'nd 
and  lived,  till  seven  years  old,  entirely  ii^norant,  was  first  tau.q;ht 
the  word  water  by  pcnirini^  it  upon  her  hand,  and  at  same  time 
tracin<j^  the  word  on  her  arm,  until  she  had  learned  that  what 
caused  this  sensation  of  touch  was  called  water.  The  names 
of  thin<i[s  or  words  she  i^ot  from  holding  her  fingers  on  the  lips 
of  one  repeating  them.  With  a  few  preliminary  steps  of  this 
kind  her  education  went  on  rapidly. 

"And  I^llen  wants  the  old  Pine  to  remember  that  existence, 
the  existence  of  a  soul,  consists  in  a  power  of  acquiring  knowl- 
edge, not  necessarily,  as  l^llen  thinks,  in  that  of  retaining  and 
thus  accumulating  't,  although  certain  provisions  are  made  for 


WHISPERINGS    OF    AN   OLD  PINE 


68 1 


this»  and  perhaps  ultimately,  with  any  soul  sufficiently  developed 
in  all  its  powers,  these  become  permanent  Thus  the  power  of 
accumulating  property  is  one  thing,  and  that  of  retaining  it 
quite  a  different  thing. 

**  Ellen  thinks  now  that  the  old  Pine  can  see  that  a  system  of 
signals,  from  small  beginnings,  and  by  the  aid  of  feeling,  or 
instinct,  which  is  active  in  the  soul,  whatever  be  its  change  of 
location,  could  soon  be  established,  from  which  commences 
the  accumulation  of  knowledge  by  each  individual  soul.  And 
Ellen  feels  sure  that  this  is  what  takes  place. 

**  But  there  has  to  be  a  sign  for  every  outside  thing  that  we 
become  acquainted  with.  And  now  we  may  realize  the  neces- 
sity of  the  machinery  of  the  body*  For  it  is  evident  that  the 
soul  cannot  directly  recognize  material  things.  Apparently  it 
lives  in  another,  that  is,  belongs  to  another  sphere,  where,  as 
Ellen  thinks,  they  don't  have  material  things ;  but,  howcv^er  that 
may  be,  a  representation  of  each  material  thing  has  to  be 
brought  into  the  immediate  presence  of  the  souU  in  order  that 
it  may  perceive  it, 

'*  Here  is  introduced  the  principle  so  well  known  in  material 
philosophy   that  things   affect  each    other   only    by  contact/ 


•  In  a  letter  to  Mr.  Benlley,  Mr.  Newton  sayst 

It  is  inconceivable  that  inanimate  brute  matter  should,  without  the 
mediation  of  something  else  which  is  not  material,  operate  upon  and 
affect  other  matter  without  mutual  contact,  as  it  must  do  if  gravitation 
in  the  sense  of  Epicurus  be  essential  and  inherent  in  it.  •  •  • 
That  gravity  should  be  innate,  inherent,  and  essential  to  matter,  so  that 
one  body  can  act  upon  another  at  a  distance,  through  a  vacuum  with- 
out the  mediation  of  anything  else,  by  and  through  which  their  action 


1 


And  this,  as  Ellen  thinks,  is  true  in  regard  to  the  soul.      It  per 
ceives  things  only  as  directly,  or  indirectly,  they   are  broui^hft 
into  intimate  relation  with  it.     And  this  is  accomplished  vvitW 
all  material  things,  whether  the  furthest  fixed  star,  or  the  ncari 
pebble,  by  the  sensations.     That  is  what  they  are  for, 

•*The  old  Pine  and  Ellen  can  sec  when  they  examine  into  ii 
what  a  wonderful  universe  this  is,  how  complete  in  all  its  partsJ 
and  how  infinitely  removed  those  parts  would  appear  to  be.       ] 

"These  things,  that  is,  every^  material  thing,  cannot  be; 
brought  up  as  a  whole  to  every  personality,  or  indeed  to  any  of 
them.  And  therefore  did  it  become  essential  to  arrange  i^ 
system  which  would  accomplish  this  in  all  cases-  Hence  that? 
of  sensations;  which,  like  the  quality  of  mercy,  Is  not  strained^ 
but  falls  equally  upon  the  just  and  the  unjust.** 

"The  old  Pine  sees,"  I  said,  "that  this  system   brings  certain' 
knowledge  to  myriads  of  beings,  thus  enabling   them    to  live 
intelligently  in  material   conditions,  and  he  can   imagine  thall 
this  may  be  accomplished  by  a  system   of  signals   similar  to 
telegraphy^  but  he  would  much  like  to  know  exactly  how  each 
of  the  sensations  acts.*'    , 

"As  Ellen  has  told  the  old  Pine/'  she  replied,  "the  great 
law  of  action  between  all  material  things  is  contact,  and  we  see 
that  this  machinery  of  the  body,  which  is  made  entirely  to  assist 
the  soul  in  its  material  life,  is  sustained  and  only  sustained  by 
the  introduction  of  sustenance,  and  that  means  material,  whether 
food  or  water,  into  the  body,  and  by  its  assimilation.     In  all  of 

and  force  may  be  conveyed  from  one  to  another,  is  to  me  so  great  an 

absurdity,  that  1  believe  no  man,  who  has  in  philosojihicai  matters  a. 
competent  faculty  for  thinfcingj  can  ever  fall  into  it. 


rHISPEF^lXGS    OF   AN     OLD      VINE 


683 


this  the  fundamental  character  of  the  soul's  susccptibHity  to  feel- 
ing is  shown  by  the  effect  which  this  sustenance  produces  on  it. 
**Aiid  this  soul,  as  we  know,  is  also  very  receptive  to  knowl- 
edge. But  all  the  sensations  come  from  the  introduction  of  mat- 
ter into  the  body.  Thus  that  of  sight  is  the  result  of  particles  of 
light  mixing  chemically  with  other  matter  in  the  eye,  and  making 
the  pictures  by  which  the  whole  outside  universe  is  instantan- 
eously brought  into  intimate  relation  with  all  intelligent  beings. 
Light  operates  similarly  in  a  camera,  which,  as  Ellen  thinks,  is 
a  demonstration  that  light  is  composed  of  matter  For  she  can* 
not  imagine  how  any  thing  can  produce  chemical  changes, 
except  matter."  • 


•  Ganot  says:  **The  choroid  is  a  membrane  between  the  retina  and 
the  sclerotic.  It  is  highly  vascubr^  and  supplies  the  nourishment  for  the 
chemical  and  physiological  processes  in  vision.  On  its  inner  surface, 
and  in  close  contact  with  the  ends  of  the  rods  and  cones,  is  a  layer  of 
densely  black  pigment  cells,  which  secrete  a  peculiar  yellowish  purple 
pigment  called  the  visual  purple^  and  which  is  rapidly  bleached  by  light. 
It  is  evidently  connected  with  the  act  of  vision,  but  its  precise  use  is 
uncertain.** 

The  Kncyclopcedia  Britannica  in  article  on  the  Eye  s;iys : 
''Recent  researches  of  lioll  and  Kuhne  have  shown  that  light  pro- 
duces chemical  changes  in  I  he  retina.  I  fan  animal  be  killed  in  the  dark, 
and  if  its  retina  be  exposed  only  to  »r/^7*:' rays,  the  retina  has  a  pecu- 
liar purple  color,  which  is  at  once  destroyed  by  exposure  to  ordinary 
light.  The  purple  matter  apparently  is  decomposed  by  light.  Ktihne 
has  also  shown  that  an  image  may  actually  ht  fixed  on  the  retina  by 
plunging  it  into  a  solution  of  alum  immediately  after  death.  Thus  it 
would  appear  that  light  affects  the  purple  matter  of  the  retina^  and  the 
result  of  this  chemical  change  is  to  stimulate  the  optic  filaments  ;  if  the 
action  be  arrested  we  may  have  a  picture  on  the  retina,  but  if  it  be  not 
arrested,  the  picture  is  evanescent ;  the  purple  matter  is  used  up,  anj 


684 


** These  pictures  In  the  eye  are  very  evanescent,  are  tfiey 
aot?"  I  asked. 

"Yes,"  she  replied^  '*but  a  copy  of  them,  by  aid  o!  the  optic 
nerve,  is  instantaneously  made  in  the  archives  of  the  brain,  for 
the  future  use  of  the  soul,  that  is,  in  the  interests  of  memory. 
For,  as  Ellen  has  told  ^he  old  Pine,  memor>^  is  a  record,  and 
the  record  of  all  such  things  as  these  is  made  by  nature  in  the 
•gray  matter  of  the  brain. 

''The  instruction  is  then  given  to  the  child,  by  parents,  or  at 
school,  or  elsewhere,  that  such  a  picture  is  that  of  an  oak,  or 
maple,  or  shell,  or  rock.  That  is,  every  material  thing  which 
reflects  light  may  make  a  picture,  always  a  similar  one,  and 
language  is  used  to  designate  it 

"  Sounds  enter  the  bodily  system  by  the  ear,  and  are  thus 
conducted  to  the  soul.  They  may  also  enter  by  the  teeth  or  by 
the  bones  of  the  head  or  body.  Their  number  is  infinite,  and 
it  being  understood  that  a  particular  sound  or  word  means  a 
particular  thing, — that  is,  by  the  use  of  language, — the  soul 
may  be  instructed  in  all  knowledge." 

"But  how,"  I  asked,  **do  sounds  affect  the  soul  to  impart 
knowledge  to  it?" 

**  This  is  but  another  illustration,"  she  replied,  **  of  the  soul's 
great  sensitiveness  to  matter,  when  brought  in  contact  with  it. 
For  the  sounds  act  as  signals,  each  particular  sound,  and  the 
soul  recognizes  their  difference,  as  it  does  that  of  a  plum, 
cherry,  or  peach,  or  any  other  combination  of  matter ;  only  the 

new  matter  of  a  similar  kind  is  formed  to  take  its  place.  The  retina 
might,  therefore,  be  compared  to  a  sensitive  plate  having  the  sensitive 
matter  quickly  removed  and  replaced  by  chemical  changes." 


WHISPERINGS   OF   AN    OLD    I'INE 


685 


plum,  cherry  or  peach,  help  sustain  the  body,  besides  produc- 
ing the  pleasurable  sensations  of  taste,  but  light  and  sound  act 
in  the  interest  of  knowledge. 

'*And  thus  material  is  collected  with  which  the  soul  may 
use  its  power  of  construction,  or  action »  \n  which  consists  its 
essential  nature.  Material  it  cannot  invent,  but  it  can  use  it, 
and,  as  Ellen  thinks,  if  not  brought  to  it  in  the  usual  manner  it 
strives  for  it*  proclaiming  by  exhibition  of  feeling  both  its  wants 
and  its  existence,  as  in  tlie  case  of  Helen  Keller  But  nature 
in  her  designs,  recognizing  the  conditions,  provides  that  the 
nccessar\^  material  for  the  performance  of  the  souTs  action  is 
furnished  to  every  sentient  being,*' 

"But  some  souls,"  I  said»**are  much  more  proficient  than 
others?** 

"Yes,"  she  rephed,  *'and  comparatively  few  very  proficient, 
and  yet  all  can  learn  enough  to  live  with  tolerable  comfort  in 
their  new  conditions." 

**Then  Kllen  thinks  that  the  power  of  action  with  the  soul  to 
use  material  for  the  construction  of  thought  within^  or  things 
without,  is  innate?** 

*'This  is  beyond  question,"  she  replied.  **  Hut  for  tliis  innate 
power  of  mind  a  creation  would  be  impossible.  This  is  the 
power  from  which  all  else  conies.  The  mind  of  man  is  limited, 
but  in  it  is  the  power  of  growth,  so  that  if  it  uses  its  oppor- 
tunity it  may  rise  to  high  position  in  this  life,  and  be  born  to 
nobler  opportunities  in  another. 

**And  thus  the  creation  of  both  matter  and  spirit  is  most 
abundantly  explained,  and  why  they  are  so  intimately  related 
to  each  other     As  Ellen  has  repeatedly  said*  matter  is  made 


by  Spirit  for  the  use  of  spirit.  There  could  be  no  universe 
witiaout  it;  no  opportunity  for  God  to  use  His  infinite  power  of 
construction*      But  now: 


^  Deep  in  unfathomable  mines 

Of  never  ending  skilly 
He  treasures  tip  His  vast  designs 

And  wor^     "'   sovereign  will.' 


-  '*But  matter  is  not  any  more  indispensable  to  spirit  than 
spirit  is  to  matter.  If  it  was  not  that  there  is  such  a  thing  as 
intelligence,  with  the  power  to  construct,  thierc  could  never 
have  beeii  any  material  for  the  purposes  of  construction^  whether 
©f  a  thought,  or  of  a  planet 

"  Then  Ellen  thinks  that  the  soul  begins  its  work  at  birth?" 

'*  Unquestionably,,  if  not  before.  When  concepts  are  intro- 
duced by  the  sensations,  the  soul  is  in  command,  although  not 
yet  accustomed  to  the  body's  machinery,  which  in  itself  is 
immature." 

"But  why,"  I  said  "Ellen,  should  sentient  beings  in  this  world 
be  so  dependent  upon  material  conditions  for  their  apparent 
existence?" 

'*It*savery  small  world,"  she  answered;  "and  it's  nothing 
strange  that  its  opportunities  should  be  limited.  That  it  is 
inhabited  by  many  beings,  learning  certain  things,  and  some  of 
them  quite  inferior  beings,  isn't  at  all  strange  to  Ellen,  for  with 
Eternity  for  improvement,  and  Infinity  for  abode,  infinite 
improvement  is  possible." 

"Well, "  I  said,  "the  old  Pine  can  see  that  Ellen  is  right,  that, 
of  necessity,  to  make  a  universe  there  must  be  matter." 


WHISPERINGS   OF   AN    OLD  I'lN'E 


687 


**Yes/'  she  continued,  **eke  there  wouldn't  be  any  moun- 
tains, or  any  houses ;  just  folks,  with  nothing  for  them  to  do,  or 
anything  for  them  to  live  In*  These  things  and  many  more 
are  necessary  to  make  a  universe.  Indeed,  Ellen  isn't  sure  it  is 
possible  to  have  too  great  a  variety.  For  we  wouldn't  want 
to  spare  the  gloss  upon  the  highest  mountains,  or  the  beauty 
gathered  in  the  smallest  valley.  Not  a  flower,  of  all  the  myriads 
that  adorn  the  earth,  nor  any  tree,  or  any  bush. 

** But  whilst  all  of  these  must  be  maintained,  and  the  laws 
which  govern  them  given  the  broadest  scope  of  operation, 
even  at  times  to  the  apparent  shutting  off  of  the  spiritual,  this 
last  will  fully  assert  itself,  guiding  and  controlling,  and  alone 
using. 

"Nature's  arrangement  is  one  of  education,  and  the  system 
used  is  the  introduction  to  the  soul  or  spiritual  part  of  existence, 
of  different  combinations  of  matter,  which  affect  it  differ- 
ently, and  all  in  such  a  way  as  to  impart  to  it  knowledge; 
each  combination  acting  as  a  new  word  in  nature's  dictionary. 
There  is  no  other  way.  The  old  Pine,  perhaps,  would  have 
made  ali  this  very  different?" 

•*No,"  I  said,  **  the  old  Pine  has  no  faculty  for  making  universes 
or  explaining  how  they  are  made.  He  couldn't  have  made  it 
at  all ;  but  he  thinks  everything  of  Ellen,  and  he  thinks  with  her 
vocabularies,  and  dictionaries,  and  signals,  telegraphic  or  other- 
wise, she  has  got  the  chart  of  material  existence  veiy  plainly 
marked  out,  so  that  the  old  Pine  can  see  how  it  is  made, 
though  he  could  not  have  made  it.  Nature's  great  system  of 
education  is  as  plain  as  that  of  a  school.  As  Ellen  says,  it  is  a 
system  of  universal  telegraphy  and  telephone  communication^ 


688 


extending  from  both  planets  and  fixed  stars  to  this  little  world 
of  ours,  and  from  this  little  world  to  the  planets  and  the  stars, 
And  the  old  Pine  is  already  thinking  of  sending  a  message  to 
Venus  some  nighti  when  she  is  shining  so  gorgeously  in  the 
heavens.  It  will  travel  to  her  at  the  rate  of  184,000  miles  per 
second,  which  is  quite  a  fair  pace,  though  one  may  have  to 
wait  a  little  for  the  answer. 

"And  then  there  will  be  all  the  fixed  stars  left  for   further    J 
communications.    The  old  Pine  thinks  electricity  is  the  begin* 
ning  and  the  end  of  universal  existence.'^ 

*<  And  Ellen  thinks  that  he  is  dreadfully  mistaken.  It  may 
be  the  beginning,  but  the  end  God  only  knows«  The  end,  as 
Ellen  thinks,  is  a  land  fairer  than  day,  where  all  these  changing 
scenes  vanish,  trouble  has  no  foothold,  and  death  no  further 
use.  But  universal  love,  universal  beauty,  and  universal  knowl- 
edge reign  instead — ^The  Good,  the  Beautiful  and  the  True. 

"Ellen  has  especially  considered  the  sensations  of  seeing 
and  hearing.  Odor,  as  is  well  known,  consists  of  infinitesimal 
particles  of  matter  thrown  off  by  odoriferous  bodies,  and  these 
find  their  way,  too,  into  the  bodily  organism  of  all  sentient 
beings,  where  like  food  and  drink  they  affect  the  spirit,  or  soul, 
causing  the  pleasurable  sensation  of  smell." 

**And  Touch?"  I  said. 

**  Touch  has  to  do  with  outside  bodies  directly  by  contact. 
And  as  pressure  may  arouse  motion  which,  as  Ellen  has  shown, 
must  be  moving  matter,  that,  entering,  will  move  a  train  of  cars ; 
so  touch,  which  of  necessity  implies  pressure,  must  arouse  or 
create  moving  matter,  which  entering  the  body  follows  the  nerves 
to  the  seat  of  the  soul,  and  delivers  the  appropriate  message. 


WIirsrERINGS   OF   AN   OLD    PINE 


689 


**  And  thus  the  old  Pine  can  see»  and  all  can  see,  that  infor- 
mation is  conveyed  to  the  soul  by  the  introduction  of  matter 
into  the  body,  and  in  no  otlier  way,  It  is  the  result  of  the 
effect  of  matter  upon  spirit,  but  this  effect  can  only  be  reached 
when  matter  is  brought  in  contact  with  the  thinking  substance, 
or  into  its  immediate  presence.  So  that  this  great  law  of  the 
combination  of  matter  not  only  makes  ever\'  possible  thing  in 
the  material  universe,  but  also  is  used  as  the  medium  for  im- 
parting all  knowledge  of  material  things  to  every  sentient  being 
in  material  conditions/* 

*'  Ellen  has  triumphed  gloriously/*  I  said,  "for  she  has  un- 
folded the  principle  of  Sensation — showing  the  processes  by 
which  it  works,  and  thus  opening  a  new  chapter  in  the  world's 
history. 

**The  old  Pine  has  never  loved  her  so  much  as  he  does  now 


*She  walks  in  beauty  like  the  night, 
Of  cloudless  climes  and  starry  skies/  " 

*' Ellen  thinks  the  old  Pine  is  especially  unhappy  in  his 
poetry/'  she  replied.  'VFor  Ellen's  eyes  are  blucg  and  her  hair 
is  golden,  so  that  it  would  be  impossible  for 

'  All  ihat*s  best  of  dark  or  bright 
To  meet  in  her  aspect  and  her  eyes/ 

*'But  she  accepts  the  compliment  for  her  explanation  of  the 
Sensations/* 


tf90 


(( 


BUT 
of 


XLVI 


what  is  the  history,  Ellenp'*  T  asked,  '*  of  the  theo 
souad?     Has  this  tindulatory  theon^  been    univer- 
sally accepted  since  Mr,  Ne\\ton*s  day?'' 

"Not  at  all,"  she  replied.      *  A  nymber  of  eminent  men  have* 
questioned  it,  but  the  old  Pine  knows  that  after  such  a  theorjr 
has  been  intrenched  behind  vested  property  interests  in  text- 
books and  teaching/it  becomes  doubly  difficult  to  get  rid  of  it. 

"Shortly  after  its  announcement  by  Mr.  Newton  the  theory 
was  questioned.  In  1799  the  French  naturalist  and  scientist, 
Lamarky  read  a  memoir  on  sound  of  perhaps  a  hundred  pagesa 
at  a  meeting  of  noted  scientists  in  Parist  in  which  he  claimed  * 
that  since  sound  passed  through  solid  bodies  as  well  as  through 
gases,  and  since  it  was  impossible  for  air  to  enter  such  solid 
bodies,  sound  was  made  by  the  peculiar  jostle  or  thrust  of  an 
exceedingly  subtle  substance  which  readily  permeates  all  or 
nearly  all  substances. 

**  Reese's  Encyclopaedia  thus  defines  sound : 

'  Sound  originates  in  the  percussion  and  vibration  of  the  parts  of  an 
elastic  substance  and  is  transmitted  by  means  of  the  elasticity  of  the 
air,  or  of  some  other  more  subtle  medium  of  a  similar  kind.* 

"Paroletti,  in  'Inquiries  Concerning  Sound,'  says: 


*  Soimd  is  propagated  by  infinitely  small  vibrations,  according  to  the 
theory  of  M.  De  la  Grance.  and  it  is  probable  that  this  takes  place 


WHISPERUJGS   OF  AN  OLD   PLNE 


693 


in  the  particles  of  a  very  light,  elastic  fluid  of  a  peculiar  natiire  and 
which  should  not  be  confounded  with  the  gases  that  compose  what  we 
know  as  the  atmosphere.* 

**  About  1825  the  present  theory  was  again  questioned  by 
Sir  G*  S.  McKcnzie*  Vice-President  of  the  Royal  Society  of 
Edinburgh.  In  the  paper  read  Mr.  McKenzie  expressed  the 
opinion  that  sound  is  an  entity,  as  follows: 

'It  is  a  groundless  expectation  that  man  is  ever  to  arrive  in  the 
progress  of  discovery  at  the  nature  or  essence  of  anything.  With 
respect  to  sound,  therefore^  we  ran  do  nn  more  than  attend  to  the 
immediate  causes  of  its  production,  and  to  the  laws  which  it  obeys  in 
its  diffusion.  In  the  present  state  of  our  knowledge  concerning  it, 
philosophers  appear  to  have  entirely  rejected  the  idea  of  its  being  a 
thing  sni  generis^  as  light  anil  heat,  and  to  have  become  content  with 
the  rather  unsatisfactory  conclusion  of  its  being  mere  mechanical 
action.  Such  a  conclusion,  however,  does  not  afford  sufficient  ground 
for  altogether  ceasing  to  observe  the  phenomena  of  sound,  and  the  cir- 
cumstances Hurler  which  it  is  made  known  to  the  sense  of  hearing* 

*The  analogy  between  sound  and  light  has  been  noted  as  remarkable, 
and  as  light  and  heat  have  been  admitted  to  be  distinct  entities,  and  as 
they  have  distinct  organs  of  sense  (the  eye  and  the  skin),  appointed  to 
them  ;  and  as  taste  and  smell  are  also  made  known  by  motion,  and 
contact  with  distinct  organs ;  and  as  there  is  a  distinct  organ  appro- 
priated to  sound,  there  is  no  reason  why  it  should  not  be  regarded  also 
as  a  distinct  entity,  although  hitherto  our  observation  has  not  been 
extended  far  enough  to  show  thai  it  is  such,' 

*' Numerous  other  writers  have  since  questioned  the  undula- 
tory  theory,  prominent  among  them  the  Rev.  A*  W.  Hall  of  New 
York,  a  Methodist  clergyman  and   a   man  of  unusual  natural 


694  n^^^       ELLEN   OR  THE 

abilities*  Mr,  Hall,  in  *Th<*  Problem  o(  Human  Life,'  abund- 
antly disproved  the  correctness  of  such  a  theory,  and.  like  Mr* 
McKenziCt  considered  sound  an  entity.  Ellen  will  close  thi« 
part  of  the  discission  with  several  quotations,  and  first  from 
an  excellent  article  entitled  *  On  the  Identity^  of  Light,  Heat, 
Electricity,  Magnetism,  and  Gravitation/  by  J.  Goodman*  M.D,p 
M,R,  C.  Sm  published  in  the  *  Memoirs  of  the  Literary  and 
Philosophical  Society  iter'  (1852): 

*  From  the  difference  of  temperature  of  bodies, —  the  facility  with 
which  we  can  increase  the  temperature  of  a  cold  body  hy  the  oppositioo 
of  one  already  heated,  and  of  cooirng  the  latter  also  by  the  same  coo- 
tact, — and  from  the  laws  of  transmission,  diffusion,  radiation^  ignition 
coctioD,  fusion,  and  volatilization,  by  this  force  ; —  I  cannot  in  spite  of 
all  modern  theories  upon  the  subject  341  d  the  teaching  of  the  schools 
draw  any  other  conclusion  than  that  this  force  is  a  land  Jit/f  imfi^^ndtr' 
abk  txuitmt^  possessing  the  ordinary  qualities  of  matttr^  hHatity^  txUn- 
aiti n^  impt'n etni f^r/'f  1 ,  /^  .  ■■■  f'l '' r,- ,  fi firactio n ,  m&tio n  :  and,  as  I  I > r ! i r  *  c:  i > 
shown  in  the  following  experiments,  momentum  also — a  property  hith- 
erto applied  alone  to  ponderable  matter.  That  heat  possesses  the  three 
former  properties  is  not  objected  to  by  philosophers,  inasmuch  as  it  is  not 
contended  that  it  enters  into  the  substance  of  the  atoms  or  elementary 
particles  of  matter^  and  occupies  with  matter  the  same  space  at  the 
same  time,  but  simply  is  described  as  filling  the  interstices  between 
these  elementary  particles.  It  is  also  as  capable  of  transmission  from 
one  substance  to  another,  as  water  when  poured  from  vessel  to  vessel. 
It  is  to  a  certain  extent  capable  of  accumulation  and  retention^  w^ithout 
renewal,  like  other  fluids  in  nature ;  we  find  that  the  retention  of  these 
latter  is  of  very  short  duration  if  left  to  evaporate,  uncovered  and  unpro- 
tected, or  in  contact  with  leaky  or  porous  substances. 

*  There  is  therefore  reasonable  ground  for  concluding,  that,  as  every 


WHISPERINGS    OF  AN   OLI 


095 


mown  substance  in  nature  is  more  or  less  porous  to  the  calorific  fluid, 
if  caloric  could  ,he  as  effectually  surrounded  l>y  substances  incapable  of 
its  transmission  as  the  liquitls  in  daily  use  can  be,  we  shoukl  be  able  lo 
pieser\ie  it  at  any  degree  of  intensity,  and  that  without  addition,  lor  any 
protracted  period*  y 

*  But  it  is  manifest  that  whatever  may  be  the  teaching  of  the  schools 
with  regard  to  the  nature  of  caloric — ^they  all  practically  denominate  it 
Dot  as  a  mere  mode  of  action  or  the  result  of  motion  among  the  par- 
ticles of  matter —  but  as  a  hond  fiih  and  genuine  substance  and  as 
endowed  with  all  the  powers  and  qualities  usually  attributed  to  real 
material  existences, 

'  The  facts  that  appear  lo  me  especially  unanswerable,  bearing  against 
modem  theory,  arc,  that  if  one  were  to  admit  for  the  sake  of  argument 
that  caloric  \%  generated  by  friction,  why  does  not  the  effect  cease  when 
the  causae  is  discontinue*!  ?  Why  does  it  not  cease  to  exist  when  friction 
ceases?  Or  else,  why  is  not  caloric  daily  and  hourly  accumulating? 
How  is  it  that  when  by  snch  heat  generated  we  have  kindled  a  fire, 
which  might  also  be  admitted  to  ilepend  for  its  development  on  motion 
of  a  chemical  nalore  occurring  among  its  own  particles,  —  how  is  it  Uiat 
by  this  same  fire,  once  produced,  we  c^tn  communicate  a  certain  degree 
of  redness  or  white  heat  to  a  piece  of  iron  or  other  substance,  without 
producing  any  motion  among  its  particles,  and  with  this  heated  metal 
we  can  communicate  warmth  to  the  air,  ignite  a  second  fire,  or  boil 
water,  which  shall  absorb  just  the  e^act  amount  of  heat  lost  by  the 
heated  iron,  and  shall  ultimately  be  able  to  retain  this  communicated 
caloric  for  a  considerable  period? 

*  I  think  that  heat  is  shown,  by  these  and  other  facts,  to  have  an  inde- 
pendent existence,  so  far  :is  our  present  ideas  of  entity  and  non-entity 
extend. 

*  Again,  if  caloric  were  admitted  to  be  the  mere  creation  of  nutter, 
iiow  is  it  that  the  other  imponderable  forces,  which  ar«  by  many  phi- 


losopliers  admitted  as  convertible  into  calortCp  and  viVe  versd^  are  nat ' 
them  also  assignetl  to  the  same  origin  and  the  same  mode  of  existence  ? 

'  It  has  already  been  shown  by  the  bbors  of  Dr,  Wollastoiij  Dr.  Far- 
aday, and  the  author  of  this  paper,  that  the  ordinary  electric  and  voltaic 
forces  are  identical ;  and  many  years  ago  the  analogy  o!  aerial  electricity^ 
or  lightning,  was  sufficiently  demonstrated  by  the  experiments  of  Dr> 
Franklin, 

P'lTie  reciprocal  infti  nutual  dependence  of  these  forces 

along  w-ith  magnetism,  ana  ine  onedience  of  electricity  to  some  of  the 
laws  of  magnetism,  and  vife  versd^  as  well  as  the  analogy  of  the  phe- 
nomena manifested  by  all  these  forces,  evince  their  Identity.  In  ilius- 
tralion  of  the  identity  of  electricity  with  magnetism,  I  read  a  paper 
before  the  British  Association  in  1843J  in  which  it  was  shown  that  a 
plate  of  glass  maintained  in  a  constant  polar  condition  by  the  simple 
current  from  the  ordinary  electrical  machine,  sustained  the  weight  of 
5  ounces  and  20  grains ;  showing  that  frictional  electricity  itself^  when 
placed  in  a  condition  resembling  magnetism  ^ — or  rather  electro-mag- 
netism—will  produce  with  them  an  equivalent  effect  proportionate  to 
its  inferior  quantity  and  powers. 

'With  regard  to  the  identity  of  light  and  heat  —  forces  which  I  hold 
to  be  so  far  identical  as  to  be  in  their  common  acceptation  simply  the 
essential  qualities  of  the  one  subtle  force  imder  investigation  —  I  refer 
to  the  experimental  labors  of  M.  Melloni  and  Prof.  Draper. 

*  We  have  therefore  deficient  only  one  link  in  the  chain  of  identity 
among  all  these  imponderable  forces,  and  that  link  is  the  identity  of  the 
force  light  or  heat,  with  electricity.  I  have  already  shown  that  there 
are  many  points  of  analogy  between  voltaic  electricity  and  the  caloric 
force.  Each  of  these  forces  is  found  occupying  the  interior  or  so-called 
interstitial  space  of  the  elements  of  bodies,  they  are  the  admitted  agents 
which  operate  upon  the   elementary  particles  or  atoms  of   matter,* 


*  This  is  not  true  of  the  other  forces.    See  report  of  British  Association,  1842. 


WHISPERINGS  OF  AN  OLD   PINE 


697 


and  are  possessed  of  essential  qualities  common  to  both,  which  are 
exhibited  in  all  their  liiminiferous  and  calorific  phenomena. 

'It  is  this  link  which  I  believe  is  discovered  and  supplied  by  the  fol- 
lowing experiments  [with  the  galvanometer],' 

**  Ellen  will  omit  the  experiments,  as  now  the  substantial 
identity  of  light,  heat,  and  electricity  is  admitted. 

*The  results  of  these  experiments  evince  to  ray  mind  more  than  ever 
the  unity  of  force.  On  every  hand  experimental  evidence  appears  to 
justify  the  conclusion  that  there  is  one  universal  force  in  nature,  which 
is  modified  by  the  accidental  and  varied  conditions  to  which  it  is  sub- 
ject, but  that  its  essential  nature  and  characteristics  are  at  all  times  the 
same,  and  evince  in  every  modification  constantly  the  same  unchang- 
able  qualities,  which  are  discoverable  by  man  under  the  denomination 
of  sensations,  as  well  as  luminous  and  calorific  properties, 

*  I  believe  that  these  experiments  indicate  and  indeed  prove  the 
identity  of  caloric  and  voltaic  force  and  that  now  the  last  required  link 
for  the  completion  of  the  entire  chain  of  identity  of  these  imponderable 
forces  is  obtained/ 

**  Mn  Herbert  in  his  work,  *  Modern  Realism  Examined,*  says: 

'And  all  the  evidence  accumulated  tends  to  extricate  us  from  the 
unintelligible  and  baffling  conceptions  of  imponderable  agents,  subtle 
fluids,  and  occult  principles  working  in  ways  wholly  unfamiliar  to  us, 
and  to  substitute  for  them  the  movements  of  infinitesimal  particles  or 
molecules,  regulateti  by  the  same  laws  of  mechanical  action  which 
masses  of  matter  appreciable  by  our  senses  obey.' 

**So  Mr.  Justice  Grove  teaches: 

'I  believe  the  day  is  approaching  when  the  two  fundamental  con- 
ceptions of  matter  and  motion  will  be  (ouud  sufficient  to  explain 
physical  phenomena.* 


698  ELLEN   OR  THE 


XLVII. 

^^ FALLEN  will  now  recapitulate  in  part.     It  has  been  shown 

-■— '  that  the  undulatory  theory  of  sound  never  had  any 
foundation,  being  built  upon  an  unproven  hypothesis.  And  it 
has  been  demonstrated  to  be  impossible  in  these  respects : 

*'  First.     Mathematically. 

"  Second.  Such  a  system  of  air  waves  as  those  supposed 
could  not  exist,  because  of  the  mobility  of  the  air.  Therefore 
the  material  representation  of  sound  would  be  impossible, 
without  which  there  can  be  no  sensation.  • 

*'  Third.     Echoes  would  be  impossible. 

**  Fourth.  The  action  of  the  megaphone  or  ear  trumpet  is 
uncxplainablc  and  would  be  impossible. 

"  Fifth.  The  uniform  speed  of  sound  cannot  be  explained. 
For  by  the  theory,  as  tested  by  experiment,  all  sounds  should 
have  different  speed  and  vary  constantly  in  their  speed. 

•'Sixth.  Waves  of  air  or  particles  of  air,  however  moved, 
are  altogether  insufficient  to  explain  the  record  of  a  grapho- 
phone  or  the  action  of  a  telephone. 

"Seventh.  It  would  be  impossible  for  sounds  to  pass  each 
other. 

•'  Eighth.  The  undulatory  part  explains  nothing,  and 
teaches  nothing. 

"These  are  among  the  objections  to  the  theory,  and  any 
one  of  them  is  fatal.     But  above  them  all    is  the   fundamental 


f 


THr  ITEW  TORK 

PUBLIC  LIBRARY 


^«T»«,  tIMAJt  ANO 
«  t 


WHISPERINGS    OF   AN   OLD    PINI 


701 


bjectton  that  the  theory  is  subversive  of  the  greatest  of  nature^ 
physical  laws,  that  by  which  things  are  made, 

**  Conversely,  Ellen  has  shown  that  sound  is  composed  of 
infinitesimal  particles  of  electrical  matter,  which  can  enter  many 
if  not  all  bodies.  It  is  caused  by  shock  or  friction  in  an  elastic 
body,  in  the  interstices  of  which  it  circulates  to  and  fro,  causing 
vibration,  which  helps  decide  the  character  of  the  sound  and  then 
throws  it  into  tlic  air.  The  particles  of  sound  because  of  their 
infinite  numbers,  and  innate  tendency  to  move,  spread  in  all 
directions,  and  are  thus  enabled  easily  to  perform  the  purposes 
for  which  they  were  made. 

*'In  this  way  sound  continues  until  the  measure  of  its  life 
is  finished,  thus  causing  it  to  exist  in  every  part  of  the  air  as 
well  as  in  the  whole  air,  which  Lord  Bacon  thought  one  of  the 
'strangest  secrets  in  sounds'  and  which  again  would  be  entirely 
impossible  under  the  undulatory  theory;  for  this  supposes  the 
character  belonging  to  every  voice  to  consist  of  the  motions  of 
the  air  particles  of  the  hypothetical  waves,  some  of  which  are 
over  seventy  feet  fn  length. 

**  Ellen  will  repeat  again  Mr.  Huxley's  criticism  upon 
hypotheses. 

'Every  hypothesis  is  bound  to  explain,  or  at  any  rale  not  to  be  incon- 
sistent with,  the  whole  of  the  facts  it  professes  to  account  for;  and  if 
there  is  a  single  one  of  these  facts  which  can  be  shown  to  be  incon- 
sistent with  the  hypothesis,  such  hypothesis  fiills  to  the  ground — it  is 
worth  nothing.  One  fact  with  which  it  is  positively  inconsistent  is  worth 
as  much,  and  is  as  powerful  in  negativing  the  hypothesis,  as  five  hundred,* 

"This  undulatory  theory  explains  none  of  the  facts  and  is 
inconsistent  with  all,  whilst,  on  the  contrary,  the  entity  theory 


70Si  ELLEK  OR  THE 

txplatiis  all  and  is  inconsistent  with  none.  Forliie  entity  tfaecny 
explains  echoes  by  the  usual  laws  of  the  reflection  of  bodies. 
The  correlative  of  sound  is  complete  as  a  tree  is  complete, 
because  it  is  made  so.  The  action  of  the  megaphone  and  ear 
trumpet  is  precisely  what  it  must  be  with  sound  an  entity  per* 
vading  the  air,  for  the  megaphone  gathers  it  and  conducts  it  as 
it  would  rain  drops  or  any  other  substance.  The  speed  of 
sound  is  inherent  and  varies  with  the  substance  it  is  passing 
through ;  just  as  a  stone  falling  in  water  and  air  moves  with 
different  speed.  And  this,  indeed,  is  a  very  general  law  of 
nature.  The  record  of  a  graphophone  and  the  action  of  a 
telephone  are  both  intelligently  and  fuUy  explained.  The 
enigma  of  sounds  passing  each  other  is  fully  explained ;  for 
they  pass  each  other  as  all  other  things  in  nature,  because 
there  is  room,  or  when  there  is  room. 

"  It  follows  that  the  whole  undulatory  theory  of  sound  has 
been  entirely  discredited.  And  with  it  of  course  fall  all  undu- 
latory theories,  and  we  see  that  by  one  system  only,  and  that 
a  substantial  one,  all  things  are  made. 

"This  is  what  common  sense  and  our  experience  tell  us  must 
be  true.  For  the  universality  of  nature's  laws,  that  is,  the  prin- 
ciple of  order,  alone  makes  possible  nature's  wonderful  works. 
Without  it  there  could  be  no  creation.  Without  it  all  success- 
ful result  is  impossible.  Ellen  can  see  that  scientists  under 
bad  leadership  might  blunder  into  the  idea  that  there  was  no 
system,  and  tongue-tied  by  authority,  for  some  time  wander  in 
the  paths  of  ignorance,  but  so  mistaken  a  conception  cannot 
last.  The  clouds  will  surely  break  and  the  magnificent 
splendor  of  the  creation,  in  whose  system  there  is  no  variable- 


WHISPERINGS  OF   AN   OLD    PINE 


703 


ness  or  shadow  of  turning,  be  made  manifest  to  all,  proclaiming 
the  infinite  wisdom  and  love;  the  infinite  wisdom  and" power  of 
Him  who  has  both  designed  and  created  the  whole,  and 
without  whose  knowledge  not  a  sparrow  falls  to  the  ground. 

"Ellen  will  close  this  visit  with  quotations  from  'Life  and 
Letters  of  Faraday/  vol.  i,  page  308,  and  an  article  on  *  Radiant 
Matter/  by  William  Crookes,  inventor  of  the  Crookes  radiom- 
eters. In  this  last  Ellen  will  not  vouch  for  the  counting,  but 
written  from  a  scientific  standpoint  it  suggests  the  infinite  num- 
ber of  molecules  that  are  supposed  to  be  hidden  from  our 
sight.  But  the  entity  sound  is  smaller  than  these,  for  it  passes 
readily  through  those  bodies  which  particles  of  air  cannot 
enter.      Mr.  Faraday  says; 

*1  may  now  notice  a  curious  progression  in  physical  properties 
accompanying  changes  of  form,  and  which  is  perhaps  sufficient  to 
induce,  in  the  inventive  and  sanguine  philosopher^  a  considerable 
degree  of  belief  in  the  association  of  the  radiant  form  with  the  others 
in  the  set  of  changes  I  have  mentioned, 

*  As  we  ascend  from  the  solid  to  the  iluid  and  gaseous  states,  physi- 
cal properties  diminish  in  number  and  variety,  each  state  losing  some 
of  those  which  belonged  lo  the  preceding  state.  When  solids  are  con- 
verted into  fiuids,  all  the  varieties  of  hardness  and  softness  are  neces- 
sarily lost.  Crystalline  and  other  shapes  are  destroyed.  Opacity  and 
color  frequently  give  way  to  a  colorless  transparency,  and  a  general 
mobility  of  particles  is  conferred. 

'Passing  onward  to  the  gaseous  state,  still  more  of  the  evident  char- 
acters of  bodies  are  annihilated^  The  immense  differences  in  their 
weight  almost  disappear;  the  remains  of  difference  in  color  that  were 
left  are  lost»  Transparency  becomes  universal,  and  they  are  all  elastic. 
They  now  form  but  one  set  of  substances,  and  the  varieties  of  density, 


704 


ELLEK  OR  nm 


haxfixkO^s,  opacity^,  ^olor,  -elastlei^,  and  fdnpai,.  which  i 
o^  solids  and  fluids  >ahnost  in&^te,  are  now  viaggi^ 
'mm^ons  m  wejght,  and  some:unmiKWc;ta]|t^s|^^^ 

*To^tho»e,  tl\trc^9tp»:wbp  a^^tt^p  W^  ^ 

ciilty  exist^  m  tii^  simpJicity  of  the  properties  it^  pc 
an  arguxnent  in  t^eir  favo];.  T^ese  persons  show  you 
tion  of  properties  in  the  mattet  we  can  appredl 
asK:ends  In  the  scale  b!  fohns,  ahd  ffie]!^  woiild  1>e  su^ 
Were  to  cease  at  the  i^eons  state?  iTli^'pb&f  Mt 
tions  ^ch  nature  mak^  at  each  step  of  the^'diiai^ 
consistently,  it  dught  to  W  gkatei^'Jn^  €ieP  pte^tf 
td the tadiant form/    --'i-  "''-'       -•*:";:•.:%  v'if-; 


.:C- 


iJiC'.J 


"This  is  in  very  refreshing  contrast;. to.  tiae_ 

talk  of  scientists  on  these  subjects.     Mr.  Crool 

;•.,.-.         ;    •  -i. -^    ;    .r    ,. ;..  ...r^irj    r.    ;..,!; 

.  ^  It  may-  be  objected  that  it  i^  hardly  consistent 
importance  to  the  presence  of  jxMr/^,  when  I  have  t 

pains  to  remove  as  much  matter  as  possible  from  the 
tubes,  and  have  succeeded  so  far  as  to  leave  only  a 
lionth  of  an  atmosphere  in  them.  At  its  ordinary  p 
phere  is  not  very  dense,  and  its  recognition  as  a 
world  of  matter  is  quite  a  modern  notion.  It  woul 
divided  by  a  million,  so  little  matter  will  necessari 
may  justifiably  neglect  the  trifling  residue,  and  apply 
to  space  from  ivhich  the  air  has  been  so  nearly  ren 
however,  would  be  a  great  error,  attributable  to  oi 
being  unable  to  grasp  high  numbers.  It  is  generally 
that  when  a  number  is  divided  by  a  million  the  qt« 
sarily  be  small,  whereas  it  may  happen  that  the  ori 
large  that  its  division  by  a  million  seems  to  make  li 
it.    According  to  the  best  authorities,  a  bulb  of  tl 


WHISPERINGS   OF   AN   OLD   PINE 


705 


before  you  (13-5  centimetres  in  diameter)  con  tains  more  than  1,000000,- 
000000,000000,000000  (a  quadrillion)  raolecules.  Now,  when  exhausted 
to  a  milUonth  of  an  atmosphere  we  shall  still  have  a  trillion  molecules 
left  in  the  bulb  —  a  number  quite  sufficient  to  justify  me  in  speaking  of 
the  residue  as  matUr, 

'  To  suggest  some  idea  of  this  vast  number,  1  take  the  exhausted 
bulb,  and  perforate  it  by  a  spark  from  the  indiiction*coil*  The  spark 
produces  a  hole  of  microscopical  fineness,  yet  sufficient  to  allow  mole- 
cules to  penetrate  and  to  destroy  the  vacuum.  The  inrush  of  air 
impinges  against  the  vanes  and  sets  them  rotating  after  the  manner  of 
a  windmill.  Let  us  suppose  the  raolecules  to  be  of  such  a  size  that,  at 
every  second  of  lime,  a  hundred  million  could  enter.  How  long,  think 
you,  would  it  take  for  this  small  vessel  to  get  full  of  air?  An  hour? 
A  day?  A  year?  A  century?  Kay,  almost  an  eternity  I  —  a  time  so 
enormous  that  imagination  itself  can  not  grasp  the  reality.  Supposing 
this  exhausted  glass  bulb^  indued  with  indestnictibilit)^,  had  been 
pierced  at  the  birth  of  the  solar  system ;  supposing  it  to  have  been 
present  when  the  earth  was  without  form  and  void ;  supposing  it  to 
have  borne  witness  to  all  the  stupendous  changes  evolved  during  the 
full  cycles  of  geologic  time,  to  have  seen  the  first  living  creature  appear 
and  the  !ast  man  disappear;  supposing  it  to  sur\Mve  until  the  fulfdl- 
ment  of  the  mathematicians'  prediction  that  the  sun,  the  source  of 
energy,  four  million  centuries  from  its  formation  will  ultimately  become 
di  burned  out  cinder  ;*  supposing  all  this — at  the  rate  of  filling  I  have 
just  described,  one  hundred  million  molecules  a  second  —  this  little  bulb 
even  then  would  scarcely  have  admitted  its  full  quadrillion  of  raolecules.t 


•The  possible  duration  of  ihe  sun  from  formation  to  extinclion  has  been  variously 
estimated  by  different  authoriliea  at  from  eighteen  million  years  to  four  hundred  mil- 
lion years.     For  the  purpose  of  this  lUustratiori  I  have  taken  the  highest  estimate. 

t  According  to  Mr,  Juhiistonc  Stoney  (**  Philosophical  Magazine,"  vol,  jtxxTi,,,  p, 
141),  I  c.  c.  of  air  contains  about  iooo,oooooo,oooooo,oocxxxi  molecules.  There- 
fore* A  bulk  IJ.5  ccntims,  diameter  contains  13.5^  X  0.5236  X  iooo,oooooopooooo,- 
000000  or  1,288252,350000,000000^000000  molecules  of  air  at  the  ordina:ry  pressure. 


7o6 


ELLEN  OR  THB 


'Bat  what  will  you  saj  if  I  tdl  y&x  that  all  these  molecitleK,  this 
quadrinioQ  of  moleculesy  will  enter  tfaiou^  the  uiicroscopjc  hole  before 
yoa  leave  this  room?  The  hole  being  unaltered  in  si^e^  the  number  of 
moleculea  undiminished^  tihis  appaxent  pazadoiE  can  only  be  expkuned 
by  again  supposing  the  size  off  the  molecules  1o  be  diinirtishe<i  ahxiosl 
infinitely — so  that^  instead  of  entering  at  the  rate  of  one  hundred 
millions  every  second,  they  troop  in  at  a  rate  ot  someihing  like  three 
hundred  trillions  a  second  I  I  have  done  the  rnxm^  but  figures  ivheu 
they  mount  so  high  cease  to  have  any  meaning,  and  such  calcubtions 
are  as  futile  as  trying  to  count  the  drops  in  the  ocean. 

'  In  studying  this  fourth  state  of  matter,  or  tadtant  matter»  we  have 
seen  that,  in  some  of  its  properties  it  is  as  materia!  as  this  table*  while 
in  other  properties  it  almost  assumes  the  chamctcr  of  radiant  energy. 
We  have  actually  touched  the  border-land  where  matter  and  forre  seem 
to  merge  into  one  another,  the  shadowy  realm  between  known-  wmd 
imknown,  which  for  me  has  always  had  peculiar  tcmptatiaos«  I 
ture  to  think  that  the  greatest  scientific  pioblems  of  the  fiiton  wiU  - 
their  solution  in  this  border-land,  and  even  beyond ;  here^  it 
me,  lie  ultimate  realities,  subtile,  far-reaching,  wonderfuL 

' "  Yet  all  these  were,  when  no  man  did  them  know. 
Yet  have  from  wisest  ages  hidden  beene ; 
And  later  times  thinges  more  unknowne  shall  show. 
Why  then  should  witlesse  man  so  much  misweene. 
That  nothing  is,  but  that  which  he  hath  seene  ?  " »  " 


Therefore  the  bulk,  when  exhausted  to  the  millionth  of  an  atmosphere,  contains 
1,28825  2,350000,ooocxx)  molecules,  leaving  1,28825 1,061 747,650000/xx)0oo  mole- 
cules to  enter  through  the  perforation.  At  the  rate  of  100,000000  molecules  m 
second,  the  time  required  for  them  all  to  enter  will  be — 

12882,510617476500  seconds,  or 

214,708510,291275  minutes,  or 

3»578475»i7«52i  hours,  or 

149103,132147  days,  or 

408,501731  years. 


WHISPERINGS   OF   AN   OLD   PINE 
She  arose  as  she  finished. 


707 


•*Ellea  has  more  than  fulfilled  her  promises/*  she  said,  *' in 
discussing  with  the  old  Pine  this  undulatorj'  theory^  of  sound. 
The  undulatory  theory  of  light  is,  if  possible,  more  intolerably 
stupid  than  that  of  sound ;  but  it  will  not  be  necessary  for 
Ellen  to  consider  that  with  the  old  Pine*  For  all  the  undula* 
tory  theories  will  fall  together,  and  the  great  physical  truths 
of  nature  be  finally  established  on  a  firm  and  consistent  basis* 
So  that  when  Ellen  comes  again  she  can  talk  upon  subjects  far 
more  interesting  and  instructive.** 

She  raised  her  eyes  to  me,  filled  with  love. 

'*The  beautiful  Ellen,'*  I  said,  *^  whose  whole  life  is  a  mission 
for  good.  The  old  Pine  hopes  that  every  part  of  it  may  abound 
in  happiness," 

"The  old  Pine  is  one  of  Ellen*s  best  friends/*  she  answ*ered; 
*'  and  then  he  has  lots  of  common  sense.  That's  why  she  likes  to 
talk  to  him.  But  Ellen  now  must  hurry  home ;  for  Gertrude  may 
want  assistance,  or  to  be  released.  And  the  pretty  Edith 
will  run  to  meet  Ellen,  and  tumble  all  over  her/* 

•*  And  the  beautiful  Ellen?" 

•*Will  bid  the  old  Pine  good-bye.*' 

The  look  of  decision  and  power  again  reigned  in  her  eye  j 
that  look  which  all  the  trees  and  plants  and  stones  and  rocks  of 
our  mountain  have  learned  both  to  respect  and  to  love.  And 
with  a  smile  for  all,  she  sprang  into  the  forest  and  disappeared. 

"Always/*  I  said,  **rt  is  the  same  sweet  Ellen — fearless,  un- 
sparing, hating  error  and  loving  Truth.'* 


APPENDIX. 


APPENDIX. 


The  following  article  is  from  the  Middlebury  (Vt.),  Register* 
December  27,  1901. 

CATHODE  IL-WS, 

A  REVIEW  OF  THE  ARTICLE  OF  PROF.  J.  J.  THOMSON,  OF  OXFORD  UNI- 
VERSrrV,  ENGLAND,  ON  CATHODE  RAYS,  IS  HARPER*S  >UGAZ1N£  FOR  SEP- 
TEMBER,  1901,  BY  JOSEPH  BArrELL,  AUTHOR  OF  "ELLEN,  OR  WHISPER- 
INGS  OF  AN   OLD    PINE/* 


A  few  weeks  since  we  sent  a  copy  of  "Ellen"  to  Prof*  J*  J,  Thom 
son  of  Oxford  University,  Englantl,  saying  in  a  letter,  that  we  perceived 
from  his  article  in  Harper*s  Magazine  of  September,  1901,  that  he  had 
abandoned  the  undulatory  theories.  We  received  very  courteous 
acknowledgement  of  the  book,  with  no  denial  as  to  his  abandonment  of 
the  undulatory  theories. 

It  is  entirely  evident  to  any  one  who  reads  Mr.  Thomson's  article 
on  cathode  rays  which  appeared  in  the  September  number  of  Harper's 
Magazine,  that  Prof.  Thomson  has  abandoned  the  undulatory  theory  of 
light,  and  therefore  of  necessity  must  soon  abandon,  if  he  has  not 
already,  the  undulatory  theory  of  sound,  and  all  other  undulatory  theo- 
ries. For  every  intelligent  physicist  knows  that,  whatever  the  laws  may 
be,  the  same  laws  govern  both  light  and  sound* 


714  APPENDIX 

Prof.  Thomson^  in  the  article  lefeired  to^  sqfi :  "  Allboiigh  in  ooii* 
seqaence  of  the  universal  acceptance  ci  the  andnlatoff  tfaeoiy  of  l^t 
a  raj  is  generally  associated  in  the  minds  of  pigpsicists  with  an  undiilft- 
tory  motion  in  the  ether,  this  araodation  is  OBiy  aoddental  and  there  is 
no  necessary  coimection  between  a  ray  and  andalatory  motioii" ;  wliidi 
could  only  be  true  when  the.  uiidulatpnr. theory  of  Ug^t  was  tintnie. 
That  is  to  say  Mr.  Thomsoni  slakes  here  a  mstinct  statemen^-^^-and  we 
believe  that  this  was  done  deliberately  and  not  aoddentally/^that  the 
nndulatory  theory  of  light  is  not  true. 

As  this  article  of  Prof.  Thomson's  is  both  a  very  aUe  and  important 
one,  unquestionably  foreshadowing  tibe  great  revctetion  now  taking 
place  in  the  ph3rsics  of  tibe  world,  we  will  examine  imne  care6i% 
what  he  says.    The  first  sentence  is  revolutionary.    It  is  this : 

''The  study  of  the  eSects  which  occur  when  a  current  of  electricity 
passes  through  gas  at  a  very  tow  pressure  lufi  recent^  led  to  results 
having  a  very  direct  bearing  on  our  ideas  of  matter  and  electricity." 

If  our  ideas  in  regard  to  these  subjects  had  undergone  or  were  under- 
going no  change,  why  this  sentence  ? 

Mr.  Thomson  goes  on  to  show  that  the  cathode  rays  are  composed 
of  material  particles,  which  move  in  straight  lines,  like  all  other  light, 
as  follows : 

"  Newton  uses  the  term,  *  ray,'  in  connection  with  his  corpuscular 
theory  of  light,  and  the  cathode  rays,  as  we  shall  see,  have  an  extraor- 
dinary resemblance  to  the  conditions  postulated  in  that  theory  for  a 
ray  of  light." 

Prof.  Thomson  then  shows,  that  cathode  rays,  like  the  ordinary 
rays  of  light,  heat  bodies  on  which  they  fall,  may  be  focused  so 
as  to  raise  a  piece  of  platinum  foil  to  a  white  heat,  and  even  char  a 
diamond. 

He  also  states  that,  "The  rays  when  they  strike  an  object  tend  to 


A r rex  D IX 


7»S 


push  it  away,  the  object  behav^ing  just  as  if!  t  was  struck  by  a  stream  of 
particles  coming  from  the  catho<ie.  This  is  prettily  shown  in  the  experi- 
ment due  to  Sir  William  Crookes,  when  the  impact  o!  the  ray  makes 
the  little  carriage  move  from  one  end  to  the  other  of  the  rails.*' 

This,  too,  is  illustrated  In  the  Crookes  radiometers  where  small  discs, 
fastened  to  an  axis,  are  made  to  revolve  slowly  or  with  great  rapidity 
according  to  the  size  of  the  stream  of  particles  intluencing  them.  And 
the  effect  is  almost  instantaneous,  coming  from  sunlight,  or  a  lamp  or 
heat  rays  of  a  stove.  Of  course  in  all  these  cases  the  stream  of  parti- 
cles must  enter  the  vacuum  through  the  glass. 

But  the  interstellar  space  is  a  vast  region  into  which  the  air  does  not 
enter,  and  therefore  similar  to  what  we  call  a  vacuum.  It  would  appear 
to  follow  with  absolute  certainty  that  the  vast  stream  of  corpuscles  of 
light  and  heat,  constantly  emitted  from  the  sun,  with  their  marvelous 
velocity  of  iS6,ooo  miles  per  second,  must  move  all  bodies  in  their  path, 
which  means  especially  the  earth  and  the  planets,  or  what  we  call  the 
solar  system. 

As  light  rays  move  in  straight  lines  the  result  of  this  would  be  to  push 
the  planets  away  from  the  sun.  This  is  the  force  of  repulsion  so-called. 
But  Prof.  Thomson  shows  that  magnetism,  which  is  unijuestionably  a 
stream  of  particles,  but  from  another  source,  deflects  the  coqmscles  of 
light  from  a  straight  to  a  curvetl  course*  Let,  then,  these  two  forces  of 
light  and  magnetism  be  ]>roperly  adjusted,  and  the  revolution  of  planets 
about  their  central  sun  is  accounted  for. 

Another  very  remarkable  thing  referred  to  by  Prof.  Thomson  is  that 
these  rays  affect  the  color  of  substances,  and  this  appears  in  such  a  way 
as  certainly  to  suggest  that  they  have  the  |K>wer  of  imparting  color ; 
that  is  that  they  are  the  color  giving  substances.  It  is  indeed  an 
interesting  thought  that  these  inTmitely  small  particles,  which  Prof, 
'ITiomson  says  are  not  over  one  one- thousandth  of  an  atom  of  hydrogen 
in  size,  are  the  pigment  or  jmit  of  the  pigment  that  gives  the  beautiful 


colors  of  the  universe,  those  which  hover  upon  the  border  of  the  clauds, 
or  those  which  nestle  In  the  exquisitely  sweet  petals  of  a  rose-  There 
certainly  are  such  pigments,  or  as  many  of  them  as  may  be  wanteiif 
and  that  they  are  of  the  character  of  these  particles  Is  now  most 
highly  probable. 

Prof.  Thomson  says,  **  That  some  substance  such  as  salt  experience 
a  pecuUat  change  in  color  when  exposed  to  these  rays ;  crystals  of  rock 
become  a  pretty  violet  blue,  lookmg  almost  like  gems — the  color  is 
unfortimately  somewhat  fugitive  if  the  cr)'stals  are  exposed  to  a  raolst 
atmosphere.  Some,  however,  in  my  possession,  which  have  been  kept 
dry,  are  still  blue,  although  they  are  now  nearly  four  years  old.*' 

Prof.  Thomson  dwells  further  upon  this  color-producing  quality  and 
then  says :  "that  the  cathode  and  Roentgen  rays  have  many  points  of 
resemblance,  they  both  affect  a  photographic  plate,  they  both  cause 
substances  against  which  they  strike  to  phosphoresce,  and  they  both 
make  gas  through  which  they  pass  a  conductor  of  electricity.  The 
cathode  rays,  too,  as  we  shall  see,  have  some  power  of  penetrating 
opaque  solids,  though  this  is  small  compared  with  that  possessed  by  the 
Roentgen  rays ;  the  essential  differences  between  the  two  rays  are  that 
the  Roentgen  rays  are  not  affected  by  a  magnet,  nor  by  an  electric 
force,  nor  do  they  carry  with  them  a  charge  of  electricity," 

Mn  Thomson  states  that  physicists  until  three  or  four  years  ago  were 
very  much  divided  in  opinion  as  to  cathode  rays  ;  the  German  physi- 
cists, with  very  few  exceptions,  holding  thai  they  were  waves  of  eiher» 
but  the  English  physicists  almost  unanimously  regard mg  them  as 
particles  of  gas  projected  with  great  velocity.  In  1892  Hertz  showed 
that  solids  were  not  absolutely  impenetrable  by  these  rays.  Lenard 
made  a  tube  which  had  in  it  a  small  window  of  very  thin  aluminum 
foil,  and  shooting  the  cathode  rays  against  this  window  they  penetrated 
it  so  as  to  be  investigated  on  the  outside. 

After  this  time,  Mr,  Thomson  says,  all  the  evidence  was  in  ^vor  of 


APrENDIX 


717 


the  particle  theory,  and  *'  showed  that  the  pajticles  of  the  cathode  rays 
are  not  ordinary  atoms  or  iwolecules  at  all,  1-»ut  something  very  much 
smaller,  for  the  mass  of  each  particle  is  only  about  one  thousandth  part 
of  that  of  the  atom  of  hydrogen,  the  smallest  mass  hitherto  recognized." 

Mr,  Thomson  fyrther  says  that  this  extreme  smallness  is  not  the  only 
remarkable  feature  about  these  particles;  "for  it  was  found  that  what- 
ever might  be  the  form  of  the  gas  in  the  tube,  or  whatever  metal  was 
used  for  the  cathode,  the  mass  of  the  particles  remained  the  same. 
Ilmt  thus  in  these  particles  we  have  something  possessing  the  proper- 
lies  of  ordinary  matter,  having  a  definite  mass,  which  is  yet  exceedingly 
small  compared  with  the  mass  of  any  known  element ;  the  particles  of 
this  new  kind  of  matter  thus  correspond  to  a  very  much  finer  state  of 
subdivision  than  that  of  ordinary  matter  into  its  molecules," 

He  then  refers  to  their  speed  as  being  enormous,  and  says:  **The 
only  velocity  with  which  we  can  compare  these  particles  js  the  velocity 
of  light,  which  is  about  186,000  miles  per  second."  And  these  parti- 
cles, be  it  remembered,  are  light.  He  then  adds  :  "Thus  in  the  tube 
near  the  cathode  we  have  bodies  smaller  than  atoms  moving  with  pro- 
digious  velocities,  a  state  of  things  which  recalls  Newlun's  corpuscular 
theory  of  light,  according  to  which  light  consists  of  very  small  particles 
(corpuscles)  moving  at  the  rate  of  186,000  miles  per  second.  Although 
this  theory  of  light  has  since  been  abandoned,  Newton's  conception  is 
realized  in  the  cathode  rays;  and  I  have  ventured  to  call  the  small 
particles  which  constitute  these  rays,  corpuscles."  One  must  be 
exceedingly  stupid  or  ignorant,  or  both,  who  in  reading  this  article  has 
not  by  this  time  perceived  that  Mr.  Thomson  has  abandoned  the 
undulatory  theories  and  knmvs  that  Newton's  corpuscular  theor)^  of 
light  is  correct.  This  is  what  has  been  demonstrated  by  the  experi- 
ments. Certainly  he  has  abandoned  the  undulatory  theory  of  light,  and 
it  won't  take  him  long  to  abandon  the  others,  if  he  has  not  already. 

Prof.  Thomson  now  calls  attention  to  the  fact  that  matter  in  the 


7l8  AWENDIX 

.ccnpnscular  state  is  not  confined  to  tiie  cathode  twfu  in  an  eiiiaiisted 
tabe*  fot  he  says  whoi  a  metal  wire  is  asade  fed  hot  in  a  good  Taamniy 
matter  in  this  state  is  given  off.  He  also  says  that  it  is  given  off  wlieQ 
fbs  metaiy  instead  of  being,  red  hot,  is  exposed  to  aWg^  light.  He 
then  refers  to  the  fact  that  in  these  cases  we  get  n^ative  dectridty  in 
thfs  gas  around  the  wirej  and  in  ibct  that  whenever  we  have  nq^tive 
electricity  in  a  gas  at  a  very  low.  {Krewose,  where  there- is  veiy  Httle 
matter  in  the  ordinary  state  for  it  tD  stick  to»  wetiind  the  electricity  is 
carried  by  the  corpuscles..  ^  He  shows  that  when  the  preasiue  d  the  gas 
is  not  low,  that  is,  when  the  air  particles  have  not  bees  tbcmMighl j 
exhausted,  that  the  corpuscles  adhere  to  die  molecules  of  gas.  And 
therefore,  he  says,  if  we  wish  to  get.matter  in  this  ecnrpoacuki  state  we 
must  remove,  as  much  oi  the  g^s  as  possible;  and  thaLtiien  we  find 
that  the  negative  electricity^  is .  always  carried  by  these  corpuscles. 
With  positive  electricity  this  is  different;,  for  this  is  always  found  on 
matter  in  the  ordinary  state,  while  negative  dectriqity .  js.  found  on 
corpuscles.  ...r,..; 

Prof.  Thomson  adds  that  this  difference  between  the  two  dectricities 
is  just  that  which  ought  to  exist  on  the  one  fluid  theory  of  electricity  due 
to  Benjamin  Franklin.  That  according  to  that  theory  electricity  was 
supposed  to  be  a  fluid ;  that  when  matter  in  the  ordinary  state  con- 
tained a  certain  quantity  of  this  fluid,  it  was  said  to  be  saturated,  and 
not  electrified ;  that  if  some  of  the  fluid  left  it  so  that  it  contained  less 
than  the  normal  quantity,  it  was  charged  with  electricity  of  one  sign ; 
that  if  some  came  into  it  so  that  it  contained  more  than  the  nonpal 
quantity,  it  was  charged  with  electricity  of  the  opposite  sign.  And  he 
then  says : 

"  Now  if  we  suppose  that  the  electric  fluid  consists  of  a  collection  of 
our  corpuscles,  the  results  of  our  experiments  will  be  exactly  expressed 
by  Franklin's  one-fluid  theory,  and  it  would  thus  seem  that  there  is 
Gome  warrant  for  the  somewhat  discredited  electric. fluid. 


APPENDIX 


7ig 


"If  the  material  of  the  cathode  rays  forms  negative  electricity,  it  is 
evident  that  it  must  be  very  widely  spread  ;  we  have  seen  that  it  occurs 
free  near  white  hot  metals  and  metals  exposed  to  the  light.  We  may 
suppose  that  it  forms  a  part  of  all  kinds  of  matter  in  the  normal  state, 
and  tltat  the  heat  and  light  which  have  to  be  applied  to  metals  are  only 
required  to  get  the  corpuscles  out  of  the  metal,  and  that  in  the  metal 
itself,  even  under  normal  conditions,  there  are  corpuscles  moving  freely 
about,  and  able  to  carry  heat  as  well  as  electricity  from  one  part  of  the 
metal  to  the  other." 

Prof,  Thomson  then  shows  that  there  are  some  substances  which 
constantly  emit  cathode  rays  without  the  aid  of  heat  or  light.  Me 
especially  mentions  uranium  and  a  new  substance  called  radium  obtained 
from  the  mineral  pitchblende.  Radium,  he  says,  has  been  shown  to 
emit  corpuscles  at  about  tvvo^thirds  the  velocity  of  light.     And  he  adds  : 

"Since  corpuscles  are  emitted  by  hot  metals,  it  seems  not  improbable 
that  that  very  hot  body,  the  sun,  may  be  emitting  corpuscles,  some  of 
which  would  strike  the  earth,  where,  stopped  by  the  earth's  atmosphere, 
and  deflected  by  the  earth's  magnetic  force,  they  would  produce 
luminosity  in  the  upper  region  of  the  earth's  atmosphere,  which  they 
would  make  a  conductor  of  electricity." 

And  he  adds  that  the  consequences  of  such  an  emission  of  corpuscles 
by  the  sun  have  been  investigated  by  several  eminent  physicists  who 
have  shown  that  very  many  of  the  properties  of  the  aurora  borealis  can 
be  thus  explained. 

In  conclusion  he  says : 
'  "  Jf  this  view  is  sustained  by  future  investigations,  we  shall  have  to 
regard  the  corpuscles  as  playing  an  important  part  in  cosmical  as  well 
as  in  terrestrial  physics.  The  possibility  of  such  a  widespread  scope 
for  their  action  lends  increased  interest  and  importance  to  the  investi- 
gation of  their  properties* 

"It  is  a  striking  instance  of  the  unity  of  physical  phenomena  on  the 


jma  largest  scale  that  an  occurrence  apparently  so  exceptional 
g  of  the  glass  in  a  small  tube  should  be  closely  connected 
M  the  most  widespread  phenomena  in  nature,  and  give  the 
their  explanation--* 

have  thus  given  a  synopsis  of  this  veT>^  remarkable  and  most 

aely  article  of  Prof.  Thomson,  which,  like  a  great  guide  board,  points 

way  to  the  physics  of  the  future,  suggesting  the  explanation  of  every 

1  element  or  so-'^^ii^'i  frtr^#.  Sn  tki*  r^hysics  of  the  past,  and  from 

!  standpoint  of  exp(  ng  that  all  things  in  the  uni- 

erse  are  made  by  one  law,  the  combination  of  what  we  call  matter  m 

s  different  conditions  and  proportions. 

This  indeed  is  a  self-evident  proposition,  for  it  is  simply  the  canying 

mt  of  the  fundamental  principle  of  science,  the  universality  of  natural 

a  principle  as  we  have  before  had  occasion  to  say  sustained  by 

ty  known    fact.      The  only    wonder  is    that  science   should  ha%*e 

so   slow   to  perceive  the   logic  of   its   own  teaching.     We    may 

well  thank  God   and  take   courage  that   we  are  emerging   from  this 

dark  age  of  science^  and  coming  upon  that  great  and  broad   ocean 

of  Truth,  where  religion  and  science  will  be  exactly  blended,  teachin| 

MS  they  should,  precisely  the  same  thing,  and  what  the  Bible  and  ail  true 

religion  has  always  taught,  that  all  things  are  created  by  an  infinite  and 

personal  God ;  that  the   order  and   nature  of  their  creation    is  the 

same  that  we   see  carried  out  in   the  things  made  by  man,  who   is 

created  after  the  image  of  God,  and  therefore  must  work,  if  he  works 

at  all,  in  accordance  with  the  laws  of  God. 

And  these  great  truths  will  assuredly  lead  to  a  better  understanding 
of  the  laws  which  control  our  moral  and  religious  being,  which  also  are 
unfolded  in  the  Bible,  and  show  that  there  is  a  connection  between  this 
and  another  life,  as  concise  and  as  definitely  marked  out  as  are  the 
boundaries  of  these  various  physical  elements  which  we  have  been 
considering. 


APPENDIX 


;2i 


SYMPATHETIC  VIBRATIONS. 


Mr,  Tyndall  refers  to  this  subject  as  follows : 

"  But  to  grasp,  in  all  its  fullness,  the  new  theory  of  musical  consonance 
some  preliminary  studies  will  be  necessary.  And  here  I  would  ask  you 
to  call  to  mind  the  experiments  (in  Chapter  III.)  by  which  the  division 
of  a  string  into  its  harmonic  segments  was  illustrated.  This  was  done 
by  means  of  little  paper  riders^  which  were  unhorsed,  or  not,  according 
as  they  occupied  a  ventral  segment  or  a  node  ii|X)n  the  string.  Before 
you  at  present  is  the  sonometer,  employed  in  the  experiments  just 
referred  to.  Along  it,  instead  of  one,  are  stretched  two  strings,  alx)ut 
three  inches  asunder.  By  means  of  a  key  these  strings  are  brought  into 
unison.  And  now  I  place  a  little  paper  rider  upon  the  middle  of  one 
of  them,  and  agitate  the  other*  What  occurs?  The  vibrations  of  the 
sounding  string  are  communicated  to  the  bridges  on  which  it  rests,  and 
through  the  bridges  to  the  other  string.  The  individual  impulses  are 
very  feeble,  but  because  the  two  strings  are  in  unison,  the  impulses  can 
so  accumulate  as  finally  to  toss  the  rider  off  the  untouched  string. 

"  Every  experiment  executed  with  the  riders  and  a  single  string  may 
be  repeated  with  these  two  unisonant  strings.  Damping,  for  instance, 
one  of  the  strings,  at  a  point  one- fourth  of  its  length  from  one  of  its 
ends,  and  placing  the  red  and  blue  riders  formerly  employed,  not  on 
the  nodes  and  ventral  segments  of  the  damped  stringi  but  at  points  up- 
on the  secoml  string  exactly  opposite  to  those  nodes  and  segments, 
when  the  bow  is  passed  across  the  shorter  segment  of  the  damped 
string,  the  five  red  riders  on  the  adjacent  string  are  unhorsed,  while  the 
four  blue  ones  remain  tranquilly  in  their  places.     By  relaxing  one  of  the 


722  APlASNDIX 

Strings,  it  is  tiirown  out  of  unison  with  the  olber,  and  Aem  alf  eforit 
to  unhorse  the  riders  are  unavailing.  That  accusiulatioa  of  imputaes, 
whieh  unison  a/one  renders  possible^  cannot  here  take  phce,  and  the 
consequence  is,  that  however  great  the  agitation  of  the  one  string  may 
be,  it  fails  to  produce  any  sensible  effect  upon  the  odi». 

'^The  influence  of  synchronism  may  be  illustrated  in  a  still  more  strik- 
ing manner,  by  means  of  two  tuning-forks  which  sound  the  same  note. 
Two  such  forks  mounted  on  their  resonant  suf^ports  are  placeed  upon 
Uie  table.  I  draw  die  bow  vigorously  across  one  of  them,  permitting  the 
other  fork  to  remain  imtouched.  On  stopping  the  agitated  fork,  die 
sound  is  enfeebled,  but  by  no  means  quenched.  Through  the  air  and 
through  the  wood  the  vibrations  have  been  omveyed  from  fork  ,to  fork, 
and  the  untouched  fork  is  the  one  you  now  hear.  When,  by  means  of 
a  morsel  of  wax,  a  small  coin  is  attached  to  one  of  die  forka^  its  powv 
of  influencii^  the  other  ceases ;  the  change  in  the  rate  of  vibration,  if 
not  very  small,  so  destroys  the  sympathy  between  the  two  foiks  as  to 
render  a  response  impossible.  On  removing  the  coin  the  untouched 
fork  responds  as  before. 

"This  communication  of  vibrations  through  wood  and  air  may  be 
obtained  when  the  forks,  mounted  on  their  cases,  stand  several  feet 
apart.  But  the  vibrations  may  also  be  communicated  through  the 
air  alone.  Holding  the  resonant  case  of  a  vigorously  vibrating  fork  in 
my  hand,  I  bring  one  of  its  prongs  near  an  unvibrating  one,  placing 
the  prongs  back  to  back,  but  allowing  a  space  of  air  to  exist  between 
them.  Light  as  is  the  vehicle,  the  accumulation  of  impulses,  secured 
by  the  perfect  unison  of  the  two  forks,  enables  the  one  to  set  the  other 
in  vibration.  Extinguishing  the  sound  of  the  agitated  fork,  that  which 
a  moment  ago  was  silent  continues  sounding,  having  taken  up  the  vibra- 
tions of  its  neighbor.  Removing  one  of  the  forks  from  its  resonant 
case,  and  striking  it  against  a  p?id,  it  is  thrown  into  strong  vibration. 
Held  free  in  the  air,  its  sound  is  audible.     But,  on  bringing  it  close  to 


APPENDIX 


723 


the  silent  mounted  fork,  out  of  the  silence  rises  a  full  mellow  sound, 
which  is  due,  not  to  the  fork  originally  agitated,  but  lo  its  sympathetic 
neighbor, 

"Various  other  examples  of  the  influence  of  synchronism,  already 
brought  forward,  will  occur  to  you  here ;  and  cases  of  the  kind  might 
be  indefinitely  multiplied.  If  two  clocks,  for  example,  with  pendulums 
of  the  same  period  of  vibration,  be  placed  against  the  same  wall,  and 
if  one  of  the  clocks  is  set  going  and  the  other  not,  the  ticks  of  the  mov- 
ing clock,  transmitted  through  the  wall,  will  act  upon  its  neighbor.  The 
quiescent  pendulum,  moved  by  a  single  tick,  swings  through  an  extreme- 
ly minute  arc ;  but  it  returns  lo  the  limit  of  its  ssving  just  in  time  to 
receive  another  impulse.  By  the  continuance  of  this  process,  the  im- 
pulses so  add  themselves  together  as  finally  to  set  the  c\ock  a-going.  It 
is  by  this  timing  of  impulses  that  a  pro]>erIy  pitched  voice  can  cause  a 
glass  to  ring,  and  that  the  sound  of  an  organ  can  break  a  particular 
window-pane,'^ 

In  the  above  the  facts  of  synchronous  vibrations  arc  correctly 
stated,  but  the  cause  given  entirely  erroneous.  The  air  because 
of  its  mobility  would  accomplish  nothing  of  the  kind,  but  the 
sound  which  we  both  hear,  and,  when  passing  through  wood 
feel. — infinitesimal  particles  of  matter, — under  such  circum- 
stances will  cause  to  vibrate  any  body  which  has  the  same  nor- 
mal vibration  as  the  body  in  which  the  sound  is  produced.  And 
it  will  so  affect  no  other  body.  The  effect  is  caused  by  the 
internal  stnicture  of  the  body,  which  will  permit  these  infini- 
tesimal particles  of  sound,  to  enter  it  and  throw  it  into  vibration. 


is  a  delicate  tightiy  stretched  membrane  or  skin  which  separates  the 
outer  ear  from  the  middle  ear  or  tympanic  cavity^  which  is  a  cavity  in 
the  temporal  bone  in  which  are  several  small  bones  whose  dimensions 
are  considerably  exaggerated  in  the  figure.  One  of  these,  the  hammer^ 
//,  is  attached  at  one  end  to  the  druniy  and  at  the  other  is  jointed  to 
the  anvily  e\  the  latter  is  connected  by  means  of  the  stirrup  bone,yi  to 
the  aval  window,  an  aperture  closed  by  a  fine  membrane,  which  sepa- 
rates the  tympanic  cavity  from  the  labyrinth.  The  tympanic  cavity  is 
also  connected  by  the  Eustachian  tube,  b,  with  the  cavity  of  the  mouth, 
so  that  the  air  in  it  is  always  under  the  same  pressure. 


APPENDIX 


725 


"The  labyrinth  is  a  complicated  structure  filled  with  fluid;  it  is  en- 
tirely of  bone,  with  the  exception  of  the  oval  window  already  mentioned 
and  the  raund  window ^  o.  The  labyrinlh  consists  of  three  parts  :  the 
Xfiitibule^  which  is  closed  by  the  oval  window  *  the  three  semi-circular 
canals,  k  ;  and  the  spiral-shaped  cochlea^  or  snail  shell,  x.  This  is  sepa- 
rated throughout  its  entire  length  by  a  division  partly  of  bony  projec- 
tion and  partly  of  membrane ;  the  upper  part  of  this  division  is  con- 
nected with  the  vestibule,  and  therefore  with  the  oval  window,  while  the 
lower  part  is  connected  with  the  round  window.  In  the  labyrinthine 
fluid  of  this  part  the  termination  of  the  auditory  nerve  is  spread,  the 
other  end  leading  to  the  brain. 

"The  membranous  part  of  this  diafram  is  lined  with  about  3,000 
extremely  minute  fibres,  which  are  the  terminations  of  the  acoustic  nerve, 
w.  Elach  of  these,  which  are  called  Cord's  fibns^  seems  to  be  tuned  for 
a  particular  note  as  if  it  was  a  small  resonator.  Thus  when  the  vibrations 
of  any  particular  note  reach  these  fibres,  through  the  intervention  of  the 
stirrup  bone  and  the  fluid  of  the  labyrinth  one  fibre  or  set  of  fibres  only 
vibrates  in  unison  with  this  note,  and  is  deaf  for  all  others.  Hence 
each  simple  note  causes  only  one  fibre  to  vibrate,  while  compound 
notes  cause  several ;  just  as  when  we  sing  with  a  piano  only  the  funda- 
mental note  and  its  harmonics  vibrate.  Thus,  however  complex  exter- 
nal sounds  may  be,  these  microscopic  fibres  can  anal>^e  them  and 
reveal  the  constituents  of  which  they  are  formed.*' 

The  following  instances  of  unison  vibration  are  from  Ganot: 
"There  are  numerous  instances  in  which  solid  bodies  are  set  in  vibra- 
tion by  the  vibrations  of  the  air.  The  condition  most  favorable  for  the 
yjrodurtion  of  this  phenomenon  is,  that  the  body  to  be  set  in  vibration 
is  under  such  conditions  that  it  can  readily  produce  vibrations  of  the 
same  duration  as  those  transmitted  to  it  by  the  air.  The  following  are 
some  of  these  phenomena : 

**  If  two  violoncello  strings  tuned  in  unison  are  stretched  on  the  same 


726  APPENDIX 

sound-box,  aa  soon  as  one  d.ibem  is  sonnde^- the  lather  is  aet  in  vftim- 
tion.    Thisisalso  thecaseif.theinterraloftbjestrinpjsan  or 

a  perfect  fifths    A  violin^string  may  abo  be  madi^  to  irRxattt  tqr.aovnd: 
ing  a  tuning-fork.     ..^      .  •: 

*^  Two  large  glasses  are  taken  of  tiie  same  diape>  and  as  neatfy  m 
possible  of  the  same  dimensions  and  ureigbty  anii^arei  brpoi^ia  unison 
by  pouring  into  them  proper  quantities  of  w»tef«*  .M  pxm-.otkt  of  theqi 
is  soimdedy  the  other  begina  to  vibrate^  even  if*  it  last  some  dtstancej 
bat  if  water  be  added  to  the^tter,  it  ceases  to yibimte^ 

''Brq^etfound.thaJt  two  ckicka^  whose  time  was. not  very  different, 
fixed  on  the  same  metallic  support,  soon  attained  cmctly  tiie  same  time*? 

We  add  Ganot's  description' of  Edison's  original  phonograph : 

'^  Edison  has  devised-an  apparatus  for  reproducing  sounds  triiich  h 
equally  remarkable  for  the  simplicity  of-its  constructions,  and  tos  the 
striking  character  of  the  result^  whidh  It  fnxxiuces. 

"  A  mouthpiece  is  closed  by  a  thin  elastic  itietal  disc  By  means  of 
a  spring  a  small  steel  point,  rounded  at  the  end,  is  fixed,  on  the  back 
of  the  disc ;  this  point  gently  presses  against  the  ^riace  of  tinfoil,  to 
which  it  transforms  the  vibrations  of  the  disc  by  the  intervention  of 
small  pieces  of  india-rubber  tubing.  Another  small  piece  of  tubing 
helps  to  deaden  the  vibrations  of  the  spring  itself. 

"  The  tinfoil  is  placed  on  the  circumference  of  a  long  cylinder  on 
the  surface  of  which  is  a  very  accurately  constructed  spiral  groove, 
the  threads  being  about  -^j^  of  an  inch  apart  The  cylinder  works  on  a 
screw  the  thread  of  which  is  the  same  as  that  on  the  cylinder ;  it  is 
turned  by  a  handle,  the  motion  being  regulated  by  a  large  fly-wheel. 

"  When  the  disc  is  made  to  vibrate,  by  speaking  or  singing  into  the 
mouthpiece,  while  at  the  same  time,  the  cylinder  is  turned  with  a  uni- 
form motion,  a  series  of  dots  or  indentations  are  produced  upon  the 
tinfoil,  which,  being  a  nonelastic  substance,  retains  them. 

"  If  now  the   part  which   the  mouthpiece  plays  be  reversed,  the 


APPENDIX 


727 


indented  tinfoil  can  be  used  to  reprcxluce  the  sound.  This  is  best 
effected  by  having  a  special  mouthpiece  of  larger  size,  with  a  diafram 
of  similar  construction.  This  is  so  adjusted  that  the  point  is  made  to 
work  along  the  indentions  in  the  groove. 

**  In  this  way  sound  has  been  reproduced  so  as  to  be  audible  to 
a  large  audience  ;  the  articulation  is  distinct  though  feeble ;  it  repro- 
duces the  quality  of  a  person's  voice  who  speaks  into  it,  but  with  a 
nasal  intonation.  Speech  may  thus  be  treasured  up  on  a  sheet  of  tin- 
foil and  kept  for  an  indefinite  period ;  the  sound  may  be  reproduced 
more  than  once  by  means  of  its  tiufoil  register,  but  after  the  second 
reproduction  the  strength  is  greatly  diminished. 

**U  the  velocity  of  rotation  is  greater  than  before,  the  pitch  of 
the  speech  is  altered ;  and  if  it  is  not  uniform,  then,  in  tlie  case  of  a 
song,  the  reproduction  is  incorrect. 

*'  There  is  great  difference  in  the  distinctness  with  which  the  various 
consonants  and  vowels  are  reproduced  ;  the  s,  for  instance,  is  very  dif- 
ficult. If  the  phonograph  be  rotated  in  the  reverse  direction,  the  indi- 
vidual letters  retain  their  character,  but  the  words  as  well  as  all  the  let- 
ters are  reproduced  in  the  reverse  order. 

"  If  the  instrmnent  be  reset  to  the  starting-point  of  the  phonographic 
record  of  a  song,  and  be  again  sung  into,  it  will  reproduce  both  series 
of  sounds,  as  if  two  persons  were  singing  at  the  same  time ;  and  by 
repeating  the  same  process,  a  third  or  fourth  part  may  be  added,  or  one 
or  more  instrumental  parts* 

"The  impressions  on  the  tinfoil  appear  at  first  sight  as  a  series  of  suc- 
cessive points  or  dots,  but  when  examined  under  a  microscope  they  are 
seen  to  have  a  distinct  form  of  their  own.  U'hcn  a  cast  is  taken  by 
means  of  fusible  metal,  and  a  longitudinal  section  made,  the  outline 
closely  resembles  the  jagged  edge  of  a  Konig's  flame. 

"  According  to  Edison's  statement,  as  many  as  40,000  words  can  be 
registered  on  a  space  not  exceeding  ten  square  inches." 


Figure  50* 
Adcr's  telepbone  without  membrane 
and  nvagnct. 


Figure  SI. 
Ader's  telephone  without  magnetic 


INDEX. 


INDEX. 


PART  I. 
GEOMETRY   AND  TRIGONOMETRY. 


ANGLE,  degree  oU  4. 
Angle,  diedral,  definition  of,  6i* 
**  MM     measure  ol,  61. 

**    how  made,  5. 
**    measure  of,  133. 
**    po^redralt  definition  of,  6i. 
••    spherical,         "        «  85. 
«    triedral,  "        "62. 

Angles,  acute,  of  right  trian^es,  functions 
*  o^  135, 136. 

«      complementary,  functions  of^  135. 
•*      curved,  93. 

"      of  triangle,  determined   from   its 
"  sides,  170. 

"       spherical,  discussion  of,  93, 
**      supplementary,  functions  of,  135. 
Apothem,  definition  of,  53. 
"         equal  to  what,  53. 
Arc,  definition  of,  3. 

"  degree  of,  4. 
Area  of  a  surface,  47. 
Authors  (and  books),  quotations  from: 
"       Burns,  142. 
"       Euclid,  13,  17,  114. 
"       Goethe,  131. 
"       Loomis,  Elias,  147. 
"       Shakespeare,  132,  141. 
"       White,  Henry  Kirke,  179. 
Axiomatic  mathematical  truths,  46. 

BASE  of  system  of  logarithms,  181. 
Briggs  system  of  logarithms,  181. 
Beauty,  perception  of,  140. 


CAVAUERI'S  conoepckm  of   liiie% 
surfaces  and  solids,  'i47* 
Chord,  connecting  two  arcs,  6. 

**    definltioiiof,  3* 
Chords,  and  aics,  rdatbiQr  o^  6b 
Circles,  and  cifcumfereno^  reviled  ocfini* 
tionof,  3. 
••     aieao^  53. 
**     concentric,  4. 
•«     definition  of*  a. 
^     generation  o^  4*  $. 
**     great,  definitioa  of,  85* 
**     nature  of,  17. 
**     polar  distance  of,  85. 
«     poles  of,  85. 
"      principles  upon  which  constructed, 

I. 
"      small,  definition  of,  85. 
•*      tangent  to  each  other,  4. 
Qrcumference,  nature  of,  7. 

"  of  circle,  divisions  of,  133. 

"  ratio  of,  to  diameter,  53. 

Circumsciibed  polygon,  definition  of,  4. 
Commensurate  quantities,  definition  of,  14. 
Complement  of  arc  or  angle,  133. 
Concentric  circles,  definition  of,  4. 
Cone,  altitude  of,  84. 
'*     axis  of,  84. 
"     convex  surface  of,  107. 
"     definition  of,  84. 
"     how  generated,  84. 
**     slant  height  of,  84. 


INDEX 


;3i 


Cone,  truncated,  definition  of,  85. 

"     volume  of,  108,  112. 
G)nes,  similar,  85. 
Constant  quantity,  definition  of,  14. 
Continuous  movement  between  limits,  137, 

175- 
Cosecant  defined,  135. 
Cosine  defined,  134. 
Cosines,  differences  between,  142. 
Cosines  of  two  arcs,  sum  and  difference  of, 

proportional  to  cotangent  of  half 

simi  and  tangent  of  half  difference, 

167,  178. 
Cosines,  table  of,  142. 
Coversed  sine  defined,  135. 
Cotangent  defined,  135. 
Creation,  order  of,  in. 
Cylinder,  convex  surface  of,  io6. 
"        definition  of,  84. 
"        how  generated,  84. 
"         volume  of,  106. 
Cylinders,  similar,  84. 
Cube,  definition  of,  73. 

DEGREES  of  arc  or  angle,  133. 
Diagonal  of  a  polygon,  25. 
Diameter,  definition  of,  3. 
Diameter,  how  divided,  6,  33. 
Difference  of  two  quantities,  square  of,  45. 


EUCLID*! 
43. 


S  demonstrations,  character  of, 


FIGURES,  equivalent,  47,  74. 
Figures,  similar,  24,  25. 
Fluctions,  147. 
Fluents,  147. 
Frustum  of  pyramid,  altitude  of,  74. 

GEOMETRY,  Davies'  Legendre's,  re- 
view of,  62,  96. 
Geometry,  Yale  College,  review  of,  8,  loi, 
105. 


INACCURACIES  of  trigonometric  tables, 
146. 
Incentives  to  study,  162. 
Increments,  142. 
Infinitely  small,  56. 
Inscribed  angle,  definition  of,  3. 
Inscribed  polygon,     "  "    3. 

Instruction,  methods  of,  160. 

KNOWLEDGE,  acquisition  of,  should 
be  made  ea^,  163. 

LAWS  governing  the  universe  may  be 
understood,.  132. 
Limit,  definition  of,  14. 

"      of  a  variable,   14. 
Line,  curved,  definition  of,  84. 

**     definition  of,  116, 

"     perpendicular,  definition  of,  92. 

"     projection  of,  6. 

**    straight,  area  of  a  surface  generated 
by,  108. 

"    straight,  divided^  25. 
Lines,  Cavalicri's  conception  of,  147. 

"      divided  externally,  25. 

**  **        harmonically,  26, 

"  **        internally,  25. 

"      how  generated,  147. 

"      Ne>»'ton's  conception  of,  147. 

"     straight,  how  divided  proportionally, 

25- 

Logarithms,  133. 

"  base  of,  181. 

"  Briggs'  system  of,  181. 

'*  discussion  of,  1 79. 

MAGNITUDE,  relative,  117. 
Mathematical  truths  of  the   kind 
called  axioms,  46. 
Minutes,  133. 


NEITHER,  or,  instead  of 
nor,  35. 


neither. 


732 


INDEX 


OBUQUE-ANGLED  trini^  |MitB 
required  for  the  tolatioii  o^  157. 

JPARALLEL0GRAM»  altkode  of,  15, 

PsualMopipedf  definition  o^  73* 

**         rectangnlar,  defiaitioii  o^  73. 
**         Ti^bltf  defiaitioii  of,  73* 
<<         Tolnme  of,  78;  79. 
iPendnliim,  osdUatiiig,  123. 
Perimeter  of  polygon,  25. 
Plane,  definition  of,  61. 
Planes,  when  parallel,  61. 
Point,  definition  of,  iifi. 
Polyedron,  definition  o^  72. 
**         diagonal  o^  74. 
«        Yoiiimeof,  74. 
Polyedrons,  similar,  74. 
Polygon,  perimeter  of ,  25. 
**       r^[iilar,  centre  of,  53. 
"  **        definition  o^  53. 

"       spherical,  8^. 
M  M        diagonal  of,  86. 

Polygons,  similar,  24,  53. 
Pony,  use  of,   161, 

Principle  of  rewards  and  punishments,  162, 
Prism,  altitude  of,  73. 

''      circumscribed  about  a  cylinder,  S4. 
"      deBnition  of,  72. 
"      how  named,  72. 
"      inscribed  in  cylinder,  84. 
"      oblique,  definition  of,  73. 
"      right.  "  "     73. 

"      triangular,  volume  of,  83. 
Projection  of  straight  line,  36. 
Proportion,  definition  of,  13. 

"  proved  by  definition,  88. 

"  treated  unintelligibly,  25. 

Proposition,  converse  of,  true,  27. 
Pyramid,  altitude  of,  73. 
"         axis  of,  74. 

"         circumscribed  about  a  cone,  85. 
•*         definition  of,  67. 


Pyrainid, 


ioscfibM 
lateiala 


128. 
**        danthd 
**        trancate 
Pyramids^  hoir  iHu 

/^UADRAKT, 

RADIUS^defia 
Ratio,  aiei 
two  and  tin 
Ration  Endid^i  del 
"      of  dfamctei 
Rectangle,  area  d 
Rdationship  of  sic 
stteant^ 
Rewardythe  hig^ 
Ri^t-anf^  tria: 
151. 

SECANT,  dcfin 
relat 
Seconds,  133. 
Sector,  definition  < 
Segment,  definitio: 
Similar  arcs,  secto 
"  polyedrom 
Sine  and  cosine  oi 


"     defined,  134 

"     of  difference 

of  cosine! 

ence   of 

radius,  i 

Sines  and  cosines, 

"    law  of,  152. 

"    of  sum  and 


INDEX 


733 


proportional  to  sum  and  difference 
of  tangents  of  arcs,  168,  176. 
of  two  arcs,  sum  and  difference  of, 
proportional  to  tangent  of  half  sum 
and  difference,  166. 
**    of  two  arcs,  sum  of  and  sine  of  their 
sum  proportional  to  cosines  of  half 
their  difference  and  sum,  167,  178. 
Size,  relative,  140. 
Sphere,  area  of,  118. 
•*      definition  of,  85. 
"      diameter  of,  85. 
**      how  generated,  85. 
••      radius  of,  85. 
•*       volume  of,  118,  125. 
Spherical  excess,  86. 
Standards  of  measure,  116. 
Straight  line,  projection  of,  36. 
Sum  and  difference   of  sines  of  two  arcs 
compared  with  tangent  of  half  sum 
and  difference,  166. 
Sum  of  two  quantities,  square  of,  44. 
Superficies,  definition  of,  116. 
Supplement  of  arc  or  angle,  134. 
Surface,  area  of,  25,  47. 

"         "  plane,  120. 

Symbols,  manipulation  of,  44. 

TABLES  of  sines,  cosines  etc.  inaccu- 
rate, 139. 
Tangent,  definition  of,  3,  135. 

''       of  sum  and  difference  of  two  arcs, 
169. 
Tangents,  law  of,  154. 


Trapezoid,  altitude  of,  25,  47. 
Triangle,  altitude  of,  25. 

**      area  of,  49. 

**      oblique-angled,  solution  of,  152. 

**      polar,  definition  of,  86,  95,  96. 

"      sides  of  mutually  proportional,  28. 

"      spherical,  definition  of,  86. 

"  **         spherical  excess  of»  86. 

Triangles,  similar  when,  28. 
Trigonometrical  formulas,  158. 

"  •*         two  methods  of 

deriving,   173. 
Trigonometric  functions,   expressions   for, 

136. 
**  "        how  related,  136, 

137.  139- 
"  •*        values  of,  137. 

Trigonometry,  plane,  defined,  1 33. 
Truth,  mathematical,  made  self-evident  by 
study,  46. 
"     of  paramount  importance,  24. 

VALUE  of  TT,  53. 
Variable  quantity,  definition  of,  14. 
Variables,  dependent  upon  the  same  varia- 
ble if  proportional  at  beginning  and 
end,  always  proportional,  175. 
Variables,  law  of  variation  of,  51. 
Versed  sine,  defined,  135. 
Vision  has  to  do   with   the  agent  which 
perceives,  as  well  as  with  the  thing 
perceived,  140. 
Volume,  definition  of,  79. 
"        measured  by,  80. 


734 


INDEX 


PART  II. 
THE  UNDULATORY  THEORIES. 


ACX>RN9  the  nucleus  of  an  <Mk»  500, 
5>7. 
Aconsdc  GgareB,  507. 
Action  wtthont  contact  nnthinkable,  47. 
Aggregation,  in  nature,  lesnkt  o^  202,  . 

**       law  of,  ao2. 
Air,  confinable,  aoi,  ai6. 
**     hypothetical   rarefactions  o^   trayel 

faster  than  condensations,  357. 
**     in  a  tube,  action  o^  different  from 

that  of  unconfined  air,  348. 
*•     mobility  of,  38a,  387. 
**     movement  of,  238. 
**     specific  heat  of,  at  constant  pressure 

and  constant  volume,  242. 
*'     vibration  of,  238,  30a 
«      waves,  hypothelical,  238,  276,  385. 
"  "       hypothetical,  plane  or  spheri- 

cal, impossible,  360. 
"  "       incapable  of  penetrating  solid 

walls,  669. 
Annealing,  64. 

Articulate  speech,  machinery  of,  647. 
Authority,  power  of,  601. 
Authors  (and  books),  quotations  from: 
"       Abbott,  Jacob,  351. 
"       Airy,  145,  196,  213,311. 
"      Alexander,  James  B.,  $56. 
"       American  Journal  of  Science,  307. 
"      American  Telephone  Practice,  426, 

445- 
"       Bacon,  204. 
"       Bell,  James,  539. 
"       Berreuil,  89. 
"       Bible,  272,  519,  572. 


Authors^  Blasema,  PSetro^  199U 

«  B^rthe,  Jame%  5491 

"  Bourseid,  Cbaiies,  444. 

•«  Biyant,  Wm.  C,  51^ 

**  Bflchner,  75. 

"  Byron,(»39. 

**  Caiwstrem,  Ignace^  619^  622. 

*•  Csrty,J.J.,4a6. 

"  ChaSis,  Rev.  Jas^  lajp  249^  274, 

-  Channliig^  Wm.  IL,  530. 

**  Grde  of  Sciences,  321. 

•*  Comdins,  &,  44. 

**  Corrdation  of  Fh^cal  Fofoe%  3794 

"  Cowper,  William,  64$,  68& 

**  Crookes,  William,  704. 

"  Deschenel,  198. 

"  Dynamic  Theory,  by  Jas.  B.  Alex- 
ander, 556. 

"  Dubois-Raymond,  43. 

"  Du  Moncel,  613. 

"  DuPrel,  75. 

**  Earnshaw,  Rev.  Samuel,  247. 

"  Economy  of  Nature,  316. 

"  Electricity  in  the  Service  of  Man, 
191. 

"  Elegy,  Gray's,  505. 

"  Encyclopccdia  Britannica,  13,  53^ 
66,  308,  401,  446,  447,  683. 

"  Encyclopaedia,  Chambers*,  53, 140, 

189,  318. 
"      Encyclopaedia  Metropolitana,  162, 

219,  312. 
"       Encyclopaedia,  Reese's,  690. 
**      Encyclopaedic  Dictionary,  30. 


i^^^^^^^ 

1 

^^^         73S                  H 

^^^H         Authurs  Faraday,  35a,  439. 

Auth  ors,  M  ayer,  A.,  44.                                                       ^^| 

^^^^^B 

Faraday^  IcttL'rs  of,  52t»  524. 

tt 

Mayer,  ProL  A.  M.,  555,                                        ^H 

^^^^^^^^^^^_ 

Faraday,    Michflel,   His  Life    and 

M 

Mccanique  Celeste,  3S2,                                          ^^M 

Work,  520. 

U 

Mcikle,  Henry,  252,  264.                                         ^^M 

^^^^^^^^^^ 

Fisher,  Rev.  George,  309, 

u 

Memoirs  of  the  Literary  and  Phil-                         ^^| 

^^^^^^^H 

Force,  351. 

o^uphical  Society  of  Manchester,                         ^^M 

^^^^^B 

Force  and  Matter,  75. 

694<                                                                      ■ 

^^^^^■^^ 

Canut,  5,   8,  9,  35,   55,  65,  lo6, 

u 

Meyer,  0.  E.,  150,                                                   ^^M 

lo§,    148,    197,   225,    284,    302, 

*l 

Millar.  W.  J.,  534.                                                 ^1 

337.  355.  358»  365.  391.  683.  724. 

II 

Miikr,  Kcmpatcr  B*,  426,  445.                                 ^^H 

^^^^^H 

('•oldingham,  John*  316, 

u 

Modem  Applications  of  Elcclricity                          ^^| 

^^^^^^^H 

Gggdman,  J.,  694. 

472.  490,  578.                                                          ^M 

^^^^^H 

Good  Works,  506,  507,  516,  518. 

II 

McHleni  Realism  Examined,  697,                            ^^U 

^^^^^^^B 

Gregory,  D.  U,  316, 

1* 

Mohr,  F.,  44.                                                           ^^1 

^^^^B 

Grove,  Justice,  697. 

It 

Moleschott,  43.                                                        ^^M 

^^^^H 

Grove,  W.  R.,  379. 

II 

Moon,  Robert,  357.                                                    ^^| 

^^^B 

Guyut,  45, 

tl 

Mother  Gcwjse,  231,                                                ^^| 

^^^H 

Hacckcl,  44. 

*« 

Munchausen,  Baron,  292.                                        ^^M 

^^^^^^K 

lialU  A.  Wilford,  541,  694. 

•• 

Nature,  533.                                                              ^H 

^^^^^^B 

Ilassenfraiz,  286, 

II 

Newton,   99,   113,    117.  119,   123,                         ^H 

^^^^^" 

HclmhoUz,  321. 

125,  131,  145,490,681,                                         ^M 

^^^^^^^B 

licrl>crt,  (.97. 

«( 

New  Vurk  Sun,  114.                                                   ^^| 

^^^^^H 

Ilersclitl,  J.  F.,  162,  219,  312. 

li 

Nicholson's  Jimrnal,  2S6,                                         ^^| 

^^^^^H 

lliggins,  \\\  M.,  311, 

" 

Oersted,  Professor,  ]88.                                              ^^M 

^^^^^H 

Hobbcs,  Thus.,  24-30,                      1 

.1 

Olmltcd,  Professor,  9.                                              ^^H 

^^^^^L 

Hook,  Robert,  613, 

II 

On  the   LI  entity  of    IJght,  lieat,                          ^H 

^^^^^B 

iiutton^s    MalhematLcal    Diction* 

Electricity,  Magnetism  and  Gravi-                        ^^| 

ar).  192,  315, 

tation,  694.                                                            ^^M 

^^^^^H^ 

Huxley,  404. 

" 

Papilion,  Ferdinand,  13-23,604,                             ^^H 

^^^H 

luf) Ulrica  Concerning  Sound,  690. 

u 

Paroletti,  690.                                                           ^H 

^^^H 

Kelvin,  Lord,  53. 

fl 

Parry's  Second  Voyage,  309,                                    ^^M 

^^^B 

Laplace,  382. 

tl 

Philosophical  Magazine,  151,  1 88,                         ^^M 

^^^B 

LcCuntc,  J..  312,  369. 

247,  285,  360,  534.                                               ^H 

^^^^^^^B 

Lef£vrv%  A.,  44, 

(tf 

Pie%se,  19.                                                                ^H 

^^^H 

Life  and  Letters  of  F'araday,  703. 

" 

Plato,  341,                                                               ^^M 

^^^H, 

LittcPs  Living  Age,  575,  578. 

" 

Poisson,  245.                                                             ^^B 

^^^^^R 

Locke,  94, 

»» 

Popular  Science  Monthly,  30,  530.                        ^^M 

^^^^H 

LoiJgc,  47. 

" 

Potter,  Professor,  2^)4,                                              ^^H 

^^^^^^^^^^^H 

London,   Edinburgh    and   Dublin 

0 

Practical     Telephony     by    James                         ^^H 

rhiiosuphical  Magazine,  154,  190, 

BeU,  539.                                                                        ^1 

191,  196.  312,  369,  372, 

H 

Preston,  S,  F\,  151,                                                 ^^M 

^^^^^^V 

Maief,  Julius^  472. 

•* 

Princtpia,  490.                                                           ^^H 

McKenzic,  G.  S>,  693, 

Problem  of  Human  life,  541 ,694.                        ^^M 

Aotbois.  Proceedings  ol   Royal  S^Utf  of  j  Box  tekphooif^  4| 


Lontion,  310,  316,  557. 
(^)tmrterly  Journal,  352,  264. 
Rafliani  Matter,  704. 
Royal  Transactions,  $li^ 
Roy,  Puul,  622. 
Sctitt,  Sir  \Yaker»  556, 
Sensation  of  Tone,  jat, 

SiUi«ian,  Prof.  460. 
SBliman'^  JuurnBLl,  55$. 
SpeiaccT,  706 » 
SpUlef ,  44*  So. 


rioyl*'^  law,  io6bt 
Brain,  r«.*a>rila  ofp^ 

CARTYMJJ 
Cathode  Si 

Choroi.l,  6Sj.  \ 
CifcuSatory  mc^ 
Ctoudsf  bow  fai3| 
Coefiicientj  Poisil 
Comets,  elemciili 


"       1eleph<me,  iUcrophoHc  and  Pho*  1  Conflagration,  dc 


ougraph,  613, 
The  Kinetic  llie(*fy  of  Gaae»,  150. 
Thompaon,  David,  6<i,  JoS* 
lliotnpaun,  t^yWanus  P,,  4?0t  S^^' 
Tboiiisoti,  Pr<if,  J.  J.,  713. 
Tmilt:  de  MetanUjutT,  245, 


Contain,  the  law 
thingii,  6S 
C^jpemicati  sj'Stei 
Coftelative  of  soi 
Cfeatiors,  contint 
Cfcatian,  the  ma 


••       Trmn»ai-lii>n^  of  the  Royal  Si^eiety,    Cr^s-talk  io  td« 


Edifihurnh,  Jjo. 
**      Transmiasbn  of  Sound  bf  Loose 

Klcctrical  Qjntact,  549, 
**      Tyiidall,  6,90,  170-184*  19^,209, 

»ao,  2aa,  232,  2JS,  242,  270,  375, 

282,  296,  J23,  ssSi  660,  662,  721. 
*'      VignoH,  F„  44. 
••       Walker,  31a 
**      Warwick^  624. 
"       Watersioti,  153. 
'*       Wekj  44. 

"       Westminster    Review,    $75*    5^*' 
"       Woodworth,  65 J, 
"      Young,  Thomas,  341. 
*•      Zeteche,  636, 

BALLS,  ivory,  movement  of,  174. 
Bell  telephone,  470. 
Blythe,  James,  experiments  by,  550, 
Bodie^j    bavmj5f    same     normal    vibration, 
actio ti  uf,  4oS, 
*•       normal  vibration  oU  293, 


Cancnt,  eletAric, 

443- 

Currents,  intermi 

**        Iclepho 

Dl\fram;  1 
for  makir 
Diafram,  in  telej 
hrarf 
"       in  telepi 
"        of  recei 
"         of  reiie 

449i 
**        of  tran: 

fram 
"        sappoa 

resul 
"        suppos 

635- 

"  ^uppos 
to  < 
6^% 


^^^^^^p 

^^^^^^^^^^^^^^^^^^^^^B^^                 ^^^^^^^1 

^^m 

^^^H              Diaframs,  cannot  be  made  to  Utk»  505* 

Electrotonic  state  of  matter,  525,  326*                    ^^^^^^ 

^^^H                               cannoL  repeat  sounds,  4JS. 

Elements,  combination  of,  the  law  of  crea-             ^^^^^1 

^^^^B               DifTerences  in  nature,  43. 

^^^^1 

^^^H               Distance  sound  may  be  heard,  460. 

Etlen^s  Mountain,  views  from,  3.                                 fl^^^| 

^^^H                DbtributiuQr  naLurt^  uf»  564, 

Energ)%  indestructible,  345.                                             ^^^1 

^^^^^              DyMuncd,  expcnnicntB  by*  5401  613, 

Krith,  explosion  near,  209.                                                ^^| 

^^^^^^^                          tbetjry  of,  regarding  the  telc- 

Essences,  artificial,  23.                                                ^^^^1 

^^^^y                                         579. 

Ether,  wholly  imaginary,  22S.                                    ^^^^^| 

Eulcr,    crittcistng    existing     mathematical                     ^^| 

^^^H                r^  AR  adapted  to  lathering  sound,  417, 
^^^H                JL^     Ear,  the  human,  585,  724. 

methods,  142,                                                          ^^M 

Existence,  spiritual,  484, 

^^^H                Ear  used  to  gather  sound,  204. 

**          universal,  end  of,  6S7, 

^^^H              Echoes,  567,  654. 

Expansion,  cause  of,  67. 

^^^H               Eddies,  causes  of,  294. 

Experiments  by  Antoine  Breguet,  620. 

^^^H               Edith,  707. 

•*            "  Hughes  and  Paul  Roy,  619, 

^^^H               Education,  nature's  method  of  developing 

*«  Zetsche,  636.                                    ^^HI 

^^^H                            the  mind,  686« 

**    I'rof.  J.  Henry,  660.                      ^^^H 

^^^1               Effect  only  by  contact,  68i. 

of  sound  conducted   by  wire,             ^^^^^| 

^^^H               Effects  have  appropriate  causes,  603. 

549-                                                    ^^H 

^^^H               Effects,  projioriiunal  to  amuunts,  202. 

with  a  telephone,  545,  548.                 ^^^^^| 

^^^H               Elastic t>aJlSf  collision  of,  344* 

sounding    board,  558.                   ^^^^^^| 

^^^H                            force,  39,  67. 

Explosions,  mtture  of,  117,  170.                               ^^^^^ 

^^^^^^^                             ma  Iter  in  mottuti,  6S, 

^^^H 

^^^^^f                                              foi,  148. 

r^ARADAY,  519.                                                            ^M 
I         "             experiments  by,  521. 

^             Elasticity,  50-^36^  67,  211. 

^^^^^^^                          coetlicient  of,  57* 

Fmii,  707. 

^^^^^ft 

Fire,  character  uf,  492, 

^^^^^^B                           flexure,  60. 

Force,  35«.354^ 

^^^^^^^B                                           59. 

*•       nature  of,  46,  352. 

^^^^^V                        of  traction,  55 

Forces,  natural,  identity  of,  694. 

^^^^^H 

"          "         known  only  by  effects,  5. 

^              Electric  figures,  507, 

^^^^L             Electricity,  a  phase  of  matter,  442, 

/"^ASES,  free  path  uf,  149, 

VJ     Gas,  ideal  ^  227,                                                                  ' 

^^^^^^L             **          connected  with  sound,  18S,  19a 

^^^^^^^B                           discoveries  in,  191,   192. 

Gertrude,  707. 

^^^^^^B                         Franklin's  theory  of,  71S. 

Graphopbone,  643. 

^^^^^^m                         from  magnetism,  525. 

*•            a  sound  producing  instru- 

^^V                                 nature  of,  337,  71S. 

ment,  493, 

^^H              Electric  spark,  337. 

*•            indentures,  photograph  of. 

^^^B              Electro-magnet,  443. 

657. 

^^^^^^H                                     gives  forth  sound,  619, 

"            record,  407-44S, 

^^^^^^H                                  volume  of,   not   changed 

**             record,  how  made,  4161 427«                              ' 

^^^^^^H                                  by  mftgnctbation,  624. 

43o»                                              ^^H 

738 


INDESt 


GraphoplMMie,  record,  how  made  and  repfo* 
dacedt4846o3. 
**  record,  indentures   of,  act 

like  piano  keys,  654. 
^  record,  made  by  paxtidef  of 

iovnd,  54S,  672. 
"  records,  how  formed,  646. 

**  **  how    reproduce 

tomid,€49. 
**  reprodnction  of  soimd  in, 

when  dufram  is  removed 
from  reproducer,  5'*^ 
"  nse  and  action  of  diaframo^ 

546. 
OnnHatioD,  5,40^  75,  396. 

•*  limited  in  its  action,  295. 

Goesses,  the  cause  of  falnndeis,  439. 

HAWKSB£1^  Francis,  eiqperiments  l^, 
aid. 
Hearii^  ampacity  of,  varies,  35. 

"       range  of,  284. 
Heat,  an  entity,  694. 
**     another  form  of  light,  79. 
'     a  substance,  224. 
•*      discussion  of,  694. 
**     generated  or  made  manifest  by  com- 
pression, 222,  224. 
"      hypotheses  of,  225. 
"     laws  of,  79. 

**     undulatory  theory  of,  similar  to  that 
of  sound,  6,  7. 
Helix  of  telephone  emits  sound,  621. 
Henry,  Prof.  J.  experiments  by,  with  tuning 

forks,  555,  660. 
Huxley's  remark  on  hypotheses,  479. 
liuyghens,  views  of,  regarding  light,  7. 
Hydrogen  gas  a  poor  conductor  of  sound, 

177- 
Hypotheses  an  undesirable  foundation  for 
science,  165. 
"  Huxley's  criticism  upon,  701. 

"  Huxley's  remark  about,  479. 

**  of  science,  422. 


IDEALISTS^  sappoiiUoii  <A,  72. 
Impo«ible,  the,  never  mdeitaken  hy 

Nature,  459. 
Indvctkm,  Electipatatic  and  Electroaii^ 

netic,423.  ^ 
Inertia,  543. 

Inertia  of  matter,  an  erroi^  45. 
Infinitely  small,  without  limte,  465. 
Infinitesimals,  a  STStem  used  iD  Nature,  431. 
Infinitesimals,  power  o^  645. 
IntfiKgenc«%  different  orders  o^  572. 

I AOQUES^  eiqierhneniB  by,  309. 


KELLER,  Hden,  Education  oi  68(X 
Kinetic  theoiy  of  gasei^  101^  14S; 

Kinneisley^  thermometer,  337. 

LAMARCK,  69a 
Laplace,  formula  of,  for  wpetd  of 
sound,  221,  233,  234,  235,  ajS; 
243,  244,  248,  249,  250b  252. 
liigeois,  eicperiments  in  odors  by,  17. 
light,  corpuscular  theory  of,  ably  discussed 
by  Prof.  J.  J.  Thomson,  713. 
**     large  distance  between  particles  of, 

though  tilling  the  air,  466. 
"     laws  of,  78. 
"     theories  of,  7,  8. 
"     undulatory    theory    of,    similar  to 

that  of  sound,  6. 
"      velocity  of,  688,  717. 
Like  produces  like,  448. 

MACHINERY,  287,  288,  353. 
Magneto>electric  induction,  525. 
Mariotte's  law,  107. 
Material  creation,  the,  564. 
Mathematicians,  369-371. 
Mathematics,  how  related  to  physics,  169. 
'*  inaccuracies  of,  130. 

''  plural  in  form  and  meaning, 

367. 


INDEX 


739 


Matter,  discussion  of,  42,  43. 

"         effect  of  upon  spirit,  432. 

**        elements  of,  combined,  the  uni- 
versal law  of  material  creation,  | 
41. 

*•        fourth  state  of,  706. 

**        infinite  division  of,  705. 

"         man  cannot  make,  505. 

**         radient,  706. 

**        solid,  liquid  and  gaseous  state  of, 
226.  I 

**        sufficient  for  all  material  purposes, 

353- 
Maxwell,  James,  370. 
Medium,  a,  necessary  to  the  existence  of 

other  things,  216. 
Megaphone,  203. 

*'  in  fog  signaling,  1 14. 

Membrane  in  telephone  assists  in  gathering 

and  delivering  sound,  498. 
Memory,  a  record,  683. 
Mercury  Telephone,  Brcguet's,  478. 
Metaphor,  use  of,  10. 
Meteorites,  79,  80. 
Meteors,  219. 
Microphone,  396,  540. 

Blythc's,  478. 
"  illustration  of,  399. 

"  magnifies  sound,  35. 

Mills,  different  kinds  of,  487. 
Mind  and   matter,    distinctions  between, 

354. 
Mind,  laws  of,  universal,  83. 
Mind  the  creative  power,  234. 
Mobility  of  fluids,  178,  195. 

"         principle  of,  382. 
Mode  of  motion,  odor  a,  24. 
Modes  of  motion,  33. 
Modulus  of  elasticity,  57. 
Modulus,  Young's,  57. 
Molecules,  extraordinary  motions  of,  152. 

"  motions  of,  226. 

Moment  of  a  force,  64. 


Momentum,  343,  348. 
Motion,  343. 

"        a  characteristic  of  various  forms 
of  matter,  569. 

"        a  property  of  matter,  43-46,  344. 

"        caused  by  pressure,  39. 

"         fundamental  law  of,  345. 

"         how  produced,  39. 

"        how  propagated  through  a  fluid, 
102. 

"        in  elastic  bodies,  344. 

"         inseparable  from  matter,  41-46, 

345- 

"  laws  of,  discussed,  112. 

"  laws  of,  not  changed,  606. 

"  modes  of,  3;^,  93,  224. 

"  nature  of,  342. 

"  of  rotation,  343. 

"  of  translation,  343. 

"  oscillatory,  343. 

"  rectilinear,  345. 

"  the  result  of  contact,  47. 

"  the  result  of  pressure,  345. 

NATURE,  circulatory  methods  of,  42. 
Nature,  forces  of,  5. 
Nature,  forces  of,  interchangeable,  346. 
"  "  intimately  related,  79. 

"       laws  of,  universal,  75-84,  92,  287, 
354. 
Nature's  laws  fixed,  605. 
Nerves  of  sensation,  function  of,  91. 
Nerve  stimulus,  72. 
Newton's     main     proposition     on    sound 

founded  on  an  hypothesis,  145. 
Newton's   main    propostion  on   sound,  re- 
view of,  by  J.  J.  Waterston,  153. 
Newton's  propositions,  errors  of,  140,  141. 
"        propositions   relating   to  sound, 

99-139. 

"        theory  of  light,  7. 
"        theory     of     sound,    objections 
to,  160. 


740 


INDI^ 


^m^ 


Nomud  vibratioiis  of  bodiei»  i86w 

ODOR,  13. 
Odor  a  mode  of  md&yo,  24*  30^  31. 
Odor  and  aoiiiidv  analogr  belweeiw  I9> 

**    nature  and  a^km  o^  687. 

"    nature  o^  465. 
Odors*  artifidally  produced,  32. 

**     carried  hy  oxygen,  i^ 

**     conqxwttion  o^  2i. 

**     diffittion  o^  17. 

**     discosiion  o^  i4-'3< 

"     hajanonyof,  19. 

**     haying  power  of  motion,  16. 

"     liow  formed,  490. 

"     operations  o^  similar  to  lonnd,  19U 
Oersted,  Dr.  H.  C,  1S9. 
Opinions,  bad,  all,  354. 

PAFILLON  on  odors,  14-23. 
Phenomena,  interdependent  parts  of 
one  whole,  14. 
Phenomena  of  ^sensation  similar,  429. 
Philosophical  magazine,  247. 
Philosophy  of  sound,  311. 
Phonautograph,  585. 
Phonograph,  $12,  726. 
Photographing  by  electricity,  413. 
Photophone,  472. 
Physical  forces,  nature  of,  5. 
Pitch  determined  by  rate  of  vibration,  283, 

291. 
Pressure,  propagation  of,  in  a  fluid,  99. 
Probabilities,  theory  of,  149. 
Pulse  in  a  tube,  340,  342,  355,  376,  386. 
Pulse  in  a  tube,  action    of,  foundation  of 

undulatory  theory  of  sound,  354-356, 

372-381- 
Pulse  in  a  tube,  speed  of,   different   from 

that  of  sound,  366. 
Pulse  in  a  tube,  velocity  of,  varies,  341. 
Pulses,  distances  of,  137. 
"      in  an  elastic  fluid,  velocity  of,  131. 
**      propagation  of,  in  a  fluid,  125. 


RADIANT  matter,  214. 
*"  <«     not  pefceptib^  al- 

fected  by  gravitatioai,  995* 
RadBnm,  7'9* 
Req^ntidation,  69&**7^« 
Red^irocal  of  a  nmnber,  64. 
Records  of  the  brain,  434. 
Reflection  of  sound,  6b 
Regnanit,  ei^eriments  by,  37^ 
Reis,  PhiHp^  53a 
Resistance,  posnUe  to  tdq)hoaic  cnirentt 

581. 
Retina,  683. 

Retina,  pictures  on,  683. 
Ritter,  views  of  regarcBng  aomd,  189. 
Roentgen  rays,  716^ 
Room  for  phenomena  of  nature,  abandairi^ 

388,389. 

SCIENTISTS,  superstitions  of,  347. 
Sensation,  described  by  Locke^  94. 
Sensation,  nerves  o^  70. 

"        result  of  contact  and  assiniila- 

tion,  91-93. 
**         result  of    material    conditions, 
353. 
Sensations,  accomplished  through  agency 
of  matter,  432. 
"         action  of,  682. 
"         all  have  similar  cause,  652. 
**         analogy  between,  19. 
<•         cause  and  use  of,  571. 
"         caused  by  matter,  453. 
"         dependent  upon  matter,  488. 
"         dependent  upon  quality  as  well 

as  form  of  matter,  57a 
"         exist  first  materially,  88. 
**         five,  677. 
**         material,  forms  of,  569. 
"         nature's  great  system  of,  677. 
Senses,  the  five,  13. 

Shock,  mechanical  effect  of,  on  parts  of  tele- 
phone, 626. 


^^^^^^V             ^^^F 

^^^^^^      741 

^^^B         Sixe,  reUttvity  of^  346. 

Sound,  correlative  of,  195,  197,  270-274. 

^^^B          SmcU,  dc6mtion  of,  30. 

"     criticism  of  the  theory  of,  5. 

^^^B                                  u(,  14, 

•*      dehnttions  of,  8,  9. 

^^^B                    sense  of|  higbly  developed,  ao. 

•*      destructiunof,  301. 

^^^B          Sonorous  figures,  506. 

"      differences  in,  how  made,  286» 

^^^B                         wftves  entirely  mythical,  515. 

•*      different  theories  of,  690. 

^^H                                    tcHj^'th  of,  463. 

*'      distance  heard,  460. 

^^^B          Soul,  activities  of,  begin  when,  685. 

"      distribution  of,  295. 

^^^^1                    and  budy,  connection  uf,  67$. 

"     clcctricab  1 88,  189. 

^^^^^^H            cannot    directly   recognize   material 

**     entirely  material,  500, 

^^^^^B 

"     entity  theory  of,   demonstrated  by 

^^^^^^^             esiaential  nature  uf,  684. 

Du  Moncel's  experiments,  613, 

^^H             *'     faculties  oi,  6S0. 

"      experiments  in,  by  Prof.  I  lenry,  555. 

^^^H             **     how  instructed,  6^7. 

"     experiments  in,  conducted  by  wire, 

^^^^B             *'     knowledge  oF,  must  be  acquired,  679 » 

449; 

^^^^B                   origin  ol^  679. 

**      experiments   in  the  conduction  of, 

^^^H              "     power  of,  501. 

562. 

^^^H              "     power  of  construction  ot,  innate,  6S4. 

"      from  the  graphophune,  considered 

^^^H          Sound,  action  of  upon  the  soul*  6S4. 

BS    reproduction  of  the  original 

^^^B                       aggregation  of,  202,  228* 

sound,  518, 

^^^^ft                       air  wave  theory  of,  41 S. 

"      great  secret  of,  556. 

^^^^H                      a  medium  necessary  to  convey,  659. 

"      heard  at   different    points  succes- 

^^^^H              *'     and  electricity,  similarity  of,    190. 

sively,  418. 

^^^^1                      and  hearing,  distinction  between^  9. 

**      heard  in  a  telephone  made  by  the 

^^^^H                      and  vibraiion,  relation  of,  36. 

initial  sounthng  hudy,  405,  440* 

^^^^^^^               an  entity,  207,  693. 

••      history  of  undulatory  theory  of,  690. 

^^^^^^H              a  substance  capalile  of  spreading  in  , 

"      how  gathered,  458. 

^^^^^^V                all  directions,  40^. 

"      inriniteaimal  particles  of  matter,  453, 

^^^^T             "    a  subtle  form  of  matter,  216. 

**      in  rarefied  air,  219. 

^^^^^^H               can  make  an  instniment  that  will 

•'      in  Keis'  Ick phone,  446, 

^^^^^^H                   reproduce  itseU,  4S3, 

*'      instruments  made  in  different  ways. 

^^^^^^H       **      carried  by  the  electric  current  like 

494. 

^^^^^^                   logs  in  a 

**      in    telephone    and    graphophone, 

^^^^^^         **      caused  by  shuck,  68,  71,  89,  207. 

operation  of,  391. 

^^^^^^^               character  of,  deilncd  by  vibration, 

•'      intensity  of,  175,  279,  284. 

^^^H          ^^^* 

**      intensity  of.  depends  upon  density 

^^^^^^B        "     collected  by  sail  of  ship,  203,  458. 

of  air  where  generated,  401,  404, 

^^^^F              **     collection  and  rejection  of,  by  the 

"      intensity  of,  in  high  mountainous 

^^^^^K                  ciir,  204« 

regions,  404. 

^^^^^H               conducted   through  copper  wire», 

**      intensity  of,  laws  of,  172,  1801 

^^B 

"            **       of,  not     dependent    upon 

^^^^^^P       **     consists  of  electrical  matter,  4^7. 

quantity  of  matter  imping- 

^^^^B             **     correlates  thought,  504^ 

ing  on  the  ear,  405. 

742 


JNBEX 


Somid,  inteii^  of,  mries  how,4os« 

"  **     of,   Tsries  with   diftsoce 

from  soundiiig  body,  401, 
*'     interferance  of,  298,  30a 
^     in  ak  spreads  in  all  ejections,  405. 
**     laws  oU  similar  to  tli08«  of  light,  6. 
**     machinery  for  prodadi^  may  be 

infinitesimal,  607. 
,    "     made  by  appropriate  imtnunents, 

491. 
**     made  hy  shock,  469. 
**     made  by  sound  prodncing  instm- 

ments,  45a* 
**     made  on  the  eaztii  heaid  at  a  great 

elevation,  402. 
**     makes  vibration,  4xa 
**     makes    vibration,    not    vibration 

soond,  660^  662. 
^     may  be  gathered,  466^ 
'    '*      memory  of,  a  record  inthe  brain, 

4«5- 
^,    motion  of,  one  of  its  properties,  568 
"     movement  of,  071* 
**     nature  0^69^ 

"     Newton's   main    propositions    on* 

founded  on  hypothesis,  145. 
"     Newton's  propositions  concerning, 

99-139. 
"     Newton's  propositions  of,  criticised 

by  Herschel,  163. 
"     Newton's  propositions  of,  criticised 

by  Lagrange,  164. 
"     Newton's  propositions  of,  criticised 

by  Waterston,  153. 
"     not  controlled  by  gravitation,  295. 
"      not  like  a  conflagration,  407. 
"      not  made  by  vibrations  of  tuning 

fork,  665. 
"      not  transmitted  in  a  vacuum,  218. 
"     objective,  10. 

"     of  electrical  character,  90,  420. 
"     of  tuning  fork  conducted  away  by 

a  stick,  661. 


Soond,  partidea  o^   how  made  in  the 

graphophaoe^  6|4. 
'*    partidea  c^  teifinltesfanid,  4S7»  607. 
**    paitldeao^wyndBafce^4|7, 
«     pamqg  from  oae  wsre  to 

near  it,  419, 
'*    permeates  in  afl  Snd&ouit  41^ 
^     phenomena  o^  eaqilaiaed  by^ 

theory,  702. 
**    phenomena  of  ^  poorible  by  eati^ 

theory,  674. 
^    pitch  o^  detemdned  by  vibfaHoo^ 

291. 
**     prodooed  by  caqrfGiioii  ol  melcsoi% 

2X9,  220. 

'   '<     produced  by  contact^  55» 
«     produced  by  step  of  a  iy»  35* 
"     produced  m  rarefied  air»  JU9* 
••     propagaUon  of,  70^  190^  JS5, 39^ 
«     qmdity  or  Hm6r£  of,  an  attenqited 

explanation  o^  59a 
**     readfly  enters  the  wire  of  a  tde- 

]^hoiie,6o2. 
**    reflected  like  lifi^t,  7. 
"     reflection  of,  567. 
"      reproduction  of,  from  graphophone 

record,  430. 
"     reproduction  of,   in'  graphophone 

when  diafram   is  removed  from 

reproducer,  518. 
"     resemblance  of,  to  electricity,  220, 

284. 
"     secret  of,  653. 
"     shaped  and  distributed  by  vibration, 

"     strangest  secret  in,  701, 

"     taken  up  and  transmitted  by  a  wire, 

533. 
"     tenuity  of,  185. 
"     theory  of,  by  Lamarck,  690. 
"     the  whole  in  all  the  air,  204. 
"      timbre^  or  quality  of,  1 97, 1 98,  200, 

339. 


^^                                                                                                       743                ^^^B 

^^^      Sonndt  transference  of,  558. 

Sun,  elements  of,  81.                                                          ^^^^| 

^^^fe                  triLnsmisaioti  of^  535, 

Superstitions  of  science,  231*                                            ^^^^H 

^^H           **     traosmission  of,  by  loose  electrical 

Symbols,  use  of,  93.                                                          ^^^^| 

^^H                    contact,  449. 

S>in  pathetic  vibration,  294,  721,  725.                                ^^^^| 

^^H           **     tianimission  uf,  through  solids,  282. 

^^^B 

^^^H           "     tnmsmittcfi  better  by  itisulated  than 

T^ASTE  aided  by  odors,  16.                                            ^^^B 
1       Telegraph  instruments,  576W                                    ^^^^M 

^^^H                     uninsulated  wirCf  61 5« 

^^^H                  Tyndall  on  reBeclion  of,  6. 

Tclcgrapbonc,  455.                                                            ^^^^H 

^^H                  Tyndall's  book  on,  review  of,  170- 

Telegraph,  447.                                                                   ^^^| 

^H                     ^^^* 

Telegrapby,  444.                                                                  ^^^| 

^^H           **     under  water,  405, 

Telephone,  391-400,  410-455,  530-640.                        ^^^^1 

^^H                 undulatory  theory  of,  discussion  of. 

Ader's,  580.                                                      ^^^H 

^H 

all  parts  of,  can  transmit  sound,                     ^^^^^1 

^^H  1          **     undulatoiy  theory  of,  fatal  inconsis- 

^H 

^^^H                     tcncies  off  276. 

^^^H 

^^H           **      undulatory  theory  of,  fatal    objec- 

Breguet^s  Mercury,  478,                                  ^^^^1 

^^^H                     Lions  to,  pointed  out   by  Henry 

common  explanation  of,  untrue,                      ^^^^| 

^^H                     Mtikle,  264,  267* 

^^H 

^^^H           '*     undulatoiy    theory  of,  impossible^ 

current  continuous,  446,  454.                         ^^^^H 

^m 

•"           currents  infinilcsimalt  635.                                      ^H 

^^^H          **     tmdnlatory  theory  of,  inconsistent, 

description  of,  582.                                            ^^^^H 

^^H 

development  of,  584*                                        ^^^^1 

^^H           **     velocity  of,  9. 

diafram  of,  su^ested  by  mem-                      ^^^^H 

^^^H           **     velocity  uf»  experiments  concerning, 

brane  of  ear  515.                                           ^^^^H 

^H 

**          discs  of  various  substances,  539.                      ^^^^B 

^^H                  vetucity  of,  inherent^  56S. 

**           evolution  of,  50S.                                                       ^H 

^^^H                   velocity  of,  in  water,  32S* 

"           experiments  wilb,  405.                                              ^H 

^^^K           **     velocity  of,  not  due  to  elastic  force 

**          expenments  with,  by  Hughes                               ^f 

^^^H                     of  the  air,  292* 

and  Paul  Roy,  619,                                                ^H 

^^^H           **     velocity  of,  uniform,  569. 

*'          explanation  of,  410, 41 4^                                        ^H 

^^H           **      waves,  attempted  photographs  of. 

**          held  against  the  chest  transmits                             ^H 

^^                     337- 

sound,  63  7 »                                                   ^^^^1 

K^      Sotmdiiif  boards,  293. 

helix  of,  emits  sound*  631.                                 ^^^|i 

^^K            *"                      action  of,  467, 55S. 

history  i>f,  613*                                                     ^^^^B 

^^H                                   experiments    with,  561* 

illustration  of,  392.                                                  ^^M 

^^m      Spectral  analysis,  80-82. 

**           invented  by  Graham  Bell,  470,                              ^^M 

^^V      Speech,  articulate,  606. 

mechanical,  533.                                                    ^H 

■                  *«        articulate,  machinery  of,  647. 

"           operated  by  induced  currents,                             ^H 

■            Spirit  affected  by  matter,  432. 

■ 

H                 "     and  matter,  connection  between,  678* 

**          ori^nal  experiments  with,  545,                             ^H 

H            Spiritual  and  material  independent,  501. 

H 

■             String  telephone,  583* 

Rcis»,445,  530.                                                      ^M 

H            Substantial*  all  things,  42. 

replaced  by  music  box,  619.                                 ^^M 

744 


l|)9iX 


Td^pbonei  bost  month  uid  fltn^^ooii-^ 
537. 

^  .      "t^i^   itticiwd  to  jnffefeiift 
pttts  of  dbpctric  tdl^ihoii^ 

"       .  ttrias-iiirey  615. 

**      *  wppoied  ▼fimtioii  ol  dhfniin 

0U620, 
*•         tfaeofy  of»  631. 
**         unial  explanadoii  of,  inconect, 

596. 
*•         Yihratkm  of  ditct  o^  54a 
<«         wirdeu,  predicted*  483. 
**         with  a  nmnber  of  dlaframi,  616. 
*     <*  *   .  with  doable  magnett  621. 
**         without  diafram,  617,  638. 
**         without  receiTer,  47S. 
**         without  vibcatii^  plate,  aiag- 
net  or  coil,  475. 
Telephones,  tpedal,  47a. 
Telephonic  currents,  578. 
Telephonic  current,  strength  of,  579. 
Thennaphone,  M^esendanger's,  633. 
Things   cannot   pertorm    any   important 
function,  they  were  not  made  to  per- 
form, 48a 
Things  made  in  various  mills,  567. 
Things,  manner  in  which  they  pass  each 

other,  390. 
Things  useful  for  what  they  were  designed, 

437- 
Thought,  how  formed,  353. 
Torsion,  angle  of,  $9. 
Torsion  balance,  59. 
Toruon,  force  of,  59. 
Touch,  688. 
Touch,  action  of,  687. 
Transmitter  must  make  sound  if  receiver 

does,  549. 
Tremor  of  a  rod  or  a  sounding  board,  293. 
Tremulous  bodies  in  elastic  and  non-elastic 


Trope^ia 

IVnth,  tbow  wiia  teem  SiS* 

Tub^  lyii^llA  esperinienl  ifi^  l«4- 

Tuning  Focfc,  action  o^  90f. 

Tuninff  iOlk.  ^utaamA  n|-  flilBiluftiill  lEwav  faw 

aatMK»66i. 


U' 


NDUUiTORY  theories,  2^ 
Undolatofy  theofiet  1^  nm^oe  wiA 
common  iciise,  4* 
Undulatory  dieoriet  like  Ptokmafc  wptiem, 

of  astioiioiny,  67a 
Undulatory  theory  of  aound  imponible^  S7. 
Universe,  materia],  moit  beautiful,  604* 
Uranium,  719. 

VACUUM,  lound  in  a,  ii6b 
Variable  reditanoe  tranmitter,  454. 
Variety  a  univeiial  law  of  nature^  987. 
Variety,  how  produced,  388L 
Vibration,  aoy,  556. 

**       anoqplitude  o^  aff^, 

**       cause  o^  68. 

',       caused  by  coDirion,  y^ 

^       definition  oi^  39^ 

**        prepares  sound  for  the  market, 

666. 
*'        made  by  sound,  explanation  o^ 

39.  89,  556,  557. 

*«        relation  of,  to  sound,  36. 

**        sympathetic,  186,  294,  649. 
Vibrations,  number,  necessary  to  sound,  291. 
Visual  purple,  683. 
Vis  viva,  201. 

Vocal  chords  may  be  artificial,  512. 
Voice  does  not  cause  diafram  to  vibrate, 

413. 
Volta-Electric  induction,  525. 


w 


ATER  waves,  illusion  of,  330. 
Water  waves  propagated  by  ^mvity. 

Waves,  as  such  cannot  bia    se^ecle^  of 
gathered,  <9Si 


INDEX 


745 


Waves,    description  of,  318,  321,  330. 
**        how  formed,  331. 
"        in  air  similar  to  water  waves,  im- 
possible, 339. 
•*        reflection  of,  196,  568. 


waves,  velocity  of,  123. 
Wheatstone,  experiments  by,  558. 


Y 


OUNG,  Thomas,  views  of,  regarding 
light,  8. 


CRITICISMS  AND  PRESS  REVIEWS 
OF  VOLUME  I. 

James  M.  Ingalls,  Lieutenant-Colonel,  United  States  Army, 
one  of  the  most  eminent  mathematicians  in  the  world,  and 
recognized  as  the  highest  authority  on  balistics,  or  the  science 
of  projectiles,  writes : 

"My  Dear  Mr.  Battell  : 

"  I  thank  you  very  much  for  the  copy  of  your  great  work  *  Ellen  or 
Whisperings  of  an  Old  Pine,'  which  I  received  a  few  days  ago.  Of 
course  I  have  not  had  time  to  read  the  800  closely  printed  pages,  but 
1  have  looked  it  over  very  carefully,  and  I  think  I  can  say  positively  that 
it  is  the  best  argument  against  the  present  accepted  theory  of  sound 
that  has  ever  been  presented  to  the  public. 

Sincerely  yours, 

James  M.  Ingalls." 

We  have  received  the  following  courteous  letter  from  Prof. 
George  F.  Barker,  of  the  University  of  Pennsylvania,  one  of 
the  most  eminent  physicists  of  America,  to  whom  we  sent  a 
copy  of  "Ellen": 

Joseph  Battell  Esq., 

My  Dear  Sir : —  I  beg  to  express  to  you  my  thanks  for  the  first  vol- 
ume of  the  second  edition  of  your  remarkable  book,  "  Ellen  ".  Obvious- 
ly there  has  been  much  thought  spent  upon  the  reasoning  contained  in 
it  and  the  criticisms  it  contains  must,  I  think,  tend  to  modify  some  of 


■;  !!i 


■I- 


•I   . 


1  bJ 

I'lf 


PRESS   REVIEWS 


749 


Of  the  second  edition,  but  eighteen  copies  were  sent  to  the 
press.  In  addition  to  the  criticisms  already  quoted  is  the 
following  review  by  Reed  Moyer,  editor,  New  Haven,  Conn., 
which  appeared  in  a  syndicate  of  papers,  including  the  Mobile, 
Ala.,  Times: 

"  A  book  that  presents  some  rather  interesting  problems  is  entitled 
'Ellen,  or  Whisperings  of  an  Old  Pine/  by  Joseph  BaltelL  The 
book  is  really  a  scientific  discussion,  but  it  takes  the  form  of  fiction^  in 
which  the  chief  characters  are  Ellen  and  an  old  Vermont  Pine.  A 
second  edition  has  just  been  issued,  and  in  the  preface  to  this  etlition, 
the  author  mentions  with  pride  the  fact  that  its  revolutionary  scientific 
theories  have  been  accepted  by  leading  scientists.  Such  questions  as 
the  nature  of  matter,  and  the  phenomena  of  sound,  light,  heat  and 
electricity  are  considered  in  a  searching  manner.  In  particular  the 
book  demonstrates  the  absurdity  of  the  undutatory  theories  taught  in 
every  text  book  of  physics*  A  great  many  mathematical  statements, 
that  are  universally  accepted,  are  exposed  in  such  a  way  that  the  candid 
reader  must  confess  that  the  author  is  correct.  The  book  is  not  above 
the  knowledge  of  the  student  of  plane  geometry  and  elementary 
physics.  The  f|uestion3  discussed  concern  the  basic  principles  of 
mathematics  and  science  and  cannot  fail  to  be  of  interest  to  every 
educated  person.  The  book  is  finely  printed  and  Iwund  and  is  pub- 
lished by  the  American  Publishing  Company,  Middlebury,  Vermonl.*' 

Mr.  H.  L.  Hind  ley,  editor  of  the  Ludlow  (Vt.),  Tribune,  and 
one  of  the  abler  reviewers  of  Vermont,  after  saying  that  the 
book  is  ** iconoclasm,  idol-breaking,"  continues: 

"It  won't  do  to  dismiss  Ellen  and  ner  conversations  with  an  impa- 
tient shrug  for  the  very  simple  and  sufficient  reason  that  there's  abun- 
dant food  for  thought  in  them.     There's  a  whole  lot  of  rot  about  mod- 


7$0  CRmCISMS  AND 

em  science,  and  the  Colonel  has  certainly  attacked  it  where  its  ^tmat 
is  a  Little  thin — to  say  nothing  about  the  sheathing  underneath.  It  b 
impossible  to  even  outline  the  arguments  of  the  book — ^read  it  yonr- 
selfp  if  you  have  time*" 

Hon.  H,  H,  Powers,  formerly  a  judge  of  the  Supreme  Court 

of  Vermont,  writes : 

"Your  work,  *  Ellen/  \%  too  profound  for  hasty  judgment,  but  I  have 
e.:amined  it  far  enough  to  discover  that  you  have  bestowed  most  care- 
ful thought  tipoa  your  reasoningp  and  I  think  have  evolved  theories  that 
stand  OQ  a  logical  basis,  and  are  worthy  the  attention  of  our  b^i 
scholars,'' 

Hon.  C.  S.  Emery,  one  of  Vernionts  most  prominent  citi- 
zens, and  member  of  the  State  Senate,  writes : 

Chelsea,  Vt.,  May  14,  1904- 

Hon.  Joseph  Battell: 

My  Dear  SrR : —  I  am  in  receipt  of  the  beautiful  volume,  "  Hllen/* 
from  your  pen,  nn^l  ^IitU  nUvays  prize  it  on  that  account  and  must  thank 
you  for  your  though tfulness. 

The  amount  of  labor  bestowed  upon  this  work,  the  thought  and  study 

required  in  mastering  the  subjects  treated,  would  seem  to  me   to  be 

enough  for  a  lifetime, 

Very  sincerely  yours, 

C.  S.  Emery. 

Of  the  first  edition  Mr.  Bryan  in  The  Commoner  says:  "A 
very  interesting  book." 

The  Louisville  Journal,  edited  by  Henry  M.  Watterson,  says: 
'*  A  book  with  much  ingenious  construction  of  the  most  vital 
truths." 


I 


PRESS   REVIEWS 


751 


Mr.  Thomas  H.  McLeod,  Middlebur>%  Vt,  formerly  a  con* 
tributor  of  the  Silliman  Scientific  Journal,  published  at  New 
Haven,  Conn.,  writes: 


We  have  received  from  the  American  Publishing  Company,  Middle- 
bury,  Vt.,  a  copy  of  Volume  L,  second  edition,  of  "Ellen  or  V^liisper- 
ings  of  an  Old  Pine." 

The  book  is  well  printed,  handsomely  bound,  and  illustrated  with 
many  views,  presenting  both  individual  subjects  and  a  panorama  of  large 
extent  and  great  historic  interest,  as  seen  from  one  of  the  highest  sum- 
mits of  the  Green  Mountain  range  in  Vermont. 

The  work  itself,  in  its  entirety,  relates  to  man  and  his  surroundings  in 
the  several  aspects  of  his  existence,  and  to  the  phenomena  in  the 
physical  world.  In  treating  of  these  subjects  no  work  in  its  conception 
so  radical  and  original  has  come  to  the  knowledge  of  the  public  for 
many  years,  nor  one  that  will  engage  the  attention  of  the  thoughtful 
for  so  long  a  period  of  time.  If  the  attainment  of  the  true  reason  of 
things  is  philosophy,  to  that  extent  the  work  before  us  may  justly  be 
termed  the  Battellian  Philosophy,  being  an  independent  consideration 
of  the  true  knowledge  of  things  by  direct  investigation,  which,  while  it 
is  carried  on  Platonically  in  free  conversations  or  dialogues,  i^  pursued 
with  a  Socratic  simplicity  and  certainty  that  would  do  credit  to  the 
great  Athenian — the  Master  mind  of  the  ages. 

It  is  also  a  credit  to  the  work  ihat  some  of  the  deductions  of  the 
Author  in  res[iert  to  the  transmission  of  light,  heat,  etc.,  which  were 
antagonistic  to  the  doctrines  taught  in  the  schools,  have  been  by  entire- 
ly independent  investigation  and  discovery  fully  verified  by  eminent 
scientists  both  in  Europe  and  America;  which  suggests  that  in  the 
future  the  other  tenets  of  the  Author's  philosophy  will  be  equally 
verified. 

A  strong  moral  lone  pervades  the  whole  discussion. 


PUBLISHED  BY 

THE  AMERICAN  PUBLISHING  COMPANY 

MIDDLEBURY,  VERMONT. 


Tbe  Motgan  Hone  and  Begisler*  Tols.  I*  and  H.    By 

Joseph  BattelL  Eleven  handled  and  seven  hundred  pages  respectively. 
Handsomely  illustrated.  Price  of  VoL  1. 1^5.009  VoL  IL  $$.$$9  ^^  ^^oo 
for  both  volumes,  postage  prepaid. 

The  Morgan  Horse  and  Register,  Vol.  III.,  is  well  under  way. 
It  will  consist  largely  of  registered  horses  of  both  sexes. 


OPINIONS  OF  THE  TRESS  ON  VOL.  I. 

VOL.  I.  of  Battell's  Morgan  Horse  and  Register  has  at  last  been  issued.  It  is  a 
volume  of  more  than  a  thousand  pages,  and  no  more  beautiful  press  work  has  ever 
been  seen.  The  volume  shows  a  vast  amount  of  research  and  personal  investigation. 
It  contains  a  great  deal  which  has  never  before  been  published,  and  will  probably 
lead  to  endless  discussion.  *  *  *  The  portraits  of  Denning  Alien,  the  Fear- 
naughts,  Lord  Ginton  and  others  are  gems  of  art  and  beauty. 

But  pictures  do  not  make  books,  and  Mr.  Battell's  Register  is  one  of  the  most 
valuable  of  recent  acquisitions  to  equine  literature,  one  that  should  be  in  the  library 
of  every  horseman  and  every  student  of  the  breeding  problem.  No  one  before  has 
attempted  a  work  of  such  magnitude,  nor  has  endeavored  to  get  at  the  evidence  on 
which  is  based  the  many  beliefs  as  to  the  ancestry  of  many  famous  ones,  and  while 
it  may  surprise  some  to  find  in  the  first  volume  the  claim  that  Seely*s  American 
Star  and  old  Pacing  Pilot  are  direct  descendants  of  Justin  Morgan,  it  must  be 
admitted  the  evidence  given  is  quite  as  conclusive  as  that  upon  which  is  based  the 
claim  that  their  ancestry  is  in  other  lines. — [Clark's  Horse  Review. 


The  Morgan  Horse  and  Register  is  the  latest  and  one  of  tbe  most  valuable 
contributions  to  horse  literature  that  wc  have  had  the  pleasure  of  examining.    •     •    ♦ 

It  has  generally  been  conceded  by  those  who  have  studied  the  subject  carefully 
that  the  family  of  horses  founded  by  Justin  Morgan  has  never  been  equalled  as  road- 
ster*  and  for  general  pmposea  where  animals  of  heavy  weight  were  not  required,  •  •  ♦ 

The  most  surprising  pedigree  in  the  work  is  that  of  Seely's  American  Star.  It 
has  long  been  claimed  by  those  who  had  investigated  the  matter  carefully  that  be 
could  not  have  been  by  Stockholm's  American  Star,  which  appeared  as  his  sire  in  the 
earlier  volumes  of  Waltace^s  Trolting  Register.  Probably  Mr.  Battell  spent  more 
time  and  money  carefully  investigating  this  pedigree  and  Cijllecting  facts  in  regard  to 
it,  than  any  other  in  the  work,  and  he  has  been  amply  rewarded.  After  giving  the 
facts  fully  upon  which  he  bases  the  pedigree^  Mr.  Battell  gives  the  breeding  of  this 
renowned  brood-mare  sire  as  follows : 

AMERICAN  STAR  (SEELY'S), 

Chestnut  or  sorrel,  with  star,  hind  feet  white,  15 ig  hands,  TO^O  pounds;  foaled 
1837;  bred  by  Henry  II*  llcrr>\  Fompton  riains,  N,  J.;  got  by  Cuburn's  American 
Star,  son  of  Cock  of  the  Rock,  by  Sherman  Morgan :  dam  bay,  stripe  in  facCt  about 
16  hands,  a  used-up  sta^e  marc  purchased  in  New  York  city  by  Mt.  Berry  at  ft 
amall  price  to  work  in  team,  breeding  entirely  unknown. 

The  chapters  on  Justin  Morgan  and  Sccly's  American  Star  arc  alone  worth  twice 
the  cost  of  the  book.  There  is  also  a  very  interesting  chapter  on  Pilot,  sire  of  Pilot 
Jr.  Mr.  Battell  traced  this  horse  through  all  the  hands  he  passed  until  he  located 
him  in  Montreal,  and  there  is  little  doubt  that  he  traced  him  from  that  point  to  hia 
breeder.  We  are  glad  to  learn  from  the  author  that  the  work  is  selling  rapidly. — 
[Amencan  Horse  Breeder. 

Lexington,  Mass. 
JosKTH  Battell,  Esq., 

Afy  Dear  Sir : — Your  valued  favor  is  received  ;  also  Vol,  I.  of  the  Morgan 
Horse  and  Register.  As  the  liook  was  received  this  morning,  I  have  had  little  time 
to  read  it*  It  ik  very  handsome  and  I  was  particularly  pleased  with  the  chaptcis 
on  the  Stars,  Pilot,  the  pacers  and  the  breeding  of  the  original  Morgan.  I  do  not 
•ee  but  your  claim  is  admirably  sustained. 

Very  truly  yours,  Edward  S,  Payson. 


No  publication  upon  the  bone  of  recent  years  has  awakened  so  great  a  public 
interest  as  this  volume  bearing  the  authorship  of  Mr,  Battell  of  Vermont. — [Mirror 
and  Farmer,  Manchester,  N,  If, 

We  have  received  from  .Mr.  Jotcph  Battell  of  Middlebury,  Vt.,  the  first  volume 
of  his  new  work.  The  Morgan  Home  and  Register.  It  is,  mechanically,  a  very  fine 
job :  line  paper,  elegant  binding  and  ill uslrat inns,  many  of  them  half-tones  from 
photographs,  and  on  fine  plate  paper,  all  go  to  make  it  an  ornament,  in  tbe  book 
line,  ht  (or  the  parlor  table.    It  contains  1000  pages.     Whatever  adds  to  the  sum 


qI  htimaii  kiiQwlrtigc  ti^  any  spedal  tiiie  is  ifiv&lii»S>le  and  to  the  BpecisJi^t  iiiiit»» 
l^etisablef  ajad  Mr,  Battell's  book  sboukl  contain  within  its  cover*  very  much  Uul  h\ 
not  only  new  i>ut  Important.  •  •  »  iVubibly  tic*  mau  livings  in  a  whuk  tliplimr, 
ever  trairekd  the  dkiance  ia  piiMuit  o(  inftirmaijon^  wrote  the  letters,  ot  tpent  th« 
ttum^  in  historical  rest^rch  that  the  ixulhof  iif  this  work  bos  (iane  In  the:  iasf  tcna 
yesLrs^  and  the  result  Is  embodied  id  tjii»  vuluipe;.  ♦  #  ♦  Xnily  **  Truth  ll^i  af  the 
bottom  ut  the  well/*  juid  Mr.  Bait«Jl  has  gone  deeper  after  it,  itayed  imrlcr  longer* 
ftntl  Ciniie  to  the  surface  with  more  iacts  in  bii  gras^  than  any  other  writer  on  the 
tttbject*  It  IH  a  ijrrat  work,  and  we  have  bad  no  time  as  yet  to  master  its  coctcnttp^ 
but  AS  time  occurs  shall  rclcr  tw  i%  again  and  a^jain,  •  •  *  [J.  W%  Thonapsoiip  I 
a»thor  uf  Maine  Bred  llon^.  ' 

The  Horseman,  Qiicagq,  Iu« 

Mk.  JosKnt  Battels  I 

Afy  I.^i'tjr  Sir  ,■ — »The  complimentary  copy  of  The  Morgan  Horse  and  RegiitCC 
which  you  are  go<id  enough  Co  bend  me  came  safely  to  hand.  It  h  by  long  odcb  the 
Bioat  complete  and  comprehensive  work  of  the  kind  cv«r  is»ued,  and  a\\  the  Irkndi 
^otX  breeders  of  the  Morgan  horse  owe  you  a  Itfe-long  ilebt  O'f  gratitudr  fi.>7  youf 
|Maiistakit>g  labor  In  the  fiekl  of  your  choice*  It  is  noi  only  uf  special  v^^t  to 
Morgan  horse  breeders,  but  to  all  others  engaged  in  the  light  harness  horse  in- 
dostTy,  ^rhe  illustrations  ser\'e  a  very  good  purpose  and  the  makeup  of  the  liook 
ivodefs  it  an  ornament  to  any  library.  I  wiU  give  it  careful  public  rc%ncw  at  the  first 
^Mm^e.    Meantime^  with  bctt  wkheih  I  am 

Youm  sincerely,  E.  C.  Walker^     **  Veritas,'* 


THE    HOME    LIBRARY. 


ILLUSTRATED  with  125  very  superior  half  tones,  consisting  of 
American  and  foreign  scenerj',  portraits  of  distinguished  authors, 
and  copies  of  celebrated  paintings.  Volume  L,  consists  of  439  pages 
besides  iDustrations. 

This  is  one  of  the  most  elegant  books  of  the  kind  ever  published, 
com  prising  13S  selections  from  Goethe,  Schiller,  Cervantes,  Burns, 
Irving,  Scott,  Campbell,  Plato,  Cicero,  Farkman,  Lowell,  Bryanl^ 
Addison,  and  75  other  standard  Authors, 

Price,  cloth  J2.00;  Morocco,  full  gilt,  I4.00, 

Volume  IL,  will  be  largely  compo&dd  of  the  choicest  &eleciions 
from  Shakespeare. 


ANNOUNCEMENT. 


\1 /E  take  this  opportunity  lo  announce  that  an  exhaustive  history 
of  the  more  prominent  stallions  of  America,  from  the  earUest 
times  to  the  present,  which  we  have  been  engaged  upon  now  for  some 
20  years,  is  rapidly  approaching  completion.  This  work  is  the  result 
of  the  most  thorough,  independent  investigation,  and  when  finished  will 
inchide  all  the  more  imi>ortaiit  stallions  which  have  contributed  to  the 
formation  of  the  American  roadster,  both  trotter  and  pacer. 

In  this  work  a  very  large  number  of  errors,  which  have  crept  into 
preceding  works  on  the  Horse,  will  be  corrected,  and  the  evidence 
given  upon  which  these  corrections  are  made.  We  are  happy  to  say 
also  that  we  have  been  able  to  trace  out  many  pedigrees  hitherto 
obscure  or  unknown,  and  some  of  them  of  vtry  great  importance, 
among  which  is  that  of  the  dam  of  Black  Hawk  ;  also  new  information 
regarding  Belle  of  Wabash,  more  complete  than,  and  antedating, 
any  hitherto  published. 

This  work,  to  a  certain  extent,  will  be  a  companion  piece  of  the 
Morgan  Register,  the  rating  of  Morgan  blood  in  the  different  stallions 
being  given  so  far  as  known.  But  it  will  also  be  complete  in  itself, 
includiug  the  principal  stallions  of  all  families,  and  by  far  the  most 
convenient  and  valuable  work  of  reference  upon  American  stallions 
which  has  yet  been  ptibltshed.  It  will  consist  of  at  least  four  and 
perhaps  five  volumes  of  1000  pages  each,  and  will  be  extensively 
illustrated  and  firmly  bound  in  three-quarter  leather.  Volume  L  we 
hope  to  publish  by  July  i,   1908. 

JOSEPH  BATTELL, 

Jan,  I,  1908. 


!kl 


JAN  2t   1969